Modeled Sojourn Time and Sensitivity for Detecting Preclinical Cancers Retrospectively by a Multicancer Early Detection Test

Abstract

Background:

Blood-based multicancer early detection tests have potential for clinical benefit, but key performance metrics for cancer screening, such as sojourn time and sensitivity of these tests for detecting preclinical disease, are not yet known.

Methods:

In a retrospective analysis of stored plasma samples in the American Cancer Society Cancer Prevention Study 3 (CPS3), GRAIL’s MCED test was evaluated for detectability prior to cancer diagnosis. Classical state-transition models for cancer screening were modified to characterize the natural history of ctDNA-shedding cancers. The sensitivity estimand for detecting preclinical cancers by the MCED test was proposed in the context of retrospective testing, and a Bayesian likelihood method was developed to estimate preclinical detectable duration and sensitivity.

Results:

Analysis of CPS3 data showed that for the 12 prespecified cancers that represent two-thirds of cancer deaths in the United States, the test had 64% estimated overall sensitivity across all stages, and 43% sensitivity during an average 1.36-year preclinical detectable window before metastasis. Untestable assumptions on state transition and sensitivity are discussed, along with limitations related to using stored plasma samples.

Conclusions:

State-transition models were developed for retrospective analysis of plasma samples from the CPS3. Estimates for the length of the preclinical detectable window and the sensitivity at screening support annual MCED screening to intercept late-stage cancers.

Impact:

Retrospective analysis of plasma samples from the CPS3 supports the potential of GRAIL’s MCED test to detect cancers early in the preclinical state.

See related In the Spotlight, p. 1484

Introduction

Cancer screening aims to detect cancers early in the preclinical phase, in order to provide better treatment options, improve quality of life, and prevent cancer death. The current paradigm that screens one cancer at a time has favorable benefit-to-harm trade-offs only for a few common cancers (e.g., breast; ref. 1, prostate; ref. 2, colorectal; ref. 3, and cervical cancer; ref. 4 and for lung cancer in the high-risk smoking population; ref. 5). Achieving broad access and adherence to screening tests for some cancers currently recommended in the United States has already proved to be challenging, e.g., lung and colorectal cancers (6, 7). For other cancers covering the majority of cancer deaths (8), such an approach is not cost-effective for population-wide screening because each cancer has relatively low incidence and mortality rates.

Blood-based multicancer early detection (MCED) tests represent a paradigm shift in cancer screening and potentially address this unmet medical need. A single blood test detects aberrant methylation signals in circulating tumor DNA (ctDNA), thereby enabling efficient screening for less common, including rare, cancers that currently do not have screening programs (9). In a large-scale case-control validation study (10), GRAIL’s MCED test yielded an overall test sensitivity of 51.5% among >50 cancer types, and 76.3% in 12 prespecified cancer types that account for approximately two-thirds of annual cancer deaths in the United States (11), including anal, bladder, colon/rectal, esophageal, head and neck, liver/bile duct, lung, lymphoma, ovarian, pancreatic, plasma cell neoplasm, and stomach cancers. When added to existing screening practices, this MCED test may substantially increase the overall cancer screening yield.

Clinical benefit for a cancer screening test is derived from detecting and treating cancers before symptoms emerge. After validation in clinically diagnosed diseases, retrospective analysis of stored samples before cancer diagnosis in a phase-3 study in the Early Detection Research Network’s five-phase framework, if available, permits evaluation of preclinical detectability (12). For GRAIL’s MCED test, a retrospective biobank study was conducted in the American Cancer Society’s Cancer Prevention Study 3 (CPS3): nearly 304,000 cancer-free participants had a blood draw at enrollment between 2006 and 2013 and were followed for cancer diagnosis in the subsequent 3 years (13). The baseline plasma samples for > 1,300 cancer cases and matched controls were assessed by GRAIL’s MCED test. This retrospective study provided preliminary evidence for the capacity to detect preclinical cancers: the average time between blood draw and cancer diagnosis among detected cancers was 323 days; the first-year test-positive rate was 15% for all cancers, and 55% for eventually fatal cancers (14). Modeled lead-time estimates varied across cancer sites and stages (15).

