Blood Never Lies: The PopPK-Based Lie Detector

Abstract

Background and Objective

Accurate assessment of drug adherence is essential for long-term oral therapies, where self-administration is unsupervised. Conventional tools such as self-reports, electronic monitors, and even therapeutic drug monitoring often fail to detect non-adherence. Population pharmacokinetic modeling improves objectivity but typically relies on a single analyte, which may still miss hidden non-adherence. We propose a bi-analyte population pharmacokinetic-based approach that uses both the parent drug and a metabolite with distinct pharmacokinetics to enhance adherence detection and reconstruct likely dosing histories.

Methods

A literature review identified spironolactone and its metabolite canrenone as suitable candidates, based on long-term use and an available population pharmacokinetic model capturing distinct elimination profiles. Virtual patients were simulated under steady-state assumptions, then exposed to various adherence scenarios. A modified Metropolis-Hastings algorithm jointly estimated individual pharmacokinetic parameters and dosing patterns by analyzing simulated drug and metabolite concentrations. The probability of taking 0, 1, or 2 tablets per day was inferred, and a posterior adherence probability was derived from the posterior distribution to quantify adherence likelihood. A receiver operating characteristic analysis was used to evaluate diagnostic performance.

Results

The combined use of parent and metabolite improved non-adherence detection compared with either alone, particularly for recent missed doses. Trough concentrations outperformed peak concentrations, especially when patients did not compensate with extra doses.

Conclusions

This probabilistic bi-analyte approach enhances non-adherence detection and is adaptable to other pharmacokinetic settings where distinct profiles and low model variability are present.

Supplementary Information

The online version contains supplementary material available at 10.1007/s40262-026-01652-2.

Key Points

Our approach uses multiple analytes to reconstruct the most likely dosing histories and classify adherence, and it can be extended to other pharmacokinetic contexts.

Applied to the spironolactone model, the method reliably detected non-adherence up to 7 days, demonstrating its practical applicability.

Introduction

Drug adherence refers to the extent to which a patient follows the prescribed dosing regimen, including the correct dose, frequency, and duration. Assessing adherence is particularly critical for orally administered medications used in long-term treatments, where the responsibility for administration lies entirely with the patient. In contrast, medications administered in controlled settings, such as hospitals or under direct supervision (e.g., intravenous infusions), offer little opportunity for non-adherence.

Non-adherence is common with extravascular drug administration, often under-reported, and difficult to detect when clinical outcomes do not immediately raise suspicion [1–3]. Undetected non-adherence can lead to suboptimal treatment, disease progression, and unnecessary therapeutic escalation. Conversely, falsely labeling an adherent patient as non-adherent may result in unjustified changes to their regimen, eroding trust and potentially introducing avoidable side effects. Various tools have been developed to monitor adherence, but most rely heavily on patient cooperation and honesty [4]. Examples include self-reported questionnaires and electronic systems such as the Medication Event Monitoring System. However, the Medication Event Monitoring System, like pharmacy dispensation records can only confirm access to medication, not actual ingestion.

The most objective assessments of adherence rely on biological markers, particularly through therapeutic drug monitoring. However, the accuracy of therapeutic drug monitoring depends on how measured drug concentrations are interpreted. In some studies, observed drug concentrations are compared to expected values derived from average pharmacokinetic (PK) parameters [5]; in others, trough concentrations are compared against the lower calibration limit [6]. A more simplistic approach involves evaluating whether a measured concentration fall within 80–120% of the therapeutic target range [7]. These methods, and others like them, often overlook inter-individual variability, applying uniform reference concentrations across diverse patient populations regardless of physiological or metabolic differences. As a result, they risk generating false negatives in slow or rapid metabolizers. Indeed, unusually high concentrations in slow metabolizers or unusually low concentrations in rapid metabolizers may be misattributed to non-adherence, when in fact they reflect normal dosing behavior influenced by individual metabolism. Furthermore, many thresholds are arbitrarily defined, and binary classification of adherence fails to capture the continuous nature of drug exposure.

To address the limitations of these conventional approaches, population PK (PopPK) modeling has been employed to refine adherence assessment [8]. This method compares measured concentrations to model-predicted ranges, accounting for patient-specific covariates and variability. Concentrations falling outside the 5th or the 95th percentiles may indicate potential non-adherence, and values below the lower limit of quantification may suggest multiple consecutive missed doses.

While PopPK modeling represents an improvement by incorporating inter-individual variability, it still relies on a single analyte measurement, making it vulnerable to “white coat adherence” [9]. A patient who has been non-adherent may resume dosing shortly before a scheduled monitoring visit. If this resumed adherence continues for a sufficient period, the measured drug concentration may fall within the expected range, effectively concealing prior non-adherence. The time required for this concealment depends on the drug’s elimination half-life (t½), which governs how quickly steady-state concentrations are reached.

