Scalable discovery and validation of order-specific electronic health record event trajectories for interpretable adverse-outcome risk estimation

Abstract

Objective:

Clinicians must estimate patients’ risk of adverse outcomes, yet many electronic health record tools represent health history as an unordered “bag of codes,” discarding temporal order. Machine learning tools that leverage sequence order may offer better predictions but often lack interpretability for clinical audit. We introduce an interpretable, order-aware framework that mines frequent event pairs (A → B) and tests whether their ordering provides prognostic information for estimating risk of adverse outcomes (C) beyond the same codes without order.

Methods:

Using the NIH All of Us Controlled Tier, 432,617 eligible participants were split 70/30 into discovery and confirmation. We combined 340,687 A → B pairs with nine outcomes (C) to create 3,066,183 candidate trajectories and tested 85,535 trajectories in this pilot using observation-aware indexing, a 90-day latency and 5-year A → B gap, inverse-probability weighting, weighted competing-risk cumulative incidence, four prespecified comparators (primary: B with no prior A), and Benjamini-Hochberg false discovery rate (FDR) in a discovery/ confirmation design.

Results:

After discovery FDR, 663 unique trajectories advanced and 171 validated for ≥ 1 horizon in confirmation. At 5 years, the median risk ratio (RR) was 2.02 versus the primary comparator and 3.89 versus a calendar-time baseline (median absolute risk difference 2.49 percentage-points). Reverse-order checks were feasible for ~ 87% of hypotheses (median A → B → C vs B → A → C RR 1.18) at 5 years.

Conclusion:

Ordered trajectories can provide interpretable, audit-ready signal beyond unordered features and can augment white-box risk estimation for adverse clinical outcomes.

1. Introduction

Quantitative risk stratification is central to modern clinical decision–making.[1,2] Widely used calculators such as the Framingham general cardiovascular risk score and CHA₂DS₂–VASc show that a compact set of clinical variables can yield useful absolute–risk estimates to guide prevention and treatment decisions.[3,4] The appeal of these traditional scoring algorithms is not only their accuracy but also transparency: clinicians can audit the inputs, understand how the score is computed, and communicate the rationale to patients. However, most classic tools treat a patient’s state as a coarse snapshot. Risk is computed from a combination of the patient’s current symptoms and binary flags on whether relevant health events have ever occurred in a patient’s history, with any potentially valuable information contained in the specifics of the individual’s unique ordered health trajectory being lost.

The digitization of health systems has subsequently enabled learning from large–scale electronic health records (EHRs), where diagnoses, procedures, and medications accrue as longitudinal event streams. Many routinely deployed approaches retain transparency by simplifying histories into unordered sets or counts of codes (“bag–of–codes”), making the decision algorithm easy to audit and explain. In contrast, sequence–aware models can leverage temporal structure and often improve predictive performance, but their complexity can hinder interpretability and clinical traceability, which are critical properties required for tools used in making high–stakes clinical decisions around treatments and plans for care. [5] There remains a practical need for methods that both quantify when event ordering adds incremental prognostic value beyond unordered co–occurrence and produce outputs that remain fully transparent for audit and downstream clinical interpretation.

In this study, we introduce a fully interpretable, scalable, and reproducible method for discovering health event trajectories that modulate risk of future adverse outcomes.[6] We mine frequent ordered pairs of clinical events (A → B) and rigorously test whether specific orderings elevate the subsequent risk of adverse health events (C) relative to clinically relevant comparators. By quantifying the incremental value of the temporal order of health events beyond “bag–of–codes” co–occurrence in a white-box manner, we aim to connect population–scale A → B → C disease trajectories with audit–ready patient-–level risk estimates that can form the basis for the next generation of clinical risk estimation tools.

1.1. Statement of significance

Problem	It is challenging for clinicians to estimate patients’ risk of future adverse clinical events.
What is already known	Clinicians use both algorithmic and EHR-based risk calculators in routine care. However, many tools summarize history as a static snapshot or an unordered “bag-of-codes,” so prognostic information within the order of events is lost. Sequence-aware models may provide better predictions but are limited in their deployment due to low interpretability and clinical auditability.
What this paper adds	We develop and share a transparent system that mines and tests ordered A → B → C health trajectories in 432,617 All of Us participants and we validate 171 ordered sequences in a pilot. Using competing-risk cumulative incidence, prespecified comparators, and a discovery → confirmation design with global FDR control, we identify auditable order-specific trajectories associated with clinically meaningful differences in downstream risk.
Who would benefit	Clinicians and informatics teams building clinical decision tools requiring risk estimates can incorporate validated temporal features into models while retaining full interpretability.

2. Related work

Risk scores and snapshot–based risk stratification.

Clinical risk scoring has a long history of producing compact, actionable estimates that support decision–making in routine care.[1,2] Examples such as the Framingham cardiovascular risk profile and CHA₂DS₂–VASc demonstrate the clinical value of transparent scoring rules derived from a small set of inputs.[3,4] Their interpretability and ease of audit are major strengths, but they generally estimate risk from a cross–sectional view of the patient or from coarse indicators of whether events have ever occurred rather than leveraging the ordering of events over time.

EHR–based machine learning and learned representations.

As EHR data have become widely available, machine–learning models trained on clinical data have demonstrated improved discrimination for important outcomes.[7] Unsupervised representation learning on EHRs has further shown broad predictive utility across disease areas.[8] These methods illustrate the potential value of large–scale EHRs for forecasting future clinical events, while also highlighting that many representations compress history in ways that do not explicitly isolate the role of event ordering.

Sequence–aware models for longitudinal EHR.

A substantial body of work applies sequence models such as recurrent neural networks, attention mechanisms, and transformers to ordered visit or event streams, with demonstrations in forecasting diagnoses and medications and in incorporating timing information for time–to–event prediction. [9–13] These approaches motivate the premise that temporality contains clinically meaningful signal. However, the learned representations produced by end–to–end sequence models are often difficult to translate into simple, patient–facing rationales or to express as clear, auditable rules that clinicians can readily inspect and base decisions upon.

Interpretability and auditability in high–stakes prediction.

For clinical tools that influence treatment choices, interpretability and traceability are highly important. Black–box predictors can face barriers to adoption when stakeholders cannot audit how predictions arise.[5] This tension between predictive performance and clinical auditability motivates approaches that preserve transparency while still incorporating temporal information when it provides prognostic value.

Disease trajectories and network medicine.

Complementing prediction–focused work, systems–level research has reframed disease as a set of interlinked processes that progress along structured pathways. [14] Network medicine emphasizes that disorders cluster within biological modules, and population–level disease networks reveal empirical comorbidity patterns across the phenome.[15,16] Dynamic phenotypic networks constructed from large medical–record corpora suggest that patients tend to develop conditions adjacent to those they already have and that network position relates to mortality risk.[17] Large registry analyses in Denmark further distilled thousands of statistically supported, directional disease trajectories, providing evidence that the sequence in which conditions arise is not random and releasing tools to explore these trajectories at scale.[18,19] Together, this literature motivates trajectory–aware models that ask not only what conditions a patient has, but how they arrived there.

Sequential pattern mining and association–rule learning in healthcare.

In parallel, association–rule learning and sequential pattern mining have developed algorithms for discovering frequent or high-–confidence temporal patterns in transactional or visit–ordered data, including healthcare data (e.g., temporal association rules and methods like SPADE).[20–24] While these approaches are powerful for pattern discovery, they often prioritize frequency– or confidence–based summaries rather than a clinician’s risk–estimation question: Given that a patient has experienced event B, does having experienced event A before B (as opposed to A and B in any order, or B without prior A) meaningfully change the absolute risk of a downstream adverse outcome over clinically relevant horizons? Moreover, many sequence–mining pipelines do not natively incorporate competing–risk time–to–event estimation, prespecified comparator cohorts, or discovery → confirmation designs that control false positives when screening large numbers of candidate patterns.

Collectively, these strands of work motivate the need for trajectory–aware risk estimation methods that remain transparent and audit–ready, while also providing principled answers on when event order adds incremental prognostic value.