In the screening literature, two performance metrics have been modeled for evaluating a screening test and projecting its potential clinical impact: the duration of the preclinical detectable phase (PCDP) for the test, commonly referred to as “sojourn time,” and sensitivity to detect preclinical diseases. Both quantities are challenging to estimate: the entry point of PCDP is not observable; sensitivity to detect preclinical cancers requires gold-standard diagnostic methods applied to all screenees at the time of screening. The test-positive rate among cancers diagnosed after blood draw in a retrospective study is a biased estimate for the sensitivity to detect preclinical cancers. As illustrated in Fig. 1A, the MCED test was retrospectively applied to plasma samples collected before clinical diagnosis. Although preclinical cancer should already be present at the time of blood draw if the plasma sample was test positive, for a portion of test negatives, a preclinical cancer may not be present at the time of blood draw, arising only later. The sensitivity for detecting preclinical cancers should, therefore, exclude cancers not present at the time of blood draw but arising after. Because of this dilution, the observed test-positive rate among the collection of cancers later diagnosed could be substantially lower than the true sensitivity. On the other hand, empirical sensitivity measured in interventional trials, specifically the proportion of screen-detected cancers among all cancers diagnosed in an assessment interval after screening, could approximate the true sensitivity for some appropriate interval (16–18).

Figure 1.

Overview of a retrospective study and multi-state models. A, Cancer status at the time of blood draw for test positives and test negatives among cancers in a retrospective study. Empty circles are for cancers arising after blood draw and so test negative. B, Three-state model for ctDNA-detectable cancers; all cancers were born to the preclinical cancer stage, a subset of which shed ctDNA into blood. Cancers eventually progressed to clinical diagnosis. C, Five-state model for ctDNA-detectable cancers; all cancers were born to preclinical early-stage cancer state, a subset of which shed ctDNA, some of which progress to clinical early-stage cancers, and others progress to preclinical late-stage cancers and then become clinical late-stage cancers.

In this work, we modeled jointly the detectable window and the sensitivity for retrospectively detecting preclinical cancers by the MCED test in the CPS 3-GRAIL study. Knowledge of the preclinical detectable window and sensitivity enables mathematical models to project the magnitude of clinical utility measures, such as reduction in late-stage cancers (19–21). To this end, the existing statistical literature has been primarily on modeling prospective studies of single-cancer screening tests, most of which are imaging-based modalities (22–24). Extensions of these methods to MCED tests and retrospective studies that account for features of ctDNA-shedding cancers and the heterogeneity among different cancer types have yet to be developed.

We present a Bayesian likelihood approach to modeling the sensitivity and the preclinical duration of cancers detected by GRAIL’s MCED test in the CPS3, pooling cancers across cancer types and accounting for heterogeneity by prior distributions. The preclinical natural history was modeled by modifying the classic three-state model or the five-state model to accommodate a mixture of ctDNA-detectable and undetectable cancers (19, 22, 24). The proposed Bayesian estimation method was applied to cancers in the CPS 3-GRAIL study across all cancer types, and to the subset of 12 prespecified cancer types responsible for two-thirds of US cancer deaths.

Materials and Methods

The CPS 3-GRAIL study

The American Cancer Society (ACS) CPS3 is a prospective, long-term cohort study of cancer incidence and mortality that recruited nearly 304,000 participants aged 30 to 65 years (23% men and 77% women) with no history of cancer (except for basal or squamous cell skin cancer) between 2006 and 2013 (13). CPS3 participants completed a lifestyle and health survey and blood draw at enrollment. Blood was collected into vacutainer tubes containing the anticoagulant ethylene diamine tetraacetic acid (EDTA). The median time to processing was 14 hours and 1 minute, and 96.1% of samples were processed within 24 hours. Participants were followed for cancer outcomes (including cancer stage identified as local, regional, or distant stage) via routine linkages of the entire cohort with population-based state cancer registries and the National Death Index. At the time of this study, follow-up for cancer and death was complete through December 31, 2015, and December 31, 2017, respectively.

For the CPS 3-GRAIL study, stratified sampling was conducted to achieve a 1:1 noncancer/cancer ratio (all 1,383 cancers available and matched 1,371 controls randomly selected into the analysis set) in the strata by age and sex. Certain cancer types that had relatively high incidence in the cohort (breast, melanoma, thyroid, uterus, and prostate cancers) were downsampled to absolute numbers of included participants comparable with other less common cancer types. The participants’ characteristics, cancer composition, and sampling scheme have been reported elsewhere (14). The plasma samples were received by GRAIL, Inc. in 2021, and cell-free DNA (cfDNA) extraction and sample analysis were performed with a locked classifier (blinded to clinical data), as previously described (10). There were no test positives in the control samples, and the analysis was focused on test results in cancer samples.