To address this limitation, we propose a bi-analyte approach that simultaneously measures both the parent drug and its metabolite. If the parent compound and metabolite have a sufficiently different terminal t½, the duration of resumed adherence required to normalize their concentrations will differ. This adds complementary information to the adherence assessment: non-adherence masked by one analyte may be revealed by the other. This terminal half-life may be governed by (i) the elimination rate constant, (ii) the distribution rate constant, or (iii) a rate-limiting metabolic step that induces a flip-flop kinetic profile in the metabolite. Our approach is grounded in PopPK modeling, which enables us to simulate expected concentration–time profiles for both analytes under various dosing scenarios. Furthermore, rather than relying on binary classification, we propose reconstructing the likely dosing history followed by the patient. The objective of this study is therefore two-fold: (1) to develop a PopPK-based tool that detects non-adherence by leveraging both parent drug and metabolite concentrations and (2) to infer the most plausible posology patterns that could explain the observed concentrations. If successful, this approach could provide clinicians with a more accurate and nuanced understanding of patient adherence by making optimal use of measured concentrations, ultimately improving therapeutic decision-making and patient outcomes.

Materials and Methods

Pharmacological Class and Population Pharmacokinetic (PopPK) Model Selection

To implement our approach, we required a model drug that met five key criteria: (1) it is used in the treatment of chronic conditions; (2) it is associated with adherence challenges; (3) it produces at least one metabolite; (4) the parent drug and metabolite exhibit distinct terminal half-lives, which result from the combined effects of their rates of absorption, distribution, metabolism, and elimination; and (5) published PopPK models are available for both compounds. We conducted a literature review to identify a candidate that satisfies these criteria and selected an appropriate published PopPK model to inform our simulations and analyses.

Probabilistic Reconstruction of Dosing Histories

The mathematical and statistical formulation is described as follows: the dosing regimen is denoted as $D=\left(\begin{array}{c}{D}_1,\cdots ,D_J\\ T_1,\cdots ,T_J\end{array}\right)$, where J is the total number of treatment days, $T_1,\cdots ,T_J$ are the administration times, and D_j represents the number of tablets taken on day j.

The concentrations at a time t are defined by:

$Y_t=\left(\begin{array}{c}{Y}_t^{A1}\\ Y_t^{A2}\end{array}\right)=\left(\begin{array}{c}{f}^{A1}(\phi ,t,D)\\ f^{A2}(\phi ,t,D)\end{array}\right)+\left(\begin{array}{c}{g}^{A1}\left(\phi ,,,t,,,D,,,\beta \right){\epsilon }_t^{\prime A1}\\ g^{A2}(\phi ,t,D,\beta ){\epsilon }_t^{\prime A2}\end{array}\right)$, where A1 and A2 represent the parent drug and its metabolite, respectively. The function f() corresponds to the structural component of the PK model, while g() captures residual variability. The vector ϕ contains the individual PK parameters, β is a parameter describing residual error, and ${\epsilon }_t\prime =\left({\epsilon }_t^{\prime A1},,,{\epsilon }_t^{\prime A2}\right)\sim N\left(0,;,I\right)$. For each virtual patient, the dataset includes a vector of measurements (Y_t1, Y_t2, … Y_th) corresponding to h blood samples. In our study, concentrations were never measured; all concentrations were simulated.

As drug concentrations depend not only on the dosing history but also on the underlying PK parameters, both sets of variables must be estimated simultaneously to correctly interpret the concentration data. Estimating the most likely dosing regimen amounts to inferring the joint posterior distribution P($\phi ,D$/(Y_t1, …Y_th)), where ϕ represents the individual PK parameters and D the dosing regimen. This joint inference is particularly important in real clinical settings, where individual PK parameters are generally unknown and cannot be directly measured, they must instead be inferred from observed concentrations. One distinctive aspect of our approach, which also constitutes its strength, is that Empirical Bayes Estimates (EBEs) are not estimated; rather, the full posterior distribution of the PK parameters conditional on the observed concentrations is used.

To perform this inference, we implemented a modified version of the Metropolis-Hastings algorithm (MHA) [10]. The MHA is a Markov Chain Monte Carlo method designed to generate random samples that converge to a specified posterior distribution. While MHA is well suited for sampling continuous variables, such as the PK parameter vector ϕ, it performs less effectively in discrete spaces, such as the space of dosing regimens.

The MHA allows for the construction of a sequence of samples (ϕ^(k), D^(k)) drawn from the joint posterior distribution P(ϕ, D ∣ Y_t1, …, Y_th). At the kth iteration, assume the current state of the chain is (ϕ^(k), D^(k)). The next state (ϕ^(k+1), D^(k+1)) is obtained through two steps:

1. Proposal step: a new candidate (ϕ∗, D∗) is generated from a proposal symmetric distribution in the neighborhood of the current state (ϕ^(k), D^(k)).