3. Materials and methods

3.1. Data source and computational environment

We performed a retrospective cohort study in the NIH All of Us (AoU) Research Program Controlled Tier environment, using the Observational Medical Outcomes Partnership (OMOP) Common Data Model as implemented in the AoU Curated Data Repository. All data extraction was executed in Google BigQuery, and downstream processing, cohort construction, and statistical estimation were performed in Python (pandas/numpy and scikit–learn). The complete analysis is parameterized through a single configuration object (including random seed, time windows, gating thresholds, and inference settings) to support reproducibility and exact reruns.

Observation periods were merged into person-level continuous intervals (treating short gaps as adjacent), and participants were eligible if they accrued ≥ 365 total days of merged observable time. Full observation-period processing rules and eligibility/attrition diagnostics are provided in Appendix C.

3.2. Discovery/confirmation split

Eligible participants were split into discovery (70%) and confirmation (30%) sets using stratified random sampling with a fixed seed for reproducibility. Stratification was performed jointly on age band, sex at birth, and race/ethnicity (derived from OMOP concept identifiers). Age bands were defined as < 18, 18–29, 30–44, 45–59, 60–74, ≥75, and Unknown.

3.3. Outcomes and competing risks

We evaluated a prespecified panel of clinically important adverse outcomes as terminal “C” events: breast cancer, ovarian cancer, colorectal cancer, lung cancer, leukemia, lymphoma, myocardial infarction, dementia, and death. Outcomes were defined as OMOP concept sets specified by ancestor concept identifiers and expanded to descendants using the OMOP concept_ancestor table at phenotype time. (For example, an “ancestor” concept such as “Malignant neoplasm of lung” may have many more specific “descendants” which represent more granular lung cancer diagnoses.).

For all non–death outcomes, death was treated as a competing event in time–to–event estimation. When an outcome and death occurred on the same calendar day, ties were resolved by assigning death to occur infinitesimally earlier so that same–day outcome/death pairs are counted as deaths rather than outcomes. For the death outcome itself, there is no competing event.

To enable trajectory mining, we transformed OMOP condition, procedure, and drug records into a deduplicated, date-stamped event ledger using a curated feature vocabulary with descendant expansion and an outcome-concept blacklist to prevent label leakage. We additionally derived categorical smoking-status and BMI features (from participant-provided information and measurements) and appended them for consistent covariate handling. Full construction and derivation details are provided in Appendix C.

3.4. Mining frequent ordered event pairs A → B

Within the discovery set, we mined candidate ordered event pairs (A → B) from the event ledger. For each participant, we constructed a chronological timeline of distinct feature identifiers (deduplicating repeated occurrences of the same feature while preserving first appearance order). From each timeline we enumerated all ordered pairs (A,B) such that A appeared earlier than B in the sequence of first occurrences. Each individual contributed at most one count to a given ordered pair. Candidate pairs were retained if they met a global minimum support threshold of 500 individuals in discovery.

3.5. Episode construction

For each candidate pair (A,B) and for each outcome C, we constructed “episodes” that define an index date, follow–up start (“time zero”), and censoring date. Episode construction begins by computing, for each person, the first observed date of A and the first observed date of B in the ledger. Based on these first–occurrence dates, we created the following cohorts:

• Ordered exposure (A → B): participants with both A and B such that B occurred after A (default policy excludes same–day pairs) and within a maximum A → B gap of 1825 days (5 years). The episode index date is the date of B (the second event).

• Primary comparator (B with no prior A): participants with B whose first A was absent or occurred after B (i.e., no A before B). The index date is the date of B.

• Reverse–order comparator (B → A): participants with both events where A occurred after B (again under the configured same–day policy) and within the same 1825–day gap. Here the index date is the date of A (the second event in the reverse ordering).

• Tertiary comparator (A with no subsequent B within the allowed gap): participants with A who did not have B occur after A within the maximum gap window. The index date is the date of A.

• Calendar–time baseline: one episode per person anchored to observation time rather than to A or B. For each participant we selected the earliest observation interval long enough to support the prespecified lookback and latency requirements and set the baseline index date to observation_period_start_date plus 1825 days (5 years).

3.6. Latency and same–day policy

To reduce reverse causation (e.g., diagnoses recorded during evaluation of an imminent outcome), follow–up did not begin at the index date itself. Instead, each episode defined time zero as

$$t_0=\text{index\_date}+L$$

with a default latency (L = 90) days.

Same–day ordering was controlled by an explicit policy. In the primary analysis, same–day A and B events were excluded, so A → B required B to occur strictly after A (and B → A required A strictly after B).

3.7. Observation interval validation

We require that both the index date and time zero fall inside the same recorded observation period for a given person. If a candidate episode’s index date fell in one interval but time zero fell outside it (e.g., because latency extended beyond the interval end), the episode was excluded.

For episodes that passed this validation, we defined the censoring date as the end date of the observation interval that contained both index and time zero. Follow–up for an episode ends when the underlying observation interval ends, even if the person has later observation periods. In the case that an episode’s (person_id, index_date) matched multiple overlapping observation periods, we used the interval with the earliest end date to avoid artificially extending follow–up.

For the B–no–prior–A comparator, the A–no–B comparator, and the baseline cohort, we additionally required sufficient history within the observation interval to support covariate measurement and history checks. Specifically, the observation interval had to start at least 1825 days before the index date. This lookback rule was not applied to the A → B or B → A cohorts (which are defined by the occurrence of both events).

3.8. Covariate construction at time zero

To adjust for measured confounding, we computed a covariate vector for each (person_id, index_date) episode, with all time–varying covariates anchored to the follow–up start (time zero) rather than to the raw index date. The covariate set used in propensity score modeling comprised:

• Demographics: age at index (index year minus year of birth), sex at birth, and race/ethnicity.

• Calendar time: calendar year of index.

• Health behaviors / anthropometrics: smoking status category and BMI category, defined as the most recent derived value observed within the 730 days prior to time zero. If none were available in that window, the value was set to Unknown.

• Socioeconomic context: an area–level deprivation index linked by ZIP3 (three–digit ZIP) and imputed to the median when missing.

• Healthcare utilization: the number of distinct visit start dates in the 365 days prior to time zero (a coarse proxy for contact intensity with the healthcare system).

• Comorbidity burden (CCI–LOO): a Charlson–derived comorbidity score computed over the 730 days prior to time zero and explicitly “leave–one–out” with respect to the exposure and outcome.[25] Concretely, we mapped condition occurrences to Charlson condition ancestor groups, then excluded any Charlson groups whose descendants overlapped with descendants of A, descendants of B, or descendants of the outcome concept set, and finally summarized remaining comorbidity as the count of distinct Charlson ancestor groups observed in the lookback window.

These covariates were merged into each cohort’s episode table before propensity score fitting and outcome estimation. The covariate list used for adjustment is fixed in the configuration and is identical across comparisons.

Using this fixed covariate set, we estimated propensity scores for cohort membership and applied inverse probability of treatment weighting (IPTW) prior to outcome estimation.[26,27] Balance diagnostics are summarized below, and full model/weighting specifications (including clipping and diagnostics) are provided in Appendix C.

3.9. Standardized mean difference (SMD) and balance gating

Because IPTW is only useful to the extent that it balances covariates, we assessed balance using the standardized mean difference (SMD) for each covariate before and after weighting.[28] For a scalar covariate (X),

$$\text{SMD}\left(X\right)=\frac{\overline{X_{\text{treated}}}-\overline{X_{\text{control}}}}{s_p}$$

where (s_p) is the pooled standard deviation. For one–hot encoded indicators, this reduces to a standardized difference in weighted proportions. We summarized balance by the maximum absolute SMD across all adjustment covariates.

We then applied an explicit balance gate: comparisons were considered adequately balanced only if the maximum absolute post–-weight SMD was ≤ 0.2. This gate was used both as a quality–control flag in reported tables and as a filter when advancing discovery findings to confirmation (candidates failing balance were excluded from confirmation testing).

3.10. Competing–risk cumulative incidence estimation

For each cohort (treated and each comparator), and for each outcome C, we estimated absolute risk over clinically interpretable horizons using the cumulative incidence function (CIF) under competing risks. Let (T) denote time from time zero to the first event and let (J) denote event type (1 for outcome C, 2 for death as a competing event, and 0 for censoring). The CIF for outcome C at time (t) is .CIF_C(t) = Pr(T ≤ t, J = 1)

We estimated CIFs using a weighted Aalen–Johansen estimator on integer days.[29] For each episode we constructed the number of days from time zero to outcome, the number of days from time zero to death (for non–death outcomes), and the number of days from time zero to censoring at the end of the containing observation interval. Event times at or before time zero were excluded so that follow–up begins strictly after latency.