Natural history, likelihood development, and Bayesian estimation using a three-state model

Individuals enter the preclinical cancer state once the disease can be diagnosed as invasive cancer by a reference standard method. Not all cancers shed a detectable level of ctDNA into the bloodstream; in addition, detectability by the cfDNA-based MCED test depends on the cancer type and stage (25, 26). We stipulate that a portion of preclinical cancers shed a detectable amount of ctDNA, and so were test positive when retrospectively tested by the MCED test, whereas others did not shed a detectable amount of ctDNA and were test negative. All cancers eventually progress to the clinical state when symptoms emerge and are clinically diagnosed (Fig. 1B). The duration of the preclinical state for the subset of the ctDNA-detectable cancers is sojourn time, a quantity that depends on the screening test and is modeled by an exponential distribution. Because this is a retrospective study, all cancers included in testing were clinically diagnosed; therefore, potential overdiagnosis by the MCED test cannot be modeled.

Two important features distinguish this model from prior models, making it more generalizable and interpretable. First, the denominator for the sensitivity in this model, as we define next, is all preclinical cancers, not just cancers entering PCDP in classical models (22, 23). The classical concept of PCDP is loosely defined, depending on the very screening test being evaluated, so the sensitivity defined therein is difficult to interpret. The second distinction, also a novel feature of the model, is that it explicitly permits a mixture of detectable and non-detectable cancers, and preclinical duration is allowed to be different between test-positive and test-negative cancers. Specifically, cancers shedding a detectable level of ctDNA may be more aggressive than cancers that do not shed a detectable level of ctDNA.

In the CPS3-GRAIL study, during the 3-year follow-up period after the blood draw at t₀, cancers were diagnosed, some of which were test positive at t₀. Let I(t) denote the probability for cancer diagnosis at time t after the blood test (t > t₀), and let I⁺(s,t) denote the probability for a cancer entering the preclinical state at time s (t₀> s), testing positive at t₀, and clinically diagnosed at t. Importantly, if the sample was positive at t₀ and subsequently clinically diagnosed at t, the cancer must have been present at t₀ because the probability of false positive for this MCED test is extremely low (∼0.5%) and so is the probability of a new cancer arising after a false positive test. I⁺(s,t) can be expressed by the product of three terms:

$$Pr\left(\mathrm{a}\hspace{0.17em}\text{ctDNA}‐\text{detectable}\hspace{0.17em}\text{cancer}\hspace{0.17em}\text{entered}\hspace{0.17em}\text{the}\hspace{0.17em}\text{preclinical}\hspace{0.17em}\text{state}\hspace{0.17em}\text{at}\hspace{0.17em}s\right)\hspace{0.17em}\times$$

$$\mathit{Pr}\left(\mathrm{clinically}\hspace{0.17em}\mathrm{diagnosed}\hspace{0.17em}\mathrm{at}\hspace{0.17em}t|\hspace{0.17em}\mathrm{a}\hspace{0.17em}\mathrm{detectable}\hspace{0.17em}\mathrm{cancer}\hspace{0.17em}\mathrm{entered}\hspace{0.17em}\mathrm{preclinical}\hspace{0.17em}\mathrm{state}\hspace{0.17em}\mathrm{at}\hspace{0.17em}s\right)\hspace{0.17em}\times$$

$$\mathit{Pr}\left(\mathrm{test}\hspace{0.17em}\mathrm{positive}\hspace{0.17em}\mathrm{at}\hspace{0.17em}{t}_0|\mathrm{a}\hspace{0.17em}\mathrm{detectable}\hspace{0.17em}\mathrm{cancer}\hspace{0.17em}\mathrm{entered}\hspace{0.17em}\mathrm{preclinical}\hspace{0.17em}\mathrm{state}\hspace{0.17em}\mathrm{at}\hspace{0.17em}s,\hspace{0.17em}\mathrm{diagnosed}\hspace{0.17em}\mathrm{at}\hspace{0.17em}t\right)$$ (A)

For simplicity and identifiability, we assume detectability is defined by the one-time MCED test at t₀, so the third probability in (A) is 1 for a detectable cancer. The mixture probability for ctDNA-detectable preclinical cancers is parameterized to be β, the sensitivity estimand for detecting preclinical cancers. This estimand is clearly a simplification, assuming that a constant β captures the average detectability in the entire duration of the preclinical state for all prevalent cancers at t₀, and that the MCED test at t₀ detects all detectable cancers. Note that the sensitivity estimand can also be interpreted as “the fraction of cancers that were detectable by the MCED test during the preclinical state.” The other two probabilities in (A) can, therefore, be parameterized as follows:

• the probability of a detectable cancer entering the preclinical state at s, denoted by J(s) × β, where J(s) is the total incidence of preclinical cancers and β is the fraction of detectable ones. For studies with a short follow-up relative to participants’ age, it is common to assume that the incidence rate within an individual is constant J(s) = J.

• the probability distribution of the preclinical duration for the subset of detectable cancers, namely, f(·), also known as the distribution of sojourn time.