2. Acceptance step: the proposed state is accepted with a probability that ensures convergence to the target posterior distribution. That is (ϕ^(k+1), D^(k+1)) = ($\varphi _{}^{\ast },D_{}^{\ast }$) with a probability $min\left(1,,,P,(\varphi _{}^{\ast },D_{}^{\ast }\mid Yt1,\cdots ,Yth),/,P,({\varphi }^{(k)},D^{(k)}\mid Yt1,\cdots ,Yth)\right)$ and (ϕ^(k+1), D^(k+1))= (ϕ^(k), D^(k)) otherwise.

For the Markov chain to converge properly, that is, for the sequence (ϕ^(k), D^(k)) to reflect samples from P(ϕ, D ∣ Y_t1, …, Y_th), the acceptance rate must be sufficiently high (typically above 30%), but not excessively so, to balance exploration and convergence.

To tackle the challenges of sampling from both continuous and discrete spaces while ensuring rapid convergence, the proposal Markov chain ϕ^(k) must evolve faster than the target chain D^(k). To achieve this, two key modifications are introduced: multiple proposals of ϕ^(k) are generated before each new state of D^(k) is considered.

Together, these enhancements enabled efficient joint sampling of both PK parameters and dosing histories. For each virtual patient, 50,000 Markov Chain Monte Carlo iterations were performed, combining Hamiltonian Monte Carlo for continuous parameter inference and simulated annealing for discrete dosing regimen optimization.

For analytical convenience, each dosing regimen was encoded as a unique integer using a triadic decomposition: $n={\sum }_{i=1}^N{D}_i\times 3^{i-1}$, where N is the number of considered days, and D_i the number of tablets taken on day i. This encoding provides a compact and unambiguous representation of all possible combinations, the number of which increases rapidly with the length of the observation window.

Simulation of Concentration Profiles Under Defined Adherence Regimens

In the absence of real clinical data, 100 virtual patients were simulated in RStudio (Version 2024.12.1 Build 563), each assigned individual PK parameter values. The simulated concentrations served as proxies for the measured concentrations of the analyte pair (parent drug and metabolite). No fixed random seed was used, so the sets of 100 virtual patients differed between the simulation sessions. The approach involved (1) generating drug concentrations from known adherence/non-adherence dosing scenarios and (2) estimating, from these concentrations, the most probable dosing regimens, to evaluate their concordance with the true regimens used in simulation.

Prior to exploring non-adherence patterns, all simulations assumed that patients had reached PK steady state. To ensure this, an initial period of full adherence was simulated, during which each virtual patient received one tablet per day for 23 days. Non-adherence scenarios were then introduced only during the final 7 days of the simulation period, reflecting clinically plausible deviations from prescribed dosing once equilibrium was established. The number of simulated days is variable and depends on the t½ of the molecules studied. The longer the t½, the longer the time needed to attain a PK equilibrium.

Two non-adherence scenarios were explored: (0–1 pill) allowing a maximum intake of one tablet per day (i.e., 0 or 1 tablet), and (0–1–2 pills) allowing for the possibility of a double dose (i.e., 0, 1, or 2 tablets) per day. Under the triadic decomposition scheme (see Sect. 2.2), for the 7-day simulation period, the total number of unique regimens is 3⁷ = 2187. The integer corresponding to perfect adherence, defined as one tablet per day for all 7 days, is n = 1093. At extremes, n = 0 represents complete non-adherence (0 tablets on all days), and n = 2187 corresponds to maximal dosing (two tablets on all 7 days). Dosing regimens involving 2 consecutive days with a double dose, or a single dose followed by a double dose, were excluded owing to their low likelihood in clinical practice.

Within each of these adherence scenarios, two additional scenarios were evaluated to reflect different clinical measurement timings: (1) concentrations measured at the trough level (i.e. 24 hours after the last dose); and (2) concentrations measured near the expected peak level called maximum concentration (C_max) [i.e., value fixed at 1 hour after the last dose]. This approach aimed to replicate plausible clinical sampling situations and identify the optimal timing for concentration measurements.

Accordingly, for each of these four scenarios, three main types of dosing regimens were investigated to avoid a combinatory explosion: (1) complete adherence (i.e., one tablet taken daily throughout the study period); (2) single-day non-adherence where one tablet was missed on a single day during the study, with this missed day systematically varied across all days of the period; and (3) 3-day consecutive non-adherence where three consecutive doses were missed, with this 3-day gap sliding throughout the study period. Two additional tests were conducted: instead of using the joint concentrations of the parent drug and its metabolite, the complete adherence regimen and two of the 1-day non-adherence regimens were re-evaluated using only the concentration of either the parent drug or the metabolite individually.