We report CIFs at 1, 2, and 5 years after time zero, treating one year as 365 days.

3.11. Effect measures: Absolute risk difference and risk ratio

To quantify the incremental risk associated with the ordered trajectory, we computed two complementary measures at each horizon (t):

• Absolute CIF difference (risk difference)ΔCIF(t) = CIF_A[RIGARW]B(t) –CIF_comp(t)

• Risk ratio (relative risk on the CIF scale) $RR(t)=\frac{{\text{CIF}}_{\text{A}\left[\text{RIGARW}\right]\text{B}}\text{(}t\text{)}}{{\text{CIF}}_{\text{comp}}\text{(}t\text{)}}$.

  Here the “comp” cohort is the comparator being evaluated.

Uncertainty intervals and two-sided p-values for horizon-specific ΔCIF estimates were computed using a Poisson bootstrap with an early-stopping rule to stabilize precision while limiting computation. [30] The resampling procedure and stopping criterion are described in Appendix C.

3.12. Information gating for reliable estimation

Not all trajectory/outcome/horizon combinations contain enough follow–up to support stable estimation. Therefore, horizons were analyzed only when both cohorts in the comparison satisfied prespecified minimum information thresholds: at least 150 individuals still at risk at the horizon and at least 20 observed outcome events by that horizon, per cohort. Comparisons failing these gates were not assigned inferential statistics and were excluded from multiple–testing correction.

3.13. Discovery/confirmation workflow and multiple testing control

We used a two–stage discovery/confirmation design to reduce the risk of overfitting and to obtain an internal replication of selected signals.

3.13.1. Discovery testing and triage

For each mined ordered pair and each outcome, we constructed episodes and estimated weighted CIFs versus the primary comparator (B with no prior A), as well as prespecified secondary comparators (including reverse order).

Within discovery, we applied Benjamini–Hochberg (BH) false discovery rate (FDR) control at α = 0.05 across all tested hypotheses (all outcomes × horizons × sequences with non–missing p–values), producing q–values.[31].

To select a clinically meaningful and directionally interpretable set for confirmation, we then applied post–hoc triage thresholds to the BH discoveries: (i) primary (RR > 1.2), (ii) primary ΔCIF > 0.005 (0.5 percentage points), (iii) primary p < 0.05, and (iv) reverse–order check RR_{vs reverse} > 1.1 (requiring that the ordered trajectory have higher CIF than the reverse ordering).

Finally, before advancing candidates to confirmation we applied the SMD balance gate (maximum post–IPTW SMD ≤ 0.2) as an additional robustness filter, excluding candidates whose covariates remained materially imbalanced after weighting.

3.13.2. Confirmation testing

For the frozen set of candidates, we rebuilt all cohorts in the independent confirmation split, recomputed covariates and propensity weights, and repeated the competing–risk CIF estimation and bootstrap inference at the same horizons under the same gating rules. We then applied BH FDR control at α = 0.05 across all confirmation p–values to obtain confirmation q–values reported in the results.

3.14. Unordered comparison for incremental value of order

To ensure temporal order provides information beyond co–occurrence, we implemented an additional comparator that removes ordering while preserving the requirement that both events occur within the same maximum time gap. For a given pair (A,B), we defined an unordered AB exposure as the union of episodes where A precedes B and episodes where B precedes A (under the same maximum gap and same–day policy), with follow–up beginning after the second event in whichever ordering occurred. We compared this unordered exposure to the standard B–no–prior–A comparator using the same time–zero alignment, covariates, IPTW procedure, SMD balance gate, and competing–risk CIF estimation.

4. Results

4.1. Analysis coverage

Starting from 633,547 persons in the OMOP source, 432,617 met the prespecified eligibility requirement of ≥ 365 total days of merged observation time and were split 70/30 into discovery (302,834) and confirmation (129,783) sets. Within discovery, we mined 340,687 frequent ordered event pairs (A → B) under a ≥ 500-person support threshold. Pairing these A → B sequences with the nine adverse outcomes (C) yielded 3,066,183 candidate three–event trajectories (A → B → C) for evaluation.

We attempted 85,535 of 3,066,183 candidate trajectories (2.79%) and successfully completed episode construction and estimation for 55,995 (65.46% of attempted), leaving 2,980,648 trajectories untested in this run due to compute constraints. These completed trajectories produced 99,933 estimable trajectory–horizon hypotheses in discovery after applying the prespecified information gates across the 1-, 2-, and 5-year horizons. Table 1.

Table 1.

Attrition of persons and trajectories across the pipeline.

Stage	Count	Unit	Retained (%)
Total Persons in Source	633,547	Persons
Eligible Persons	432,617	Persons	68.28%
Persons in Discovery Set	302,834	Persons	70.00%
Persons in Confirmation Set	129,783	Persons	30.00%
Candidate Sequences Mined (Discovery)	3,066,183	Three-Event
		Trajectories
Candidate Sequences Attempted (Discovery)	85,535	Three-Event	2.79%
		Trajectories
Candidate Sequences Completed (Discovery)	55,995	Three-Event	65.46%
		Trajectories
Unique Trajectories after FDR (Discovery)	663	Three-Event	1.18%
		Trajectories
Unique Trajectories Validated in Confirmation	171	Three-Event	25.79%
		Trajectories

4.2. Discovery-to-confirmation yield

Across the 99,933 discovery hypotheses with non-missing inferential statistics, global Benjamini–Hochberg control at FDR α = 0.05 identified 5,095 discoveries. Because statistical significance alone can select clinically negligible effects in large-scale screens, we applied the prespecified triage criteria intended to prioritize signals that were directionally interpretable as risk elevation, clinically meaningful on the absolute-risk scale, and suggestive of order-specificity. After triage, 2,369 trajectory–horizon hypotheses remained, spanning 1,372 distinct A → B sequences.

We then applied the IPTW balance gate as a robustness filter before confirmation. Requiring acceptable post-weight covariate balance (maximum absolute SMD ≤ 0.2) for both the primary comparison (A → B vs B with no prior A) and the reverse-order comparison (A → B vs B → A) reduced the candidate set from 2,369 to 924 trajectory–horizon hypotheses, corresponding to 663 distinct A → B → C trajectories advanced to the independent confirmation split.

In the confirmation set, these candidates were re-estimated under the same episode construction rules, covariate definitions, weighting strategy, competing-risk estimation, and information gates. Under confirmation-set BH FDR control (α = 0.05) and the same balance requirements, 171 distinct A → B → C trajectories validated for at least one horizon Fig. 1.

Fig. 1.

Covariate balance (“love”) plots for two illustrative sequences. (A) Chronic lung disease → hearing loss → lung cancer. (B) Diabetes mellitus → visual disturbance → myocardial infarction (MI). Points show standardized mean differences (SMD) for baseline covariates before and after inverse probability of treatment weighting (IPTW). Values closer to 0 indicate improved balance. (IPTW, inverse probability of treatment weighting; SMD, standardized mean difference.).

4.3. Overview of validated trajectory–outcome signals

Validated trajectories spanned multiple clinically important outcomes. In this pilot, validated signals were concentrated in outcomes with higher incidence and/or longer observable follow-up (e.g., myocardial infarction, dementia, lung cancer, and death), while rarer malignancies contributed fewer validated trajectories under the minimum-events and minimum-at-risk gates. 96 validated trajectories mapped to myocardial infarction, 39 to dementia, 22 to lung cancer, 8 to death, 3 to leukemia, and 3 to colorectal cancer. (No trajectories for breast cancer, ovarian cancer, or lymphoma validated in this initial pilot). Table 2.

Table 2.

Aggregated summary statistics for validated signals (confirmation), by outcome and horizon.