Plugging in the parameters and integrating over s, the probability for a preclinical cancer testing positive at t₀ and clinically diagnosed at t is

$$I^{+}\left(t\right)={\int }_0^{t_0}J\left(s\right)\beta f\left(t-s\right)ds=\beta J{\int }_0^{t_0}f\left(t-s\right)ds=\beta J\exp \left\{-\left(t-t_0\right)\lambda \right\}$$ (B)

Similarly, let I⁻(t) denote the probability for testing negative at t₀ and a cancer clinically diagnosed at t. Testing negative at t₀ could result from the test failing to detect a prevalent cancer, or a new cancer arose only after t₀. Therefore, I⁻(t) can be expressed as the sum of two probabilities:

$$Pr\left(\text{undetectable}\hspace{0.17em}\text{cancer}\hspace{0.17em}\text{present}\hspace{0.17em}\text{at}\hspace{0.17em}{t}_0\hspace{0.17em}\text{and}\hspace{0.17em}\text{test}\hspace{0.17em}\text{negative},\hspace{0.17em}\text{clinically}\hspace{0.17em}\text{diagnosed}\hspace{0.17em}\text{at}\hspace{0.17em}t\right)\hspace{0.17em}+Pr\left(\text{cancer}\hspace{0.17em}\text{entered}\hspace{0.17em}\text{preclinical}\hspace{0.17em}\text{state}\hspace{0.17em}\text{after}\hspace{0.17em}t,\hspace{0.17em}\text{clinically}\hspace{0.17em}\text{diagnosed}\hspace{0.17em}\text{at}\hspace{0.17em}t\right)$$ (C)

$$=\hspace{0.17em}J\hspace{0.17em}\mathrm{-}\hspace{0.17em}J\beta \hspace{0.17em}\exp \left\{\mathrm{-}(t\hspace{0.17em}\mathrm{-}\hspace{0.17em}{t}_0)\lambda \right\}\mathrm{.}$$ (D)

Standard approximation of exp(−λt) by 0 was used to establish (D; ref. 22). The derivation of (D) is found in Supplementary Materials and Methods S1. Importantly, the exponential distribution of preclinical duration for test-negative cancers can have different hazard (λ₀) from that for test-positive cancers (λ), as shown in Fig. 1B, though it has no impact on I⁻(t). It follows that I(t) = I⁻(t) + I⁺(t) = J. Let p(t) = I⁺(t)/I(t) denote the conditional probability of test positive at t₀ given a cancer later diagnosed at t, expressed as

$$p\left(t\right)\hspace{0.17em}=\hspace{0.17em}\beta \hspace{0.17em}\exp \left\{\mathrm{-}(t\hspace{0.17em}\mathrm{-}\hspace{0.17em}{t}_0)\mathrm{\lambda }\right\}\mathrm{,}$$ (E)

so that the instantaneous detectability p(t) after t₀ is decreasing exponentially after blood draw from sensitivity β. Using the conditional probability expressed in (E), binomial likelihood can be constructed for estimating the hazard λ and the sensitivity β, using test-positive or -negative data for every cancer diagnosed after blood draw (Supplementary Materials and Methods S1). The sampling scheme was accounted for by inverse probability weighting.

When cancers were combined into equally spaced time intervals (Δt) after the blood draw, e.g., first year, second year, and third year, the test-positive rate for the k^th interval (k = 1,2,...) can be shown to be

$$p_k\mathrm{=}\frac{\beta }{\lambda }\left[\exp \left\{\mathrm{-}\lambda \left(k\mathrm{-}1\right)\mathrm{\Delta }t\right\}\mathrm{-}\exp \left\{\mathrm{-}\lambda k\mathrm{\Delta }t\right\}\right]$$ (F)

So test-positive rates in the intervals also decrease exponentially from β, p_k = p_k−1 exp(−λ) and p_k< β for any k (derivation found in Supplementary Materials and Methods S1).

A Bayesian estimation procedure was implemented by the R rstan package, putting prior distributions on both sensitivity and mean sojourn time (MST). This is particularly important to accommodate potential heterogeneity in distributions of sojourn time and test sensitivity in different cancer types. A prior distribution was used for β, and a prior distribution was used for λ. The other benefit of using Bayesian estimation is to leverage the sensitivity data from the prior large-scale validation study in clinically diagnosed cancers [Circulating Cell-Free Genome Atlas Substudy 3 (CCGA3)]. The prior distribution for β in the primary analysis was assumed to be a Beta distribution with its mean at 70% to 80% of the corresponding CCGA3 sensitivity, representing a potential degradation of sensitivity from clinically diagnosed cancers to preclinical cancers. A simulation experiment was conducted to evaluate the consistency of maximum likelihood estimators for the three-state model (Supplementary Table S1).