Performance Evaluation

Using MHA, we obtained, for each patient, a distribution of plausible dosing regimens along with their associated frequencies. Figure 1 illustrates a representative histogram for a single patient of P(D ∣ Y_t1, …, Y_th), displaying the ten most frequent regimens with the measured drug concentrations, regardless the value of ϕ.

Fig. 1.

Histogram displaying the ten most frequent (%) dosing regimens compatible with the measured trough concentrations (i.e., 24 h after the last dose) of both the parent drug and the metabolite for the adherent patient. The green bar represents the true adherence regimen (i.e., one tablet per day for 7 consecutive days). Orange bars indicate non-adherent regimens that were also compatible with the measured trough concentrations (i.e., 24 h after the last dose) of both the parent drug and the metabolite. Striped bars denote regimens with a frequency equal to or lower than that of the adherence regimen

In this context, the posterior adherence probability associated with a given regimen represents the cumulative sum of the frequencies lower than that of the adherent regimen (bar highlighted in green). In other words, the posterior adherence probability reflects the estimated posterior probability that the patient followed that particular regimen. Thus, the higher the posterior adherence probability, the more likely the regimen is considered to have been followed. In this example, the adherence regimen is more frequently suggested than all but one regimen, resulting in a posterior adherence probability of 98.4%.

The posterior adherence probability was calculated for all simulated virtual patients. Based on these values, a classification threshold was defined to differentiate adherent from non-adherent behavior. Patients with posterior adherence probabilities above this threshold were classified as adherent, while those below were classified as non-adherent. To evaluate diagnostic performance, we computed sensitivity and specificity. Specificity is defined as the proportion of truly adherent patients correctly classified as adherent. Sensitivity refers to the proportion of non-adherent patients correctly identified as non-adherent because the optimal classification threshold may depend on the scenario considered (e.g., sampling time and/or adherence pattern), receiver operating characteristic (ROC) curves were generated for each scenario to assess performance across threshold values.

Results

Selected PopPK Model for Application

Antihypertensive drugs are among the most prescribed pharmacological classes globally. Used in the long-term management of chronic conditions, they are also notably affected by adherence challenges (only 48.5% of patients remain adherent after 1 year of follow-up [11]). Spironolactone, an aldosterone antagonist within this class, has an active metabolite, canrenone. It is not considered a first-line treatment for hypertension and is typically reserved for cases of resistant hypertension or primary hyperaldosteronism. It may also be used in the management of heart failure. This drug-metabolite pair was selected as a model because of the markedly different PK profiles: spironolactone has a short t½ (approximately 2 h), while canrenone exhibits a significantly longer t½ (approximately 16 h).

Two published PopPK models were identified for these analytes. One, developed exclusively in a pediatric population, was excluded because of limited applicability to adult care. The selected model [12], constructed using data from both pediatric and adult patients, provides separate parameterizations for each group, enabling appropriate use in our adult study population. The parameters are summarized in Table 1.

Table 1.

Population pharmacokinetic model parameter estimates for adults

Parameters	ALAG1	Ka (L/h)	CL (L/h)	V2 (L)	Q (L/h)	V3 (L)	Fm	CLM1 (L/h)	CLM (L/h)	V4 (L)	Q1 (L/h)	V5 (L)	Spir	Can
Value	0.156	5.22	629	517	89.9	777	0.7	217	17	189	60	448
IIV (%)	–	97	40.7	34.4	28.4	–	–	42.8	28.1	17.4	26.3	29.8
Error (%)													29.1	13.3

ALAG1 lag time, Can canrenone, CL apparent clearance of Spir from central compartment, CLM apparent clearance of Can from central compartment, CLM1 apparent metabolic clearance of Spir to Can, (CL,V2) covariance = 0.112, Error proportional residual error for Spir or Can, Fm fraction metabolized from Spir to Can, h hour, ka absorption rate constant, Q apparent intercompartmental clearance of Spir, Q1 apparent intercompartmental clearance of Can, Spir spironolactone, V2 apparent central volume of distribution of Spir, V3 peripheral volume of distribution of Spir, V4 apparent central volume of distribution of Can, V5 apparent peripheral volume of distribution of Can

Adherence Classification

Using the MHA approach, we reconstructed all dosing regimens compatible with the measured concentrations of the drug and its metabolite for each tested regimen, across all evaluated scenarios. For each individual, this process yielded a distribution of plausible dosing regimens, each associated with a specific frequency of occurrence (see Sect. 2.4).