Outcome	Horizon (Years)	Validated Signals (n)	RR (Baseline) — Median [IQR]	RR (Primary) — Median [IQR]	RR (Reverse) — Median [IQR]	ΔCIF — Median [IQR]
colorectal_cancer	5	3*	4.31	2.94	0.93	0.87%
death	5	8	5.18 [3.90, 7.80]	2.89 [2.50, 3.23]	1.35 [1.26, 1.42]	0.93% [0.67, 1.33]
dementia	1	6	6.99 [4.47, 7.76]	3.11 [2.20, 3.33]	1.22 [1.04, 1.54]	0.83% [0.47, 0.91]
dementia	2	19	4.74 [3.65, 6.11]	2.20 [2.03, 2.47]	1.23 [0.97, 1.38]	0.91% [0.68, 1.23]
dementia	5	35	3.75 [2.94, 4.64]	2.01 [1.77, 2.41]	1.19 [1.09, 1.35]	1.82% [1.25, 2.65]
leukemia	2	2*	4.87	4.37	1.34	0.41%
leukemia	5	3*	4.04	3.58	1.23	0.82%
lung_cancer	1	5	12.00 [9.31, 19.68]	8.58 [6.90, 9.38]	1.74 [1.49, 1.76]	0.95% [0.78, 1.43]
lung_cancer	2	12	9.64 [6.95, 14.13]	5.88 [3.14, 7.97]	1.31 [1.16, 1.56]	1.57% [0.93, 1.82]
lung_cancer	5	22	6.36 [4.67, 7.51]	3.24 [2.72, 3.99]	1.15 [1.02, 1.28]	1.97% [1.14, 2.30]
myocardial_infarction	1	33	4.77 [3.50, 6.76]	2.26 [2.01, 2.58]	1.18 [1.08, 1.61]	1.13% [0.85, 1.57]
myocardial_infarction	2	61	4.19 [2.94, 5.47]	2.16 [1.81, 2.40]	1.25 [1.04, 1.41]	1.62% [1.32, 2.30]
myocardial_infarction	5	83	3.51 [2.72, 4.14]	1.86 [1.64, 2.12]	1.17 [1.04, 1.32]	3.01% [2.47, 3.91]

^*Interquartile range (IQR) values not shown when less than 5 validated signals are present.

Across validated signals, effect sizes were heterogeneous but consistently directionally elevated relative to the primary comparator (B with no prior A). At the 5–year horizon, the median RR versus the primary comparator was 2.02 with interquartile range (IQR) 1.74–2.60), and the median absolute risk difference (ΔCIF) was 2.49 percentage–points (pp) (IQR 1.63–3.29 pp), with the largest validated absolute separations reaching 7.08 pp. Table 3.

Table 3.

Sample of 15 significant validated hypotheses at the 5-year time horizon and their risk ratios versus all comparators.

Sequence	Outcome	Horizon (Years)	Risk Ratio (vs Baseline)	Risk Ratio (vs Primary)	Risk Ratio (vs Reverse)	Risk Ratio (vs A, no subseq. B)	q-value (Confirmation)
Recurrent major depression → Coronary atherosclerosis	Dementia	5	6.5644	2.4136	1.3876	1.85	<1e-6
Peripheral nerve disease → clopidogrel	Dementia	5	5.9232	2.1694	1.1032	1.9855	<1e-6
Type 2 diabetes mellitus → Acquired absence of organ	Myocardial infarction	5	4.2031	2.2185	1.1431	1.8517	<1e-6
Diabetes mellitus → Pneumonia	Myocardial infarction	5	4.053	1.936	1.1917	1.9938	<1e-6
Type 2 diabetes mellitus → Kidney stone	Myocardial infarction	5	4.0146	2.7016	1.3517	1.556	<1e-6
Diabetes mellitus → Visual disturbance	Myocardial infarction	5	3.9312	2.4609	1.6312	1.8482	<1e-6
Hematopoietic system finding → Gastrointestinal hemorrhage	Death	5	3.8794	2.7931	1.4422	2.1461	<1e-6
Degeneration of intervertebral disc → Kidney stone	Myocardial infarction	5	3.8287	1.961	1.2287	1.8028	0.0313
Pneumonia → ergocalciferol	Myocardial infarction	5	3.7952	1.9944	1.3394	1.396	0.0313
vancomycin → Chronic kidney disease	Dementia	5	3.751	1.908	1.1392	1.188	0.0313
Peripheral nerve disease → Urinary tract obstruction	Myocardial infarction	5	3.7014	1.5816	1.1706	2.0285	<1e-6
Diabetes mellitus without complication → Dysphagia	Myocardial infarction	5	3.4117	1.665	1.2136	1.3677	<1e-6
Pneumonia → Anemia	Dementia	5	3.5603	1.592	1.1226	1.3333	<1e-6
metoprolol → Degeneration of intervertebral disc	Myocardial infarction	5	3.5073	1.8298	1.1177	1.1432	<1e-6
Anemia → ipratropium	Myocardial infarction	5	3.451	1.3704	1.1264	2.0425	<1e-6

Support for validated trajectories was substantial: the median number of distinct A → B episodes contributing to each validated trajectory was 1822 (IQR 1175–2560; range 505–8275). Reverse-order comparators (B → A) were estimable for 87% of validated hypotheses at the 5 year time horizon, and when estimable, the median RR comparing A → B → C to B → A → C was 1.18 (IQR 1.04–1.34). Fig. 2.

Fig. 2.

Distribution of effect sizes across validated A → B → C trajectories. Only outcomes with ≥ 5 validated signals are included in boxplots. The figure summarizes the spread of cumulative incidence and risk ratios for validated sequences versus their comparators across outcomes and follow-up. Medians and interquartile ranges are indicated. Higher values reflect larger excess risk relative to comparators. (RR, risk ratio.).

A central goal of this framework is to isolate information attributable to ordering rather than to co-occurrence alone. Consistent with this aim, validated trajectories retained elevated risk relative to the primary comparator (B with no prior A) and showed directionally concordant behavior against tertiary comparators (A without a subsequent B within the allowed gap) and a calendar-time anchored baseline. In general, effects versus the calendar-time baseline were larger, while effects versus A-only or reverse-order comparators were attenuated, as expected when comparators share more clinical context with the ordered exposure.

To directly address whether ordering adds information beyond simply observing that both events occur, we constructed an unordered AB exposure that collapses A → B and B → A into a single “AB (any order)” cohort, aligned time zero to the second event, and compared this unordered exposure to the same primary comparator (B with no prior A) using the identical weighting and competing-risk estimation procedure.

Across the confirmation set, 486 unique trajectory–outcome pairs were evaluable under this definition, yielding 1,458 unordered trajectory–horizon estimates. After dropping 45 imbalanced unordered runs, 1,413 balanced unordered estimates remained. The unordered AB exposure still carried elevated downstream risk versus the primary comparator, but the magnitude was systematically different from the ordered A → B effect. Specifically, the median RR for unordered AB versus B with no prior A was 1.57 at 1 year (IQR 1.20–2.21), 1.53 at 2 years (IQR 1.26–1.94), and 1.51 at 5 years (IQR 1.28–1.80).

To quantify the incremental change attributable to ordering, we compared ordered and unordered risk ratios across horizons. The median absolute difference in log risk ratios was |ΔlogRR|=0.109, corresponding to an ≈11.5% typical multiplicative separation between ordered and unordered effect sizes on the RR scale. Taken together, these results indicate that co-occurrence of A and B is indeed often informative, but conditioning on the order of A and B frequently changes estimated risk in a nontrivial way.

Supplementary results.

Additional robustness and sensitivity analyses including alternative propensity specifications, comparisons to covariate-adjusted outcome models, latency/max-gap sensitivity checks, and the specificity-vs-background diagnostic are summarized in Appendix D.

A complete dissemination-ready table of all confirmation-estimated trajectory–horizon results accompanies the manuscript in the Supplementary Materials, including cohort sizes (suppressed/rounded as required), weighted CIFs, ΔCIFs, risk ratios versus each comparator, and uncertainty intervals.

5. Discussion

This study introduces an order-specific yet fully transparent framework for extracting prognostic signal from longitudinal EHR histories. Concretely, each validated signal is a human-auditable rule of the form “event A is first observed before event B within a prespecified gap,” paired with horizon-specific absolute risk estimates for a future outcome C and evaluated against prespecified clinical counterfactuals anchored at a common index and time zero. By design, these outputs can be inspected directly: Clinicians and informatics teams can see the defining events, the temporal constraints, the comparators, and the resulting absolute incidence differences at 1-, 2-, and 5-year horizons.