Five-state model including early-stage progressing to late-stage cancers

We now extend the three-state model to the five-state model, including cancer stages stratified as early-stage (localized and regional) and late-stage (distant) cancers (Fig. 1C). All cancers entered the “early preclinical state” at time s with the constant incidence rate J, a portion of which shed a detectable level of ctDNA into the blood.

• The ctDNA-detectable, early-stage cancer had competing probabilities for either progressing to the “early clinical state” or the “late preclinical state” at time x, whichever occurred first. For the MCED-detectable cancers, assume the exponential distributions for the preclinical duration x − s of two competing paths, one with hazard λ₁, and the one λ₂. From the “late preclinical state” at x, an MCED-detectable cancer has the late-stage preclinical duration (exponential distribution with hazard λ₃) to reach the final state—clinical diagnosis at late stage.

• The ctDNA non-detectable, early-stage cancers progressed either to the early clinical state or the late preclinical state, though with different competing hazards ${\mathrm{\lambda }}_1^0$ and ${\mathrm{\lambda }}_2^0$ from those of ctDNA-detectable cancers. Once the cancer entered the late preclinical state, the two paths merged (Fig. 1C): either non-detectable or detectable early-stage cancers could progress to the late preclinical state. We assume the same hazard λ₃ for the late preclinical state progressing to the late clinical state. Typically, once a cancer metastasized, a much higher amount of ctDNA was shed into the bloodstream (25, 26). In the prior case-control study, nearly all stage IV cancers were detectable by the MCED test (10).

Let β_E and β_L denote the sensitivity for detecting early-stage preclinical cancers and the sensitivity for detecting late-stage preclinical cancers at the time of blood draw t₀, respectively. In Supplementary Materials and Methods S1, with additional assumptions, we derive that the conditional probability of test positive given early-stage cancers that were diagnosed at t is

$$p_{\mathrm{E}}\left(t\right)=Pr\left(\text{test}\hspace{0.17em}\text{positive}\hspace{0.17em}\text{among}\hspace{0.17em}\text{early}‐\text{stage}\hspace{0.17em}\text{cancers}\hspace{0.17em}\text{diagnosed}\hspace{0.17em}\text{at}\hspace{0.17em}t\right)$$

$${=\beta }_E\left[exp\left\{-\left({\lambda }_1+{\lambda }_2\right)\left(t-t_0\right)\right\}\right],$$ (G)

and the MST for being early-stage is $\frac{1}{{\lambda }_1\mathrm{+}{\lambda }_2}$, the window of opportunity for cancer interception. The conditional probability of test positives among late-stage cancers that were diagnosed at t is

$$p_L\left(t\right)=Pr\left(\text{test}\hspace{0.17em}\text{positive}\hspace{0.17em}\text{among}\hspace{0.17em}\text{late}‐\text{stage}\hspace{0.17em}\text{cancers}\hspace{0.17em}\text{diagnosed}\hspace{0.17em}\text{at}\hspace{0.17em}t\right)$$

$${\beta }_E\left[\frac{{\lambda }_3}{{\lambda }_1+{\lambda }_2-{\lambda }_3}\left[exp\left\{-{\lambda }_3\left(t-t_0\right)\right\}-exp\left\{-\left({\lambda }_1+{\lambda }_2\right)\left(t-t_0\right)\right\}\right]\right]$$

$$+{\beta }_{L}exp\left\{-{\lambda }_3\left(t-t_0\right)\right\}.$$ (H)

and the MST for being in late-stage state is $\frac{1}{{\lambda }_3}$. Note that cancers not detectable by the MCED test could have different distributions for preclinical duration at early stages (Supplementary Materials and Methods S1), though not affecting the conditional probabilities. Weighted binomial likelihood was constructed by adding individual likelihood contributions from test positives and test negatives among early- and late-stage cancers, with weights accounting for downsampling of certain cancer types. A simulation experiment was conducted to evaluate the consistency of maximum likelihood estimators for the five-state model (Supplementary Table S2). The Bayesian estimation was implemented by rstan to account for potential heterogeneity in different cancer types and to stabilize the estimation.

Results

Test-positive rate depended on cancer characteristics and decreased with time after blood draw

Figure 2 shows the test-positive rate among all cancers or a subset of the prespecified 12 cancers responsible for two-thirds of US cancer deaths that were diagnosed in the first, second, and third year after blood draw. As noted in the Methods section, these test-positive rates tend to be lower than the sensitivity of the MCED test to detect preclinical cancers at the time of blood draw (estimated in Table 1). Among all cancers diagnosed in the first year, the MCED test-positive rate at the baseline blood draw was 15.4% (Fig. 2A). The test-positive rate decreased to 6.1% for cancers diagnosed in the second year and 2.4% for the third year. The test-positive rates were substantially higher in the 12 prespecified cancers and 40.7%, 17.6%, and 8.0% for the three yearly intervals, respectively (Fig. 2C). Consistently, cancers diagnosed at the distant stage had a higher test-positive rate than regional and localized cancers (Fig. 2B and D).