The posterior adherence probabilities corresponding to the adherence regimen across the virtual population are shown in Fig. 2, under the scenario where double dosing is not permitted and trough concentrations are used as measurements. As detailed in Sect. 2.4, the posterior adherence probability reflects the likelihood that a given patient followed the prescribed regimen. In Fig. 2a, posterior adherence probabilities for adherent individuals are broadly distributed but tend to be higher, indicated by green-colored dots, as expected from their full adherence. Very low posterior adherence probabilities observed in a subset of adherent individuals are attributable to unusually high, yet plausible, individual clearance values, given the substantial inter-individual variability in clearance in the population model (40.7%). In these individuals, full adherence can result in lower-than-expected concentrations, which reduces the posterior support for the adherence regimen relative to alternative dosing patterns. In contrast, Fig. 2b shows posterior adherence probabilities for non-adherent individuals, with a clear clustering of lower values (orange dots), consistent with non-adherent behavior.

Fig. 2.

Distribution of adherence posterior adherence probabilities (%) across 100 virtual patients in the 0–1 tablet scenario using trough concentration measurements (i.e., 24 h after the last dose) of both the parent drug and the metabolite, following a an adherent regimen or b a non-adherent regimen. Each dot represents the posterior adherence probability of a virtual patient. Green dots indicate higher posterior adherence probabilities (suggestive of adherence), while orange dots indicate lower posterior adherence probabilities (suggestive of non-adherence)

To define a classification threshold for adherence detection, we conducted ROC curve analyses for the various scenarios outlined in Sect. 2.3. Prior to this, we applied the method to two specific non-adherent regimens: one missed dose on day 2 or day 6 of the consultation week, using either individual analytes or both. This comparison illustrates the superior performance of the bi-analyte approach over single-analyte methods. Figure 3 presents the corresponding ROC curves, with the area under the curve (AUC) indicated for each scenario. An AUC of 0.5 denotes random classification; higher AUCs indicate better performance. When only the parent drug was measured (Fig. 3a), both day 2 and day 6 curves lie close to the diagonal, suggesting limited discrimination. With only the metabolite (Fig. 3b), the day 2 curve remains near the diagonal, but the day 6 curve improves to an AUC of 0.66. However, when both analytes are used (Fig. 3c), the day 2 curve shows no improvement, while the day 6 curve markedly improves (AUC = 0.938), demonstrating that combining both analytes enhances detection of non-adherence, especially when the missed dose is closer to the sampling date.

Fig. 3.

Receiver operating characteristic curves comparing adherent individuals to two non-adherent profiles (missed dose on day 2 [D2] or day 6 [D6]), using trough concentration (i.e., 24 h after the last dose) of a only the parent drug, b only the metabolite, or c both analytes. Each curve represents a non-adherence profile (D2 or D6) over a 7-day period. The solid black diagonal denotes random classification (area under the curve [AUC] = 0.5); the dashed line represents the upper performance boundary. Area under the curve values are provided for each case

Having established the advantage of the bi-analyte approach, we then applied the method to the full set of proposed scenarios. Figure 4 shows ROC curves under the constraint of no double-dosing, comparing performance using either trough concentrations (Fig. 4a) or C_max values (Fig. 4b). For both measurement types, non-adherence occurring closer to the sampling day yields higher AUCs, indicating improved detectability. However, while the trough-based curves generally perform well, the C_max-based curves are less informative, most yielding AUCs below 0.67, except for two with AUC = 1.

Fig. 4.

Receiver operating characteristic curves comparing adherent individuals to various non-adherent profiles (one or three consecutive missed doses) using trough concentrations (i.e., 24 h after the last dose) of the parent drug and the metabolite (a) or maximum concentration (i.e., 1 h after the last dose) of the parent drug and the metabolite (b), without allowing double-dosing. Each curve corresponds to a missed dose (days 1–7 [D1–D7]) or three consecutive missed doses (days 123–567 [D123–D567]) over 7 days. The solid black diagonal indicates random classification (area under the curve [AUC] = 0.5); the dashed line indicates the upper performance limit. AUC values are noted

When double-dosing is allowed (Fig. 5), the results remain largely consistent. Using trough concentrations (Fig. 5a), all AUCs exceed 0.5 and increase with proximity of non-adherence to the sampling date. In contrast, when using C_max values (Fig. 5b), most curves remain near the diagonal, with only three scenarios achieving AUCs substantially above 0.5, indicating limited utility of C_max for adherence classification under this condition.

Fig. 5.

Receiver operating characteristic curves comparing adherent individuals to various non-adherent profiles (one or three consecutive missed doses) using trough concentrations (i.e., 24 h after the last dose) of the parent drug and the metabolite (a) or maximum concentration (i.e., 1 h after the last dose) of the parent drug and the metabolite (b), with double-dosing allowed. Each curve corresponds to a missed dose (days 1–7 [D1–D7]) or three consecutive missed doses (days 123–567 [D123–D567]) over 7 days. The solid black diagonal indicates area under the curve [AUC] = 0.5; the dashed line indicates maximum performance. AUC values are displayed for each case

Discussion

Non-adherence to medication is common, difficult to detect, and often under-reported. Conventional adherence assessment tools are limited by their reliance on patient cooperation, single timepoint measurements, and failure to account for inter-individual variability. As a result, these methods may misclassify patients, often conflating physiological differences in drug metabolism with true non-adherence [13]. To address these limitations, we developed an objective classification method that leverages all available PK information—not only the concentration of the parent drug but also that of its metabolite(s). Our approach enhances the detection of non-adherence and enables the reconstruction of likely dosing histories based on the combined profiles of parent and metabolite concentrations.