In this pilot, we validated 171 distinct A → B → C sequences, with effects that were non-trivial in magnitude and consistent across multiple comparators and sensitivity analyses. However, over 97% of sequences possible with the current set of selected health events have yet to be analyzed, indicating many more meaningful trajectories likely exist. Furthermore, the system can be easily tweaked for evaluation of any set of predictor conditions, procedures, drug exposures, or covariates and any desired set of outcome events by adjusting the event and outcome vocabulary list, allowing the potential for a wide variety of future analyses using this method.

At 5 years, the median absolute risk difference between an ordered sequence and the primary comparator (“(B with no prior A) → C”) had a median RR of 2.02 (IQR 1.74–2.60, maximum 5.28). These effect sizes are large enough to be relevant to clinical decision making in settings where baseline risks are modest and interventions carry cost or harm.

A central interpretive point is that these trajectories are intended as prognostic signals, not mechanistic claims. An ordered trajectory that is strongly associated the later adverse outcome can be clinically useful even when it is not verified as biologically causal in a strict sense. We are validating that the rule “A precedes B” consistently stratifies downstream incidence under clearly specified comparators and time alignment without claiming that intervening on A would necessarily change C. Determining which sequences may indeed indicate a shared patho-physiological mechanism is an interesting direction for future study, which we discuss and motivate with plausible illustrative examples in Appendix B.

Nonetheless, several components of the design aim to mitigate confounding by co-existing trajectories. The covariate set includes utilization and a broad comorbidity summary (CCI-LOO) computed prior to time zero, which absorbs some of the shared morbidity burden that generates correlated trajectories. In addition, the reverse-order comparator is particularly informative when feasible. Comparing A → B to B → A conditions on experiencing both events and asks whether the ordering itself is associated with differential downstream incidence. While reverse-order checks are not always estimable (because some A, B pairs rarely occur in both directions under the same gap and latency constraints), when they are available they provide a stricter control against “both-events” confounding.

The specificity analysis reported in Appendix D (replacing condition A with alternative common antecedents D while holding B and the outcome fixed) acts as an empirical test for the hypothesis that A is merely a generic marker of high-risk context. The observation that many validated A→B signals lie in the upper tail of their D→B background distributions suggests that for many trajectories, the prior event carries information beyond what would be expected from “any common antecedent to B.”.

A key potential source of selection bias in our pipeline is the requirement for sufficient observable time to reliably establish the temporal order of events and ascertain downstream outcomes within the AoU OMOP data. While 633,547 persons appear in the OMOP source, 432,617 (68.3%) met the prespecified eligibility criterion of ≥ 365 total days of merged observation. Importantly, attrition diagnostics indicate that most excluded individuals had very limited recorded observation rather than being just below the threshold (median total observed days = 0; 75th percentile = 15 days; ~78% had < 30 observed days and only a small fraction fell in the 180–364 day range), which is consistent with minimal or absent EHR observation-period coverage for some consented participants.

Because observation periods can be fragmented, we merged overlapping intervals and treated short gaps as adjacent (primary definition: a ≤ 1-day gap). Varying this “adjacent gap” definition across a wide range (0–30 days) produced no meaningful change in the number meeting the ≥ 365-day eligibility criterion or the longer continuous-span requirement used for lookback/latency–anchored episodes (<20-person change across settings), suggesting that our conclusions are not sensitive to reasonable alternative merging strategies.

The eligible analytic cohort was demographically similar to the full OMOP source (maximum absolute standardized mean difference = 0.133), with near-identical sex-at-birth and race/ethnicity distributions and only a modest shift toward older ages in the analytic cohort (mean age 55.3 vs 53.0), and the discovery/confirmation split was essentially perfectly balanced by stratified sampling (maximum absolute SMD = 0.001). Taken together, these checks support interpreting our results as representative of AoU participants with sufficiently long and stable EHR observation to support longitudinal trajectory inference, while acknowledging that participants with minimal recorded observation time are underrepresented by design. A csv file with a detailed breakdown of the demographics of participants in both the original OMOP source and after the observation period filtering is provided as Supplementary Material.

5.1. Limitations

These analyses are observational, and several limitations follow from the data-generating process and from the design choices needed to make large-scale trajectory screening feasible. Residual confounding remains possible even after propensity weighting and balance gating, especially for factors that are poorly measured or not represented in the OMOP tables used here (e.g., subtle socioeconomic factors, care access, or un-recorded clinical severity). Phenotype misclassification and measurement timing are also unavoidable: diagnoses, procedures, and drug exposures are recorded when they are coded, not necessarily when the underlying condition began, and this can shift apparent ordering, particularly when two conditions are evaluated in a clustered diagnostic workup. The explicit latency reduces (but cannot eliminate) reverse causation, and same-day ordering is excluded in the primary analysis. However, both choices trade sensitivity for interpretability and may remove clinically meaningful near-simultaneous sequences.

The framework is also constrained by observability. EHRs and OMOP observation periods encode when a record is considered observable, but real-world care is intermittent, and missingness is often informative. Even within the eligible cohort, requiring that index and time zero lie in the same observation interval and censoring follow-up at interval end can preferentially weight participants with stable, contiguous capture and can attenuate long-horizon estimates for those with fragmented records. In addition, AoU dissemination rules (cell suppression and rounding) appropriately protect privacy but necessarily coarsen some granular subgroup summaries and can blur fine-scale heterogeneity.

5.2. Future directions

Two directions are especially promising. First, extending from ordered pairs to higher-order trajectories can capture richer clinical context while remaining interpretable. In many settings, the relevant information is not just that “A precedes B”, but that a patient traverses a short path of events with characteristic spacing (e.g., A → B → D) or that the time gap Δt_A→B is itself prognostic. A natural extension is to mine and validate short path motifs with explicit gap constraints, while preserving the current episode construction principles.

Second, the most clinically actionable use of validated trajectories is likely as components of a composite risk representation rather than as standalone “one-rule” predictors. Because this pipeline yields calibrated, horizon-specific absolute incidence estimates, validated trajectory indicators can be integrated into transparent risk estimators that remain auditable—for example, a sparse additive model over validated sequences, or a patient-specific directed “trajectory graph” in which observed events activate downstream risk annotations. This would move from population-scale discovery toward patient-level decision support: the model would surface not only a risk number, but also the specific, interpretable temporal patterns in that patient’s record that contribute to the estimate, alongside the comparator-defined meaning of each contribution.

Taken together, these results support our claim that temporal structure can be incorporated in a way that remains legible, auditable, and directly expressible as clinical rules, while still providing measurable incremental value in adverse-outcome risk estimation.

6. Conclusion

We developed and demonstrated a fully transparent, order-aware framework for adverse-outcome risk estimation from longitudinal EHR data. Instead of collapsing a patient’s history into an unordered “bag of codes,” the method generates simple, auditable sequential rules of the form A → B (first occurrence of event A preceding first occurrence of event B within a prespecified gap), aligns follow-up to a clinically interpretable time zero after a fixed latency, and estimates horizon-specific absolute risks for downstream adverse outcomes C using weighted competing-risk cumulative incidence. This design makes every component of a signal (including events, ordering constraints, comparators, and time alignment) directly inspectable and clinically traceable.

Applied to 432,617 eligible All of Us participants in a discovery/confirmation design with prespecified comparators and global FDR control, the pipeline validated 171 order-specific A → B → C trajectories in this pilot. Across validated signals, ordered trajectories consistently stratified risk relative to the primary comparator (B with no prior A), and where estimable, reverse-order comparisons supported the claim that ordering itself can carry incremental prognostic information beyond simply observing both events. The additional unordered AB analysis further reinforced this point: while co-occurrence of A and B was often informative, conditioning on their sequence frequently produced nontrivial changes in estimated risk, indicating that temporal structure can add value in ways that remain fully interpretable.

These findings support a pragmatic path toward trajectory-aware clinical decision support that preserves auditability. Validated ordered trajectories are not mechanistic or causal claims, but rather reproducible prognostic features that can augment transparent risk estimation tools and help clinicians understand why risk differs across patients with superficially similar code sets. Future work should scale evaluation to the far larger space of candidate sequences, extend beyond event pairs to short higher-order motifs and time-gap–dependent trajectories, and integrate validated temporal rules into composite, interpretable risk estimators with external validation and prospective evaluation to assess transportability, robustness, and clinical utility.

Glossary

A, B, C

Placeholder letters for clinical events used in trajectory notation: A and B are upstream events in a sequence. C is a downstream outcome event.