Figure 2.

Test-positive rates for cancers diagnosed in the first, second, and third year after blood draw. A, All cancers. B, All cancers stratified by stage. C, Prespecified 12 cancer types. D, Prespecified 12 cancer types stratified by stage.

Table 1.

Estimates of test sensitivity for preclinical cancers and mean sojourn time by cancer group.

​	All cancers		Prespecified 12 cancersa
	Test sensitivity	MST	Test sensitivity	MST
Three-state model	​	​	​	​
All stages	29% (23%, 36%)	0.90 (0.76, 1.08)	64% (49%, 79%)	1.17 (0.92, 1.53)
Five-state model	​	​	​	​
Localized/regional	20% (15%, 27%)	0.80 (0.64, 1.02)	43% (27%, 61%)	1.36 (0.92, 2.15)
Distant	88% (74%, 97%)	0.95 (0.76, 1.20)	87% (72%, 97%)	0.62 (0.36, 0.91)

NOTE: For the three-state model pooling stages together, β (0.4,0.6) was used as prior for sensitivity, and γ (0.25,0.25) for the hazard of the exponential distribution for sojourn time; for the five-state model, β (0.3,0.7) was used as prior for early-stage sensitivity, β (7,3) for late-stage sensitivity, and γ (0.25,0.25) for hazard of all sojourn time distributions. Results with alternative prior distributions are shown in Supplementary Materials and Methods S1.

^aIncludes anal, bladder, colon/rectal, esophageal, head and neck, liver/bile duct, lung, lymphoma, ovarian, pancreatic, plasma cell neoplasm, and stomach cancers.

The lead time distribution was heterogeneous across cancer types

The lead time for a ctDNA-detectable, test-positive cancer was directly observed in this retrospective analysis. Figure 3A shows the distributions of lead time by cancer type, which demonstrates heterogeneity across cancer types. Esophageal and pancreatic cancers had the shortest lead times, whereas plasma cell, kidney, ovary, and unmapped cancers had the longest lead times. Except for a few common cancers, there is generally a limited number of detected cancers for any cancer type, so cancer-specific lead time may not be reliable. In Fig. 3B, when cancers were grouped into the prespecified 12 cancers versus others, the lead time for the group of prespecified 12 cancers (median 0.94 years) was longer than for other cancers (median 0.54 years).

Figure 3.

Observed lead time in the CPS3-GRAIL study. A, Distribution of lead time by cancer type. Unmapped cancers refer to cancers with incomplete clinical data so that could not be classified based on the definitions of invasive cancer types by ICD-O-3.1 site and histology. B, Distribution of lead time by cancer type category (prespecified 12 cancers and other cancers).

The exponential distribution fitted well for modeling sojourn time

Figure 4A shows the distribution of lead time for all cancers being detected by GRAIL’s MCED test. The red curve is the density of the fitted exponential distribution, indicating a good fit by an exponential distribution. The test-positive rate was computed for cancers diagnosed in each quarter after the blood draw. As derived in the Methods, if the preclinical duration was distributed as an exponential distribution, then these quarterly test-positive rates would decrease at an exponential rate. Figure 4B shows the fitted linear line to the logarithm transformed test-positive rates among all cancers, suggesting that despite heterogeneity, the exponential distribution for the preclinical duration across cancer types fitted well to the observed data. Similar patterns were observed when limiting to the prespecified 12 cancers (Fig. 4C and D).

Figure 4.

Assessments of the exponential distribution assumption for modeling sojourn time. A, Empirical distribution of lead time for all cancers and the fitted line by an exponential distribution. B, Logarithm of quarterly test-positive rate among all cancers decreases linearly with time of cancer diagnosis after blood draw. The size of dots corresponds relatively to the number of cancers in that interval. C, Distribution of lead time for the cancer type category of 12 prespecified cancers and the fitted line by an exponential distribution. D, The logarithm of the quarterly test-positive rate for 12 prespecified cancers decreases linearly with the time of cancer diagnosis after blood draw. The size of dots corresponds relatively to the number of cancers in that interval.

Estimated mean sojourn time and sensitivity

The maximum likelihood estimators for the three-state model (5) and for the five-state model (7, 8) were evaluated in simulated datasets (Supplementary Materials and Methods S1). Simulation results showed the estimators are consistent and robust against differential distributions of preclinical duration between test positives and test negatives. Table 1 shows the Bayesian estimates of MST and sensitivity. When localized, regional, and distant cancers were combined for all cancer types, the three-state model estimated that MST was 0.90 years with 95% credible interval (0.76, 1.08), and the modeled sensitivity estimate was 29% with 95% credible interval (23%, 36%). For the prespecified 12 cancers, MST was longer [1.17 years, 95% credible interval (0.92, 1.53)], and the mean sensitivity drawn from the posterior distribution is much higher [64%, 95% credible interval (49%, 79%)].

When the five-state model was fitted to all cancers, separating preclinical duration and sensitivity for localized/regional cancers (early-stage) and distant (late-stage) cancers, the sensitivity for all early-stage cancers was 20% [95% credible interval (15%, 27%)], whereas the sensitivity for distant-stage cancer was 88% [95% credible interval (74%, 97%)]. The preclinical duration was similar in the early and late stages, 0.80 [95% credible interval (0.64, 1.02)] and 0.95 [95% credible interval (0.76, 1.20)] years, respectively. For the 12 prespecified cancers, the sensitivity in the early stage was 43% [95% credible interval (27%, 61%)], and the preclinical duration was 1.36 [95% credible interval (0.92, 2.15)] years, which was twice as long as the duration in the late-stage [0.62, 95% credible interval (0.36, 0.91)] years. As a robustness analysis, using different priors for sensitivity yielded similar results (Supplementary Table S3).

Discussion

The CPS3 biobank study with stored plasma samples before cancer diagnosis presented a unique and unprecedented opportunity to examine the detectability of preclinical cancers using GRAIL’s MCED test. We developed a novel Bayesian likelihood approach to estimating preclinical duration and sensitivity for ctDNA-shedding cancers in this retrospective study. Classical three-state and five-state models were modified to account for features of ctDNA-shedding cancers and the retrospective study design. The results provided a preliminary assessment of preclinical latency and detectability of cancers screened by GRAIL’s MCED test.

Sensitivity for screening preclinical cancers in a retrospective study is not directly estimable but can be modeled with distributional assumptions on sojourn time; for example, the exponential distribution has been widely used in the cancer screening literature (22, 23). A key differentiator of our framework from other multi-state models used in screening is that the sensitivity is defined for all preclinical cancers that are to be tested in the single blood draw, not just the detectable cancers entering PCDP as commonly defined in the cancer modeling literature. The entry point of PCDP when cancer becomes theoretically detectable is an elusive concept that depends on the screening test being studied, and so the sensitivity as previously defined in the window of PCDP can be problematic and difficult to interpret and compare.

Our work includes other methodological innovations. First, the exact time of cancer diagnosis was used in the likelihood, instead of being typically binned by screening rounds, improving the precision of resulting estimators. Second, by developing the binomial likelihood for detectable cancers, the background cancer incidence rate was conditioned out, reducing one parameter for estimation. Third, compared with classical modeling of interventional trials, the sojourn time we inferred in this retrospective study is specifically for ctDNA-detectable, test-positive cancers. The estimation is valid even if test-negative cancers have differential duration of latency. For example, cancers with no or low ctDNA shedding may be less aggressive. Finally, the Bayesian framework by rstan leverages their prior performance of GRAIL’s test in case-control data as the prior distribution, improving the identifiability and stability of estimation.

Several important results were obtained from this analysis. When a three-state model was fitted, the mean sojourn time for all cancers was estimated to be 0.9 years, consistent with the previous report and supporting annual screening by GRAIL’s MCED test (14). The modeled sensitivity at the time of blood draw was 29% [95% credible interval (23%, 36%)] for all cancers, accounting for downsampling of low-shedding cancers, almost doubling the test-positive rate (15%) among all cancers diagnosed in the first year after blood draw. Clearly, the raw test-positive rate in a retrospective study could severely underestimate the sensitivity of GRAIL’s MCED test in preclinical cancers. Notably, the proxy measure of sensitivity in the prospective trials—the proportion of screen-detected cancers among all cancers diagnosed in a follow-up interval—could be higher or lower than the true sensitivity, depending on the length of chosen interval relative to the mean sojourn time of cancers being screened (18). This result illustrates the advantage of the three-state modeling approach: with the exponential distribution assumption for preclinical duration, a relatively precise estimate of test sensitivity can be estimated from the CPS3. Indeed, model diagnosis suggested that the exponential distribution fitted well to preclinical duration (Fig. 3), supporting the modeled estimates for MST and sensitivity.