The objective of the proposed framework is not to estimate individual PK parameters or dosing histories, which are inherently weakly identifiable under sparse sampling, but to assess the compatibility of strict adherence, obtained by sampling from the posterior distribution of PK parameters, with the observed concentrations. Given this objective, the proposed framework shares fundamental limitations with therapeutic drug monitoring approaches based on plasma concentration measurements. In the presence of high intra-individual variability, individual PK parameters may vary substantially over time, making changes in observed exposure statistically and mechanistically indistinguishable from those resulting from non-adherence. For instance, a transient increase in clearance may produce a decrease in concentration that could be erroneously interpreted as missed doses. Similarly, when residual variability is high, the resulting low signal-to-noise ratio implies that observed concentrations are largely dominated by noise, such that a wide range of dosing histories remains compatible with the data. Finally, non-linear pharmacokinetics further confound inference, as violations of superposition and dose–exposure proportionality allow distinct dosing regimens to generate similar concentration–time profiles. Under these conditions, inference on adherence from concentration data alone may be unreliable, irrespective of the statistical methodology employed.

To further assess the robustness of the proposed framework, a sensitivity analysis was conducted to evaluate the impact of misspecification of inter-individual variability, as requested by the reviewers. The inter-individual variability of clearance (defined as the square root of the clearance omega) was scaled by factors of 0.5 and 2 relative to the reference PopPK model. Across all scenarios, discriminative performance remained high, indicating strong robustness of the method to misspecification of population variability (see Supplementary Material). Beyond single-occasion inference, an important strength of the framework lies in its ability to accumulate evidence across repeated sampling occasions. By sequentially updating adherence probabilities, the method naturally lends itself to an adaptive (Markovian) decision process in which classification uncertainty is progressively reduced over time, provided that inter-occasion variability remains limited. The formal development of such an adaptive framework, however, lies beyond the scope of the present work.

Extremely low posterior adherence probabilities observed in some adherent individuals (Fig. 2a) primarily reflect elevated clearance values rather than true non-adherence. Such elevated clearance could, in principle, arise from genetic polymorphisms affecting drug metabolism. Although this explanation is unlikely in the present proof-of-concept application—as spironolactone is not known to exhibit clinically relevant metabolic polymorphisms—similar situations may occur for other drugs. In such settings, failure to account for rapid or ultra-rapid metabolizer phenotypes may lead to the misclassification of adherent patients as non-adherent. More broadly, the ability of the proposed framework to correctly discriminate adherence from non-adherence critically depends on the adequacy of the underlying PopPK model. When genetic polymorphisms are known and incorporated into the model, either at the individual level or through appropriate population-level structures (e.g., bimodal clearance distributions), their impact can be explicitly accounted for. Conversely, unrecognized metabolic polymorphisms constitute a form of model misspecification that may bias posterior inference—a limitation shared by all concentration-based adherence assessment methods.

Several alternative strategies have been proposed to assess medication non-adherence, each addressing some of the limitations inherent to concentration-based approaches, but with different trade-offs. For instance, the aggregate adherence metric proposed by Knights and Rohatagi [14] summarizes adherence through cumulative systemic exposure and is particularly suited for population-level analyses. However, its cumulative nature prevents discrimination between distinct dosing histories that may result in similar concentrations at a given sampling time. Similarly, Al-Taani et al. [7] evaluated adherence using concentrations measured in both plasma and saliva; while the use of multiple biological matrices provides complementary information, adherence classification relied on predefined therapeutic ranges and did not explicitly address PK variability or the identifiability of dosing histories. In contrast, our approach explicitly embeds an adherence assessment within a PopPK framework and relies on a probabilistic reconstruction of dosing histories based on the posterior distribution of PK parameters, rather than on binary threshold-based criteria. This enables assessment of the compatibility of strict adherence with the observed concentrations while explicitly acknowledging that multiple dosing patterns may remain plausible.