Aalen-Johansen estimator (AJ)

A competing-risk survival estimator that generalizes Kaplan-Meier to estimate cumulative incidence when competing events (e.g., death) can occur.

Adjacent observation periods

Observation periods for the same person that overlap or are separated by only a very small gap (in this pipeline, 1 day or less) and are therefore merged into a single continuous interval for eligibility and follow-up.

All of Us Research Program (AoU)

A U.S. National Institutes of Health (NIH) program that provides a large, diverse research cohort and associated health data for approved research uses.

AoU Controlled Tier

A privacy-protected AoU data access tier with specific disclosure controls (e.g., small-cell suppression and rounding) for reporting results.

AoU Workbench

The secure analysis environment provided by All of Us for running code against AoU data.

Artifacts (analysis artifacts)

Intermediate files written by the pipeline (e.g., mined sequences, episodes, results) so analyses can be reproduced or resumed without rerunning every step.

At-risk count

The number of people who are still being followed (not yet had the outcome and not censored) at a given time horizon.

A→B

An ordered event pair meaning event A is observed before event B for a given person.

A→B→C

A three-event trajectory: A occurs before B, and C (an outcome) is evaluated during follow-up after time zero.

Baseline comparator

A comparator cohort intended to represent background risk: one calendar-time-anchored episode per person, not tied to a specific A or B event.

Benjamini-Hochberg procedure (BH)

A multiple-testing method that controls the false discovery rate (FDR) when many hypotheses are tested. Produces q-values.

BigQuery

Google Cloud’s SQL-based data warehouse used here to query OMOP tables at scale.

Blacklist

A list of outcome-related concepts (typically all descendants of the outcome concept set) that are excluded from predictors/features to prevent label leakage.

BMI

Body mass index, a weight-for-height measure (kg/m^2) used as a covariate in this study via categorical bins.

Cache / cached

Saving intermediate results (e.g., dataset splits or derived tables) so that reruns produce identical outputs and do not repeat expensive computations.

Calendar-time anchored

Anchored to a fixed position within a person’s observation period (e.g., observation period start plus lookback), rather than anchored to A or B.

Candidate sequence

An ordered event pair (A→B) that occurs often enough in the data to be tested for association with downstream outcomes.

CCI-LOO (leave-one-out Charlson)

A Charlson Comorbidity Index variant computed while explicitly excluding Charlson components that overlap with the exposure sequence or the outcome concept set, to reduce overadjustment.

Censoring

Ending a person’s follow-up before the outcome occurs, typically because their observation period ends or the study window ends.

Charlson Comorbidity Index (CCI)

A summary score of comorbidity burden based on the presence of specific chronic conditions. Higher scores generally indicate greater baseline illness burden.

Clinical concept (OMOP concept)

A standardized OMOP vocabulary item representing a condition, drug, procedure, or other clinical entity (identified by a concept_id).

Comparator cohort

A group constructed to answer a specific counterfactual question (e.g., B without prior A), used to compare against the A→B sequence group.

Competing event / competing risk

An event that prevents the outcome of interest from occurring or being observed. In this study, death is treated as a competing event for non-death outcomes.

Concept ID (concept_id)

A numeric identifier for an OMOP standardized concept.

Concept set

A collection of OMOP concepts used to define an exposure or outcome phenotype, often built by specifying one or more ancestor concepts and including descendants.

Concept_ancestor table

An OMOP vocabulary table that encodes hierarchical relationships between concepts (ancestor and descendant), used to expand concept sets.

Confidence interval (CI)

A range of plausible values for an estimated quantity (e.g., risk difference) that reflects sampling uncertainty.

Confirmation set

A held-out subset of participants used to re-run analyses on a frozen list of hypotheses as an internal replication step.

Confounding

Bias that occurs when the exposed and comparator groups differ in factors that also affect the outcome. Addressed here via covariate adjustment and weighting.

Covariate

A variable used for adjustment in statistical models (e.g., age, sex, comorbidity score).

Covariate balance

How similar the covariate distributions are between groups (sequence vs comparator), often assessed after weighting.

Cumulative incidence function (CIF)

The probability that an outcome has occurred by a given time, accounting for censoring and (when applicable) competing events.

Deduplication

Removing repeated records so that each unique unit is counted once (here, one record per person, date, and feature).

Descendant

A more specific OMOP concept that falls under a broader ancestor concept in the vocabulary hierarchy.

Descendant expansion

The process of including all descendant concepts of an ancestor concept when defining a concept set, so that specific codes roll up into a broader phenotype.

Discovery set

The subset of participants used to mine candidate sequences and run initial (exploratory) hypothesis tests.

Dissemination rules

Privacy rules governing what can be reported publicly from controlled data (e.g., small-cell suppression and rounding).

Domain tables

OMOP clinical data tables (e.g., condition_occurrence, drug_exposure, procedure_occurrence) that store dated events.

Drop missing/invalid

A data-cleaning step that removes rows with missing dates (unparseable/blank) or invalid date ranges (e.g., start date after end date) before downstream processing.

Early stopping (bootstrap)

Stopping bootstrap resampling once the uncertainty estimate stabilizes to a predefined precision threshold, to save computation.

Effective sample size (ESS)

A weighted-sample diagnostic that approximates how much information remains after weighting. ESS decreases when weights are highly variable.

Electronic health record (EHR)

Digitized clinical data from health care encounters (diagnoses, medications, procedures, labs, etc.).

Eligibility

Criteria for including participants in the analysis (e.g., sufficient total observed time within merged observation periods).

Episode

A per-person analysis record with an index date, a follow-up start (time zero), and a censor date. Episodes are the units used in time-to-event analyses.

Event ledger (events_df)

A person-level table of dated events after mapping raw OMOP records to analysis features and restricting events to observation periods.

False discovery rate (FDR)

The expected proportion of false positives among results declared significant when testing many hypotheses.

Feature

An analysis-friendly representation of one clinical concept or rolled-up group of concepts used to define A, B, covariates, or outcomes.

First-observed date

For a given person and feature, the earliest date that feature is recorded. Used to order A and B events.

Frozen list

A list of hypotheses selected in discovery (after FDR control and effect-size triage) that is carried forward unchanged into confirmation.

Gap (maximum allowed A→B gap)

The maximum time allowed between A and B for an event pair to count as an A→B sequence (e.g., up to 5 years).

Gating thresholds

Pre-specified minimum data requirements for running an analysis at a given horizon (e.g., minimum at-risk count and minimum outcome events per group).

Greenwood-type variance

A closed-form (analytic) approximation for the variance of a cumulative incidence estimator. Included as an alternative to bootstrap-based uncertainty estimates (but not used for the primary analysis in this study).

Horizon (risk horizon)

The follow-up time at which risk is summarized (e.g., 1, 2, or 5 years after time zero).

Immortal time bias

A time-related bias that can occur if people must survive or remain outcome-free for a period in order to be classified as exposed, leading to biased effect estimates.

Index date

The anchor date for an episode (e.g., the date of event B for A→B sequences and B-no-prior-A comparators, or the baseline anchor date for baseline episodes).

Integer-day time scale

Measuring follow-up time in whole days (rather than fractions), which simplifies merging with date-based EHR records and competing-risk estimation.

Interval-aware censoring

Censoring that uses the end of the specific observation interval containing time zero as the follow-up end date, rather than assuming continuous observation beyond that interval.

Invalid

Data entries that fail basic validity checks (e.g., a start date after an end date, or dates that cannot be parsed into a valid datetime).

Inverse probability of treatment weighting (IPTW)

A propensity-score weighting method that reweights participants so that measured covariates are balanced between the sequence group and comparator group.

IQR

Interquartile range: the range from the 25th to the 75th percentile, used to summarize variability.

Label leakage

A modeling pitfall where predictors contain information that is part of (or downstream of) the outcome definition, artificially inflating apparent predictive performance or associations.

Latency

A pre-specified delay between the index date and time zero (start of outcome follow-up), used to reduce reverse causation and near-term diagnostic workup effects.

Logistic regression

A statistical model for binary outcomes, here used to estimate propensity scores.

Lookback requirement

A required amount of prior observed time before the index date (e. g., 5 years) used to measure baseline covariates and confirm absence of prior events.

Love plot

A plot used to display covariate balance (typically standardized mean differences) before and after weighting.

Missing

Absent or unparseable values (e.g., a date that cannot be converted to a valid datetime).

Normalized to datetimes

Converting date columns to a standard datetime format so they can be compared and used for time calculations. Unparseable entries are treated as missing.

Observation interval

A single contiguous time span during which a person’s health data are considered observable (often after merging overlapping/adjacent observation periods).

Observation period (OP)

In OMOP, a recorded time span when a person’s data are expected to be captured in the dataset. A person can have multiple observation periods.

OMOP Common Data Model (CDM)

A standardized database schema and vocabulary for observational health data developed by the Observational Medical Outcomes Partnership.

One-hot encoding

Representing a categorical variable with multiple binary indicator columns (e.g., separate 0/1 flags for each smoking category).

OP-aware (observation-period-aware)

A rule that requires key episode dates (index date and time zero) to fall within the same observation period/interval, so follow-up and covariates are defined where data are actually observed.

P-value

A measure of statistical evidence against a null hypothesis. Smaller values indicate data less compatible with the null under the model assumptions.

Participant-Provided Information (PPI)

Survey data provided directly by AoU participants, used here for derived covariates such as smoking status.

Phenotype

A rule-based definition that maps raw EHR codes into a clinical event of interest (e.g., myocardial infarction) using concept sets and timing rules.

Phenotyping (phenotype time)

The process and timing of applying phenotype definitions (including descendant expansion) to EHR data to identify the first occurrence of outcomes within observation periods.

Poisson bootstrap

A resampling method that repeatedly reweights observations with random Poisson(1) counts (instead of sampling with replacement) to estimate uncertainty for statistics such as ΔCIF.

Primary comparator

The main comparator used for inference. Here, the primary comparator is typically B-no-prior-A (Event B with no prior A event).

Propensity score (PS)

The estimated probability of being in the sequence group (A→B) versus a comparator group, conditional on measured covariates.

Q-value

An FDR-adjusted p-value. The smallest FDR level at which a given test would be called significant under the BH procedure.

Random number generator (RNG) seed

A fixed value used to initialize random operations (e. g., train/test splits, bootstrap resampling) to make results reproducible.

Residual confounding

Confounding that remains after adjustment because important factors are unmeasured, measured imperfectly, or modeled inadequately.

Reverse causation

When early symptoms or diagnostic workup for the outcome influence the apparent exposure sequence, creating a spurious association.

Risk ratio (RR)

The ratio of cumulative incidence between two groups at a given horizon (CIF_sequence divided by CIF_comparator).

Rounding down (to nearest multiple of 5)

A disclosure-control rule in which reported counts are rounded down to reduce the risk of re-identification.

Same-day policy

A rule for handling cases where A and B occur on the same date (e.g., exclude same-day pairs so that B must be strictly after A).

Sensitivity analysis

An analysis that varies key design or parameter choices (e.g., latency or gap) to assess whether conclusions are robust.

Single observation period (OP)-aware index

For baseline episodes, a single index date per person defined relative to the observation period start plus the required lookback, ensuring time zero remains within that same observation interval.

Small-cell suppression

A disclosure-control rule that hides table cells with small counts (e. g., counts below a threshold) to reduce re-identification risk.

Standardized mean difference (SMD)

A unitless measure of covariate imbalance between groups. Values closer to 0 indicate better balance.

Statistical power

The ability of a study to detect an association if one truly exists. Larger sample sizes and more events increase power.

Strata / stratification

Subgroups defined by participant characteristics (e.g., sex, race/ethnicity) used for balanced splitting or reporting.

Support threshold

A minimum number of occurrences required for a candidate sequence to be tested, intended to avoid unstable estimates.

Suppression propagation

When a primary count is suppressed, derived quantities (like percentages or risks) are also suppressed to prevent back-calculating the hidden count.

Survival (time-to-event) analysis

Methods that model the time until an event occurs, accounting for censoring. Here implemented with competing-risk cumulative incidence estimation.

Tie-breaking rule (same-day death)

A convention used when death and a non-death outcome occur on the same recorded day: death is treated as occurring infinitesimally earlier so the outcome is not counted after death.

Trajectory

A temporally ordered pattern of events (e.g., A→B) evaluated for association with downstream outcomes.

Trajectory-aware

Designed to explicitly use the ordering and timing of events across visits, rather than treating history as an unordered set.

Trajectory-horizon combination

A specific (A→B sequence, outcome C, and follow-up horizon) hypothesis tested and reported.

Two-sided test

A statistical test that considers deviations in either direction (higher or lower risk) when computing a p-value.

Weight clipping (99th percentile)

Capping very large IPTW weights at a high percentile to reduce instability from extreme weights.

Weighted analysis

An analysis in which each participant contributes with a weight (e.g., IPTW) rather than equally, to adjust for measured confounding.

ZIP3

The first three digits of a U.S. ZIP code. Used here as a coarse geographic identifier for linking to area-level socioeconomic measures.

ΔCIF (risk difference)

The absolute difference in cumulative incidence between two groups at a given horizon (CIF_sequence minus CIF_comparator).

Appendix B:. Illustrative trajectories

Illustrative trajectories: clinical coherence and literature anchoring.

As discussed, the primary purpose of the identified trajectories is for use as signals for elevated risk to clinicians regardless of if they are causal or share a particular mechanism. However, we believe interesting future work could aim to identify whether a subset of these trajectories indeed point towards an evolving underlying pathology. To motivate this potential, we analyze a few illustrative trajectories with plausible mechanisms that warrant further exploration below.

Chronic lung disease → hearing loss → lung cancer.

Individuals who developed hearing loss after chronic lung disease had higher subsequent lung–cancer risk than those with the same “B” event but no prior chronic lung disease, with ΔCIF of 2.14 pp (95% CI 0.70–3.50 pp) and a risk ratio of 3.96 at the 5 year time horizon. The A → B sequence also exceeded B → A risk (RR 1.20), supporting an ordering–sensitive trajectory rather than simple comorbidity clustering.

This sequence seems to be biologically and clinically coherent. First, chronic lung disease (often dominated in routine coding by COPD/emphysema) is repeatedly shown to be associated with substantially increased lung–cancer incidence and mortality, including associations that persist after smoking adjustment. Systematic reviews/meta–analyses and large observational studies synthesize a mechanistic picture in which chronic airway inflammation, oxidative stress, impaired epithelial repair, and immune dysregulation create a pro–tumor milieu that elevates oncogenesis risk in COPD beyond smoking alone.[32,33].

Second, hearing loss as an intermediate “B” event is plausible in chronic lung disease populations: systematic reviews and cohort studies report higher prevalence/risk of hearing impairment in COPD, with proposed mechanisms including chronic hypoxemia/ischemia, systemic inflammation, oxidative stress, and shared exposures such as smoking.[34,35] Smoking itself is also consistently associated with worse hearing outcomes longitudinally, supporting the interpretation that “hearing loss after chronic lung disease” can act as a marker of cumulative exposure and systemic microvascular/oxidative injury along a pathway that also increases lung–cancer risk.[36,37] Finally, although uncommon, otologic manifestations (including hearing loss) can occur in lung cancer via neuro–otological paraneoplastic syndromes or metastases to the temporal bone, providing an additional (rare) route by which auditory symptoms can appear along the cancer detection pathway.[38,39].

Hypertensive disorder → cataract → myocardial infarction

Relative to incident cataract without prior hypertensive disorder, those with hypertension preceding cataract had higher myocardial infarction risk at the five year horizon (2.88 pp (95% CI 2.00–3.70 pp), RR 2.40) and exceeded the reverse ordering (A → B > B → A, RR 1.14).

A large meta–analysis concluded that hypertension increases cataract risk (with particularly notable associations for posterior subcapsular cataract), supporting mechanistic A → B biological plausibility via chronic vascular/oxidative injury.[40].

More interestingly, however, is that cataract can also plausibly “carry” cardiovascular signal. Ophthalmic aging/oxidative stress phenotypes often track systemic vascular aging. In a large prospective cohort, cataract extraction (a strong proxy for clinically significant cataract) was associated with higher subsequent coronary heart disease risk, including increased risk of nonfatal myocardial infarction, even after adjustment for major coronary risk factors.[41] Similarly, population–based analyses have reported increased subsequent ischemic heart disease risk among individuals with cataract diagnoses.[42] Taken together, the temporally ordered trajectory (hypertension → cataract → MI) is biologically coherent as a pattern in which cataract functions as a sentinel of cumulative vascular/oxidative burden among hypertensive patients, identifying a subgroup with higher downstream MI risk.

Diabetes mellitus → visual disturbance → myocardial infarction

Diabetes followed by a coded visual disturbance showed a large and graded association with MI versus incident visual disturbance without prior diabetes. At five years, ΔCIF was 4.47 pp (95% CI 2.90–6.10 pp, RR 2.46), and the A → B ordering exceeded B → A (RR 1.63). This pattern is in consonance with literature linking diabetic retinopathy to future cardiovascular events and mortality, consistent with widespread microvascular disease and shared pathobiology between micro- and macrovascular complications.[43,44].

Fig. B1.

Cumulative incidence curves for the illustrative sequences versus the baseline comparator. Curves display estimated cumulative incidence functions over follow-up. Greater separation indicates larger absolute risk differences between the sequence cohort and its comparator. (CIF, cumulative incidence function; CI, confidence interval.).

Appendix C:. Detailed methods

Observation time and cohort eligibility.

In OMOP, each participant has one or more observation periods, or date intervals during which their record is considered observable. Because observation periods can be fragmented, we first computed person–level merged observation by combining overlapping intervals and also combining intervals separated by short gaps. In this study, two intervals were treated as adjacent if the next interval began within 1 day of the current interval’s end.

For each person, we summed the number of calendar days covered by these merged intervals (counting endpoints inclusively) and required at least 365 total days of merged observation to be eligible for analysis.

Construction of the event ledger.

To convert raw OMOP concepts into analysis–friendly “events,” we curated an event vocabulary in which each analysis feature corresponds to an OMOP concept chosen for analysis and its descendant concepts. For each curated feature, descendant expansion was again performed via the concept_ancestor table, yielding a mapping from raw domain concepts to a higher–level feature identifier used throughout mining and episode construction.

To prevent label leakage, we built a blacklist consisting of all descendant concept identifiers used to define any outcome. Any raw event concept that descended from an outcome definition was excluded from the predictor event mapping, ensuring that outcome–defining codes could not appear as candidate A/B events or covariate events in the mined trajectories.

Using this curated mapping, we assembled a person–level event ledger (events_df) by extracting events from OMOP domain tables (condition occurrences, procedures, and drug exposures), mapping each raw concept to its curated feature identifier, and retaining only events whose dates fell within an observation period (i.e., event_date between observation_period_start_date and observation_period_end_date). The resulting ledger was deduplicated to one record per (person_id, event_date, feature_id), producing a day–level event stream per participant.

Derived covariate events (smoking and BMI).

In addition to clinical domain events, we derived two supplementary covariate variables and represented them as categorical events for consistent handling: smoking status and BMI category. Smoking status was derived from AoU participant–provided information (PPI) responses and categorized as Ever, Never, or Unknown. BMI was derived from OMOP measurements of body mass index (with outlier filtering) and categorized as Underweight, Normal weight, Overweight, Obese class I, Obese class II+, or Unknown. These derived categories were assigned explicit internal concept identifiers and appended to the derived covariate table.

Propensity score weighting and covariate balance diagnostics.

For each comparison, we estimated a propensity score (PS) for cohort membership and applied inverse probability of treatment weighting (IPTW) to reduce confounding by measured covariates. Specifically, we fit a logistic regression model predicting membership in the “treated” cohort (A → B) versus the comparator cohort using the covariate vector described above, with categorical variables one–hot encoded (including explicit missingness indicators).

Let $\left({\widehat{e}}_i\right)$ denote the fitted propensity score for individual (i). We computed unstabilized IPTW as

$$w_i=\left\{\begin{array}{c}1/{\widehat{e}}_i\\ 1/(1-{\widehat{e}}_i)\end{array}\right.$$

with propensity scores clipped away from 0 and 1 for numerical stability and weights clipped at the 99th percentile to limit the influence of extreme weights.

Poisson bootstrap with early stopping.

Uncertainty intervals and two–sided p–values for ΔCIF(t) were computed using a Poisson bootstrap. In each bootstrap replicate, individuals were reweighted by independent Poisson(1) multipliers, and the weighted Aalen–Johansen CIF was recomputed for each cohort. Confidence intervals were formed from empirical quantiles of the bootstrap distribution, and p–values were computed from the bootstrap mass on either side of zero for ΔCIF (two–sided).

To manage computation while maintaining stable uncertainty estimates, the bootstrap used an early–stopping rule: we began with 100 replicates and extended up to 250 replicates, checking every 20 replicates and stopping when the ΔCIF confidence–interval half–width stabilized to ≤ 0.2 percentage points absolute or ≤ 5% relative.

Dissemination rules.

All reported counts, cohort sizes, and derived tables adhere to AoU Controlled Tier dissemination rules: any cell with count < 20 is suppressed, and all other cohort size counts are rounded down to the nearest multiple of 5. Suppression propagates to derived estimates (including CIFs, risk differences, and q–values) in outputs to prevent back–calculation of small values.

Appendix D:. Extended results & sensitivity analyses

IPW and covariate weighting models.

Because a simple logistic propensity model can miss nonlinearities or interactions in cohort assignment, we repeated propensity estimation for the subset of trajectory–outcome pairs in the confirmation set for which the primary IPTW analysis passed the prespecified balance check using a gradient-boosted tree model on the same covariate set and re-computed IPTW and balance diagnostics.

Among 420 trajectory–outcome pairs, the boosted propensity model achieved the same balance criterion for 372 (88.6%). Across the valid/balanced subset (n = 1,116 horizon-specific estimates), effect sizes were highly concordant between the logistic and boosted propensity approaches: the correlation between log risk ratios was 0.967. This strong agreement suggests that the main inferences are not narrowly dependent on the functional form of the propensity model and provides some reassurance against concerns that unmodeled interactions in treatment assignment dominate the observed signals.

To further ensure that IPW estimates are not sensitive to unmodeled interactions or functional form assumptions, we also compared IPTW-based estimation to a conventional covariate-adjusted outcome model in the confirmation subset. Specifically, for a representative set of 25 trajectory–outcome pairs (75 horizon-specific endpoints), we fit both a multivariable logistic regression of event-by-horizon on exposure plus the full covariate set, and an IPW-weighted logistic regression using the same IPTW weights. Among the 75 endpoints, 60 had sufficient events to fit the multivariable logistic regression model. Across these 60, the two approaches were highly concordant: the correlation between log odds ratios was 0.957, the median absolute difference in log OR was 0.066, and the direction of association agreed in 100% of the comparisons. This agreement suggests that the main inferences are not an artifact of relying on IPW alone and provides additional reassurance that residual interaction-driven misspecification does not dominate the observed signals.

Sensitivity analyses for latency and maximum A → B gap.

We evaluated whether top validated signals were qualitatively stable to two time-window choices that can influence trajectory definition: the latency between index and follow-up start and the maximum allowable A → B gap. In one-at-a-time sensitivity analyses, varying latency (30/90/180 days) holding the A → B gap at 5 years, and varying the A → B gap (1/5/10 years) holding latency at 90 days, produced directionally consistent estimates and largely preserved the relative ranking of the strongest signals (Spearman ρ = 0.93–0.98; median rank shift 0–1).

Specificity vs background.

As an additional diagnostic to help distinguish “trajectory-specific” signals from broader background risk, we computed a specificity metric that situates each validated ordered trajectory’s risk elevation relative to a background distribution of alternative sequences (substituting other common prior events D for A while holding B and outcome C fixed). In a randomly sampled set of validated, balanced signals (n = 25), the ordered trajectory’s RR frequently lay in the far upper tail of its background distribution (median percentile rank 91; IQR 80–95) and was typically larger than the background median (median RR_A/median(RR_D) = 1.45, IQR 1.30–1.70). This upper-tail enrichment exceeded what would be expected under a uniform-null distribution of percentile ranks (one-sided binomial p_≥90% = 1.62 × 10⁻⁷; p_≥95% = 1.69 × 10⁻⁴).

Appendix D. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.jbi.2026.105008.

Data availability

The full source code and configuration files are available in the supplementary materials, and the Zenodo DOI for the source code and configuration files are available in the manuscript.