When the natural history of preclinical cancers was further modeled by including transition from early stage to late stage, the MST estimate in the early stage was 1.36 years [95% credible interval (0.92, 2.15)] and the associated sensitivity was 43% for the prespecified 12 cancers, representing a promising window for intercepting these cancers at an early stage when screened annually. These 12 cancer types have been shown to shed a higher amount of ctDNA, consistent with longer MST and high sensitivity estimates at the early-stage state. Furthermore, sensitivity for cancers at the distant stage was estimated as ∼87%, close to the sensitivity readout in the previous case-control study (10), suggesting that late-stage cancers shed ctDNA throughout metastasis, so detectability does not decrease from clinical late-stage disease to preclinical late-stage disease.

The sensitivity estimates from this analysis are generally lower than those reported in the previous case-control study, likely due to changes of cancer type and stage mix when moving from clinically diagnosed cancers in CCGA3 to preclinical cancers in the CPS3. One limitation of this study is that the plasma samples have been stored for up to 15 years and were collected differently from the specifications for GRAIL’s MCED test, e.g., EDTA tubes rather than Streck tubes in the MCED test protocol. The normal procedure for the MCED test involves a second spin when processing the sample; however, these samples were processed without one. In addition, thawing was required before processing samples. These conditions may lead to degradation of cancer signals and thus test performance.

The strength of our inferences is obviously limited by sample size and by strong negative correlations of the fundamental parameters—mean sojourn time and sensitivity—in our model framework. Predictions based on the five-state model are more variable than three-state model predictions. In Table 1, the preclinical duration for the 12 prespecified cancers was 1.17 years [95% credible region (1.12, 2.43)] when estimated using the three-state model and 1.58 years [95% credible region (0.92, 1.55)] when estimated using the five-state model. The difference is likely attributable to the rather limited sample size for the 12 prespecified cancers. On the other hand, both models yield similar predictions for the 12 prespecified cancers that are consistent with the observed detection data (Supplementary Table S4). When all cancers are included, and therefore sample size is larger, the preclinical duration is more agreeable between the five-state model and the three-state model.

In summary, the CPS3 cohort provided an unprecedented opportunity to study the preclinical window of detectability for GRAIL’s MCED test. The strengths of this modeling analysis include a well-designed large cohort that accumulated a large number of cancers (∼1,300), the conceptual and methodological innovations in developing a likelihood-based method for the analysis of retrospective studies and robust estimation of both preclinical duration and sensitivity for the MCED test. The preclinical detectable window was longer and the sensitivity at screening was greater for the 12 prespecified, high-shedding cancers, supporting annual MCED screening to intercept late-stage cancers (27).

Supplementary Material

Supplementary Mats and Methods

The main file for supplementary Materials and Methods.

Supplementary Table S1

Consistency and robustness of MLEs for the three-state model.

Supplementary Table S2

Consistency and robustness of MLE for the five-state model.

Supplementary Table S3

Estimates of test sensitivity and mean sojourn time (MST) by cancer group using less informative priors on test sensitivity.

Supplementary Table S4

Comparison of observed and model-predicted detection rate for cancers diagnosed in different time intervals.

Data Availability

Codes for data analysis and simulation assessment are available at the first author’s GitHub website: https://github.com/JamesYuDai/ACS-sojourn-sensitivity. The original dataset is available from the ACS by following the ACS Data Access Procedures (https://www.cancer.org/content/dam/cancer-org/research/epidemiology/cancer-prevention-study-data-access-policies.pdf) for researchers who meet the criteria for access to confidential data.

Authors’ Disclosures

J.Y. Dai reports other support from GRAIL, Inc. during the conduct of the study. C.A. Clarke reports other support from GRAIL, Inc. during the conduct of the study. E. Hubbell reports other support from GRAIL, Inc. outside the submitted work; a patent for MCED Patents held by GRAIL, Inc. pending and issued; and ownership of stocks in GRAIL, Inc. and Illumina. No disclosures were reported by the other authors.

Authors’ Contributions

J.Y. Dai: Conceptualization, resources, data curation, formal analysis, investigation, methodology, writing–original draft, writing–review and editing. E.G. Luebeck: Conceptualization, formal analysis, investigation, methodology, writing–original draft, writing–review and editing. W.D. Hazelton: Conceptualization, formal analysis, methodology, writing–original draft, writing–review and editing. C.A. Clarke: Conceptualization, resources, data curation, formal analysis, investigation, writing–original draft, writing–review and editing. E. Hubbell: Conceptualization, formal analysis, methodology, writing–original draft, writing–review and editing. A.V. Patel: Conceptualization, resources, data curation, investigation, methodology, writing–original draft, writing–review and editing.