Importantly, the method is not limited to a parent drug-metabolite pair. It can be extended to several other PK contexts, including: (i) concentrations of several analytes (more than 1); (ii) drug concentrations measured at several times, for example, one or several times when we are completely sure the patient is adherent and a new time when the adherence question arise (iii); drug concentrations measured at the same time in several matrices, for example plasma and red blood cells; and (iv) co-administered compounds with distinct pharmacokinetics, such as fixed-dose combinations (e.g., Truvada). A major limitation of the proposed framework lies in the limited availability of PopPK models suitable for such configurations, particularly models that jointly describe parent drugs and metabolites, multiple co-administered drugs, or the same compound across different biological matrices. This scarcity currently restricts the extension of the method to more complex settings, underscoring the need for robust PopPK models that explicitly capture these kinetic relationships. In addition, a key requirement for these broader applications is that the analytes involved must exhibit sufficiently distinct kinetic behaviors to allow for accurate classification. In the parent–metabolite context, the method is only reliable when there is a sufficiently large difference between the terminal half-lives of the parent drug and the metabolite. More precisely, we defined an arbitrary threshold for the metabolite-to-parent drug ratio greater than 2.

These conditions are fulfilled in our reference case, spironolactone, which justifies its selection. Spironolactone is the parent compound with a short terminal t½ (~2 hours) and a long-acting metabolite (~16 hours), making it an ideal model for demonstrating the method’s potential. However, because of these terminal t½, the detection window is inherently limited. Non-adherence occurring more than 7 days prior to the consultation is unlikely to impact measured concentrations. Although the illustrative application focuses on non-adherence occurring within a short time window prior to sampling, this choice reflects a deliberately stringent configuration involving a parent drug with a short elimination half-life and a more persistent metabolite. Spironolactone (t½ ≈ 2 hours) and its active metabolite canrenone (t½ ≈ 16 h) constitute a well-documented example of such a contrast [15], selected to evaluate the framework under demanding conditions. Importantly, the proposed approach is not intrinsically limited to this time scale. Longer effective detection windows are expected in settings involving drug–metabolite systems with larger half-life contrasts or co-administered compounds with markedly different pharmacokinetics, such as the combination of tacrolimus (t½ ≈ 12 h) and posaconazole (t½ ≈ 30 h) in lung transplant recipients [16–18]. In these contexts, longer-term non-adherence patterns, including white-coat adherence, are expected to be more readily detectable because of the increased amount of exploitable PK information.

Furthermore, it is important to note that the longer the observation period, the greater the number of possible dosing regimens, consequently increasing the computational time required for the method to converge to the most probable regimens. For example, assuming the patient can take 0, 1, or 2 tablets per day, a 7-day period yields 3⁷ = 2187 possible dosing regimens. The exhaustive evaluation of all candidate dosing regimens is computationally intensive, with an order-of-magnitude computation time of approximately 30 minutes per patient for 3⁷ possible regimens using a standard sequential implementation. However, because likelihood evaluations for the different candidate regimens are independent, the approach is naturally amenable to parallelization, enabling substantial reductions in wall-clock computation time without altering the underlying model or statistical inference.

When an adherence assessment relies not on a fixed dosing time but on a dosing window, the proposed framework remains conceptually valid and fully applicable. In this setting, uncertainty in dosing time can be incorporated by expanding the set of candidate dosing regimens to include plausible administration windows rather than fixed timepoints. However, allowing for such flexibility inevitably enlarges the space of candidate regimens, resulting in a substantial increase in computational cost. This limitation is therefore primarily practical rather than methodological and reflects the combinatorial nature of the inference problem rather than a conceptual restriction of the approach.

This framework ultimately enables classification of patients into adherent and non-adherent groups. As with any classification system, it is prone to false positives and false negatives. To assess and calibrate performance, we constructed ROC curves, allowing sensitivity and specificity to be adjusted based on the clinical context and acceptable risk levels. Threshold selection is drug specific and must be tailored to therapeutic consequences [19]. Favoring specificity reduces false positives but risks missing non-adherent patients (false negatives), which may delay intervention. Conversely, prioritizing sensitivity increases the detection of non-adherence (true positives) but may wrongly classify adherent patients (false positives), potentially eroding trust in the clinician–patient relationship. Regardless of the approach, it is essential to inform the patient about the drug monitoring process to preserve transparency and trust. Ultimately, the goal is to avoid wrongly labeling an adherent patient as non-adherent, which underscores the importance of achieving an appropriate balance in sensitivity.

We define adherence as complete conformity to the prescribed regimen in terms of dose, frequency, and duration. Admittedly, this definition may be overly strict. A more nuanced approach would define adherence as encompassing all dosing regimens that yield equivalent therapeutic outcomes—whether in terms of efficacy or safety. However, such a definition is context dependent and may vary across drug classes and clinical priorities. For example, missing a single contraceptive dose may have more immediate and significant consequences than missing a dose of a statin [20, 21]. This variability highlights the importance of interpreting adherence within the appropriate pharmacological and clinical context. A more precise definition would require a model that links drug exposure to its effects, that is, a PK-pharmacodynamic model. However, developing and applying such a model lies beyond the scope of the present study.

To apply our approach using the selected PopPK model, the use of simulated (virtual) patients was necessary. As outlined in Sect. 2.3, each simulation session required data from 100 patients, and over 50 different adherence scenarios were tested—amounting to more than 5000 individual profiles. Exploring additional scenarios would have further increased this number substantially. Moreover, real patient data would require absolute certainty regarding the dosing regimen, as the analytical performance of the method depends on accurate ground truth, which cannot be reliably obtained because of limitations in patient self-reporting and monitoring. Given these constraints, virtual patients were essential for the development of the method.

To better reflect clinical practice, our evaluation focused on trough concentrations, as these are most commonly used in routine therapeutic drug monitoring. Comparing the use of a single analyte versus a dual-analyte approach revealed that the bi-analyte framework outperformed the mono-analyte approach across the tested non-adherence scenarios (Fig. 3). In the 1-day and 3-day non-adherence scenarios (Fig 4), sensitivity and specificity were highest when we assumed no compensatory behavior (i.e., no double intake). In contrast, allowing for a double intake, where patients “make up” for missed doses, led to significantly reduced classification accuracy (Fig. 5). This is because a double intake can restore drug concentrations to levels resembling adherence, masking prior non-adherence. Furthermore, as expected, longer durations of non-adherence were more reliably detected. In the 1-day non-adherence scenario, sensitivity and specificity reached approximately 90% when non-adherence occurred 6 days before consultation (Fig. 5a), whereas allowing for a compensatory double dose dropped the classification performance below usable levels (Fig. 5b). The same trend was observed in the 3-day non-adherence case. These findings highlight that strategic compensatory behavior can prevent detection, complicating accurate classification.

We also evaluated whether C_max-based concentrations (around time to C_max) would improve detection, given that higher concentrations might amplify the signal. Surprisingly, trough concentrations outperformed C_max (Fig. 5). We hypothesize that this is due to the impact of residual variability. Because the proportional error scales with concentration, variability becomes amplified at higher concentrations, reducing reliability. Therefore, for this method to be viable in clinical practice, the PopPK model must exhibit a residual error below 30%. Exceeding this threshold compromises classification reliability and undermines clinical utility. The main causes of excessive residual error include: (i) analytical errors exceeding 10%, in violation of US Food and Drug Administration and European Medicines Agency standards; (ii) oversimplified models built from sparse data; or (iii) unaccounted inter-occasion variability, which renders both the parent drug and metabolite levels unpredictable. Another explanation relates to inter-individual PK variability. In our framework, individual PK parameters (commonly referred to as EBEs) are not estimated. Instead, the internal Markov chain samples from the full posterior distribution of individual PK parameters conditional on the observed concentrations, thereby sampling from the posterior distribution of PK parameters. In parallel, an external Markov chain explores candidate dosing regimens that are compatible with the same observations. The lower performance observed with C_max-based sampling can be interpreted as a consequence of greater posterior uncertainty in absorption-related processes when only peak information is available. This increased uncertainty broadens the range of PK-dosing combinations compatible with the data, thereby reducing discrimination between adherent and non-adherent regimens, even though the full posterior is explored.

To our knowledge, no existing method attempts to identify non-adherence by explicitly leveraging the likelihood equation to reconstruct the most probable dosing regimen actually followed by the patient. While we acknowledge that alternative strategies may offer different advantages, what sets our approach apart is its foundation on two key principles: (i) the integration of complementary information from multiple analytes to enhance discriminatory power and (ii) the recognition that certain non-adherent dosing patterns can generate concentration profiles indistinguishable from those of adherent patients, and must therefore be accounted for probabilistically. Our method remains subject to optimization, particularly in terms of computational efficiency, and must be further evaluated for its transferability to drugs with different PK characteristics and therapeutic contexts.

Conclusions

We present a novel likelihood-based framework for detecting and reconstructing patient non-adherence using bi-analyte PK data. By integrating information from both the parent drug and metabolite, and accounting for the overlap between adherent and non-adherent profiles, our method provides a more nuanced classification of adherence behavior. While further validation and optimization are needed, especially for broader drug classes, this approach offers a promising step toward more accurate, individualized adherence monitoring in clinical pharmacology.

Supplementary Information

Below is the link to the electronic supplementary material.

Funding

Open access funding provided by Université de Toulouse. No funding was received for the preparation of this article.

Declarations

Conflicts of Interest

Chaiben Sahira, Gandia Peggy, Duly-Bouhanick Béatrice, Goldwirt Lauriane, and Concordet Didier have no conflicts of interest that are directly relevant to the content of this article.

Ethics Approval

Not applicable.

Consent to Participate

Not applicable.

Consent for Publication

Not applicable.

Availability of Data and Material

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Code Availability

Not applicable.

Authors’ Contributions

SC, PG, and DC designed the work and analyzed and interpreted the data. SC and DC created the code used in the work. All authors drafted the work and revised the work critically for important intellectual content. All authors approved the version to be published and agree to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved.