Individualized Treatment Rules Research Articles

On quantifying heterogeneous treatment effects with regression‐based individualized treatment rules: Loss function families and bounds on estimation error

SummaryHeterogeneity in response to treatment is a pervasive problem in medicine. Many researchers have proposed individualized treatment rule methods for this problem, which personalize treatment recommendations based on an individual's recorded covariates. A challenge with using these methods in practice is that they determine a treatment rule, rather than quantify treatment benefit. This can be problematic, as a recommended treatment could be burdensome and have negligible improvements in outcome for some individuals. With the aim of helping practitioners make informed modelling choices, we identify two families of loss functions to use with individualized treatment rule methods. Under the assumption of correct model specification, estimation with a loss function from one family ensures that the model's treatment recommendations can be interpreted in terms of the risk difference, while the other family of loss functions ensures that the model's treatment recommendations can be interpreted in terms of the risk ratio. We also derive two upper bounds for a model's error in risk difference and risk ratio estimation. Each upper bound can be calculated using observed data and can provide insight to practitioners regarding model error in estimating treatment effects. We illustrate our contributions with simulation studies as well as with data from the ACTG‐175 AIDS study.

Developing an individualized treatment rule for Veterans with major depressive disorder using electronic health records.

Efforts to develop an individualized treatment rule (ITR) to optimize major depressive disorder (MDD) treatment with antidepressant medication (ADM), psychotherapy, or combined ADM-psychotherapy have been hampered by small samples, small predictor sets, and suboptimal analysis methods. Analyses of large administrative databases designed to approximate experiments followed iteratively by pragmatic trials hold promise for resolving these problems. The current report presents a proof-of-concept study using electronic health records (EHR) of n = 43,470 outpatients beginning MDD treatment in Veterans Health Administration Primary Care Mental Health Integration (PC-MHI) clinics, which offer access not only to ADMs but also psychotherapy and combined ADM-psychotherapy. EHR and geospatial databases were used to generate an extensive baseline predictor set (5,865 variables). The outcome was a composite measure of at least one serious negative event (suicide attempt, psychiatric emergency department visit, psychiatric hospitalization, suicide death) over the next 12 months. Best-practices methods were used to adjust for nonrandom treatment assignment and to estimate a preliminary ITR in a 70% training sample and to evaluate the ITR in the 30% test sample. Statistically significant aggregate variation was found in overall probability of the outcome related to baseline predictors (AU-ROC = 0.68, S.E. = 0.01), with test sample outcome prevalence of 32.6% among the 5% of patients having highest predicted risk compared to 7.1% in the remainder of the test sample. The ITR found that psychotherapy-only was the optimal treatment for 56.0% of patients (roughly 20% lower risk of the outcome than if receiving one of the other treatments) and that treatment type was unrelated to outcome risk among other patients. Change in aggregate treatment costs of implementing this ITR would be negligible, as 16.1% fewer patients would be prescribed ADMs and 2.9% more would receive psychotherapy. A pragmatic trial would be needed to confirm the accuracy of the ITR.

Do machine learning methods lead to similar individualized treatment rules? A comparison study on real data.

Identifying patients who benefit from a treatment is a key aspect of personalized medicine, which allows the development of individualized treatment rules (ITRs). Many machine learning methods have been proposed to create such rules. However, to what extent the methods lead to similar ITRs, that is, recommending the same treatment for the same individuals is unclear. In this work, we compared 22 of the most common approaches in two randomized control trials. Two classes of methods can be distinguished. The first class of methods relies on predicting individualized treatment effects from which an ITR is derived by recommending the treatment evaluated to the individuals with a predicted benefit. In the second class, methods directly estimate the ITR without estimating individualized treatment effects. For each trial, the performance of ITRs was assessed by various metrics, and the pairwise agreement between all ITRs was also calculated. Results showed that the ITRs obtained via the different methods generally had considerable disagreements regarding the patients to be treated. A better concordance was found among akin methods. Overall, when evaluating the performance of ITRs in a validation sample, all methods produced ITRs with limited performance, suggesting a high potential for optimism. For non-parametric methods, this optimism was likely due to overfitting. The different methods do not lead to similar ITRs and are therefore not interchangeable. The choice of the method strongly influences for which patients a certain treatment is recommended, drawing some concerns about their practical use.

Individualized treatment rule characterization via a value function surrogate.

Precision medicine is a promising framework for generating evidence to improve health and health care. Yet, a gap persists between the ever-growing number of statistical precision medicine strategies for evidence generation and implementation in real-world clinical settings, and the strategies for closing this gap will likely be context-dependent. In this paper, we consider the specific context of partial compliance to wound management among patients with peripheral artery disease. Using a Gaussian process surrogate for the value function, we show the feasibility of using Bayesian optimization to learn optimal individualized treatment rules. Further, we expand beyond the common precision medicine task of learning an optimal individualized treatment rule to the characterization of classes of individualized treatment rules and show how those findings can be translated into clinical contexts.

A reluctant additive model framework for interpretable nonlinear individualized treatment rules

A reluctant additive model framework for interpretable nonlinear individualized treatment rules

Estimated Average Treatment Effect of Psychiatric Hospitalization in Patients With Suicidal Behaviors

Psychiatric hospitalization is the standard of care for patients presenting to an emergency department (ED) or urgent care (UC) with high suicide risk. However, the effect of hospitalization in reducing subsequent suicidal behaviors is poorly understood and likely heterogeneous. To estimate the association of psychiatric hospitalization with subsequent suicidal behaviors using observational data and develop a preliminary predictive analytics individualized treatment rule accounting for heterogeneity in this association across patients. A machine learning analysis of retrospective data was conducted. All veterans presenting with suicidal ideation (SI) or suicide attempt (SA) from January 1, 2010, to December 31, 2015, were included. Data were analyzed from September 1, 2022, to March 10, 2023. Subgroups were defined by primary psychiatric diagnosis (nonaffective psychosis, bipolar disorder, major depressive disorder, and other) and suicidality (SI only, SA in past 2-7 days, and SA in past day). Models were trained in 70.0% of the training samples and tested in the remaining 30.0%. Psychiatric hospitalization vs nonhospitalization. Fatal and nonfatal SAs within 12 months of ED/UC visits were identified in administrative records and the National Death Index. Baseline covariates were drawn from electronic health records and geospatial databases. Of 196 610 visits (90.3% men; median [IQR] age, 53 [41-59] years), 71.5% resulted in hospitalization. The 12-month SA risk was 11.9% with hospitalization and 12.0% with nonhospitalization (difference, -0.1%; 95% CI, -0.4% to 0.2%). In patients with SI only or SA in the past 2 to 7 days, most hospitalization was not associated with subsequent SAs. For patients with SA in the past day, hospitalization was associated with risk reductions ranging from -6.9% to -9.6% across diagnoses. Accounting for heterogeneity, hospitalization was associated with reduced risk of subsequent SAs in 28.1% of the patients and increased risk in 24.0%. An individualized treatment rule based on these associations may reduce SAs by 16.0% and hospitalizations by 13.0% compared with current rates. The findings of this study suggest that psychiatric hospitalization is associated with reduced average SA risk in the immediate aftermath of an SA but not after other recent SAs or SI only. Substantial heterogeneity exists in these associations across patients. An individualized treatment rule accounting for this heterogeneity could both reduce SAs and avert hospitalizations.

Variable selection in high dimensions for discrete-outcome individualized treatment rules: Reducing severity of depression symptoms.

Despite growing interest in estimating individualized treatment rules, little attention has been given the binary outcome setting. Estimation is challenging with nonlinear link functions, especially when variable selection is needed. We use a new computational approach to solve a recently proposed doubly robust regularized estimating equation to accomplish this difficult task in a case study of depression treatment. We demonstrate an application of this new approach in combination with a weighted and penalized estimating equation to this challenging binary outcome setting. We demonstrate the double robustness of the method and its effectiveness for variable selection. The work is motivated by and applied to an analysis of treatment for unipolar depression using a population of patients treated at Kaiser Permanente Washington.

Robust sample weighting to facilitate individualized treatment rule learning for a target population

Summary Learning individualized treatment rules is an important topic in precision medicine. Current literature mainly focuses on deriving individualized treatment rules from a single source population. We consider the observational data setting when the source population differs from a target population of interest. Compared with causal generalization for the average treatment effect that is a scalar quantity, individualized treatment rule generalization poses new challenges due to the need to model and generalize the rules based on a prespecified class of functions that may not contain the unrestricted true optimal individualized treatment rule. The aim of this paper is to develop a weighting framework to mitigate the impact of such misspecification, and thus facilitate the generalizability of optimal individualized treatment rules from a source population to a target population. Our method seeks covariate balance over a nonparametric function class characterized by a reproducing kernel Hilbert space and can improve many individualized treatment rule learning methods that rely on weights. We show that the proposed method encompasses importance weights and overlap weights as two extreme cases, allowing for a better bias-variance trade-off in between. Numerical examples demonstrate that the use of our weighting method can greatly improve individualized treatment rule estimation for the target population compared with other weighting methods.

A Precision Treatment Model for Internet-Delivered Cognitive Behavioral Therapy for Anxiety and Depression Among University Students

Guided internet-delivered cognitive behavioral therapy (i-CBT) is a low-cost way to address high unmet need for anxiety and depression treatment. Scalability could be increased if some patients were helped as much by self-guided i-CBT as guided i-CBT. To develop an individualized treatment rule using machine learning methods for guided i-CBT vs self-guided i-CBT based on a rich set of baseline predictors. This prespecified secondary analysis of an assessor-blinded, multisite randomized clinical trial of guided i-CBT, self-guided i-CBT, and treatment as usual included students in Colombia and Mexico who were seeking treatment for anxiety (defined as a 7-item Generalized Anxiety Disorder [GAD-7] score of ≥10) and/or depression (defined as a 9-item Patient Health Questionnaire [PHQ-9] score of ≥10). Study recruitment was from March 1 to October 26, 2021. Initial data analysis was conducted from May 23 to October 26, 2022. Participants were randomized to a culturally adapted transdiagnostic i-CBT that was guided (n = 445), self-guided (n = 439), or treatment as usual (n = 435). Remission of anxiety (GAD-7 scores of ≤4) and depression (PHQ-9 scores of ≤4) 3 months after baseline. The study included 1319 participants (mean [SD] age, 21.4 [3.2] years; 1038 women [78.7%]; 725 participants [55.0%] came from Mexico). A total of 1210 participants (91.7%) had significantly higher mean (SE) probabilities of joint remission of anxiety and depression with guided i-CBT (51.8% [3.0%]) than with self-guided i-CBT (37.8% [3.0%]; P = .003) or treatment as usual (40.0% [2.7%]; P = .001). The remaining 109 participants (8.3%) had low mean (SE) probabilities of joint remission of anxiety and depression across all groups (guided i-CBT: 24.5% [9.1%]; P = .007; self-guided i-CBT: 25.4% [8.8%]; P = .004; treatment as usual: 31.0% [9.4%]; P = .001). All participants with baseline anxiety had nonsignificantly higher mean (SE) probabilities of anxiety remission with guided i-CBT (62.7% [5.9%]) than the other 2 groups (self-guided i-CBT: 50.2% [6.2%]; P = .14; treatment as usual: 53.0% [6.0%]; P = .25). A total of 841 of 1177 participants (71.5%) with baseline depression had significantly higher mean (SE) probabilities of depression remission with guided i-CBT (61.5% [3.6%]) than the other 2 groups (self-guided i-CBT: 44.3% [3.7%]; P = .001; treatment as usual: 41.8% [3.2%]; P < .001). The other 336 participants (28.5%) with baseline depression had nonsignificantly higher mean (SE) probabilities of depression remission with self-guided i-CBT (54.4% [6.0%]) than guided i-CBT (39.8% [5.4%]; P = .07). Guided i-CBT yielded the highest probabilities of remission of anxiety and depression for most participants; however, these differences were nonsignificant for anxiety. Some participants had the highest probabilities of remission of depression with self-guided i-CBT. Information about this variation could be used to optimize allocation of guided and self-guided i-CBT in resource-constrained settings. ClinicalTrials.gov Identifier: NCT04780542.

Longitudinal self-learning of individualized treatment rules in a nutrient supplementation trial with missing data.

Longitudinal outcomes are prevalent in clinical studies, where the presence of missing data may make the statistical learning of individualized treatment rules (ITRs) a much more challenging task. We analyzed a longitudinal calcium supplementation trial in the ELEMENT Project and established a novel ITR to reduce the risk of adverse outcomes of lead exposure on child growth and development. Lead exposure, particularly in the form of in utero exposure, can seriously impair children's health, especially their cognitive and neurobehavioral development, which necessitates clinical interventions such as calcium supplementation intake during pregnancy. Using the longitudinal outcomes from a randomized clinical trial of calcium supplementation, we developed a new ITR for daily calcium intake during pregnancy to mitigate persistent lead exposure in children at age 3 years. To overcome the technical challenges posed by missing data, we illustrate a new learning approach, termed longitudinal self-learning (LS-learning), that utilizes longitudinal measurements of child's blood lead concentration in the derivation of ITR. Our LS-learning method relies on a temporally weighted self-learning paradigm to synergize serially correlated training data sources. The resulting ITR is the first of this kind in precision nutrition that will contribute to the reduction of expected blood lead concentration in children aged 0-3 years should this ITR be implemented to the entire study population of pregnant women.

Estimating heterogeneous treatment effects versus building individualized treatment rules: Connection and disconnection

Estimating heterogeneous treatment effects is a well studied topic in the statistics literature. More recently, it has regained attention due to an increasing need for precision medicine as well as the increased use of state-of-art machine learning methods in the estimation. Furthermore, estimating heterogeneous treatment effects is directly related to building an individualized treatment rule, which is a decision rule of treatment according to patient characteristics. This paper examines the connection and disconnection between these two research problems. Notably, a better estimation of the heterogeneous treatment effects may or may not lead to a better individualized treatment rule. We provide theoretical frameworks to explain the connection and disconnection and demonstrate two different scenarios through simulations. Our conclusion sheds light on a practical guide that under certain circumstances, there is no need to enhance estimation of the treatment effects, as it does not alter the treatment decision.

P001 - A comparison of methods to develop individualized treatment rules on real data

P001 - A comparison of methods to develop individualized treatment rules on real data

Estimating individualized treatment rules in longitudinal studies with covariate-driven observation times.

The sequential treatment decisions made by physicians to treat chronic diseases are formalized in the statistical literature as dynamic treatment regimes. To date, methods for dynamic treatment regimes have been developed under the assumption that observation times, that is, treatment and outcome monitoring times, are determined by study investigators. That assumption is often not satisfied in electronic health records data in which the outcome, the observation times, and the treatment mechanism are associated with patients' characteristics. The treatment and observation processes can lead to spurious associations between the treatment of interest and the outcome to be optimized under the dynamic treatment regime if not adequately considered in the analysis. We address these associations by incorporating two inverse weights that are functions of a patient's covariates into dynamic weighted ordinary least squares to develop optimal single stage dynamic treatment regimes, known as individualized treatment rules. We show empirically that our methodology yields consistent, multiply robust estimators. In a cohort of new users of antidepressant drugs from the United Kingdom's Clinical Practice Research Datalink, the proposed method is used to develop an optimal treatment rule that chooses between two antidepressants to optimize a utility function related to the change in body mass index.

Relative contrast estimation and inference for treatment recommendation.

When there are resource constraints, it may be necessary to rank individualized treatment benefits to facilitate the prioritization of assigning different treatments. Most existing literature on individualized treatment rules targets absolute conditional treatment effect differences as a metric for the benefit. However, there can be settings where relative differences may better represent such benefit. In this paper, we consider modeling such relative differences formed as scale-invariant contrasts between the conditional treatment effects. By showing that all scale-invariant contrasts are monotonic transformations of each other, we posit a single index model for a particular relative contrast. We then characterize semiparametric estimating equations, including the efficient score, to estimate index parameters. To achieve semiparametric efficiency, we propose a two-step approach that minimizes a doubly robust loss function for initial estimation and then performs a one-step efficiency augmentation procedure. Careful theoretical and numerical studies are provided to show the superiority of our proposedapproach.

Invited Commentary: On the Mathematization of Epidemiology as a Socially Engaged Quantitative Science.

Ensuring that patients with opioid use disorder (OUD) have access to optimal medication therapies is a critical challenge in substance use epidemiology. Rudolph et al. (Am J Epidemiol. 2023;XXX(X):XXXX-XXXX) demonstrated that sophisticated data-adaptive statistical techniques can be used to learn optimal, individualized treatment rules that can aid providers in choosing a medication treatment modality for a particular patient with OUD. This important work also highlights the effects of the mathematization of epidemiologic research. Here, we define mathematization and demonstrate how it operates in the context of effectiveness research on medications for OUD using the paper by Rudolph et al. as a springboard. In particular, we address the normative dimension of mathematization and how it tends to resolve a fundamental tension in epidemiologic practice between technical sophistication and public health considerations in favor of more technical solutions. The process of mathematization is a fundamental part of epidemiology; we argue not for eliminating it but for balancing mathematization and technical demands equally with practical and community-centric public health needs.

Flexible inference of optimal individualized treatment strategy in covariate adjusted randomization with multiple covariates

To maximize clinical benefit, clinicians routinely tailor treatment to the individual characteristics of each patient, where individualized treatment rules are needed and are of significant research interest to statisticians. In the covariate-adjusted randomization clinical trial with many covariates, we model the treatment effect with an unspecified function of a single index of the covariates and leave the baseline response completely arbitrary. We devise a class of estimators to consistently estimate the treatment effect function and its associated index while bypassing the estimation of the baseline response, which is subject to the curse of dimensionality. We further develop inference tools to identify predictive covariates and isolate effective treatment region. The usefulness of the methods is demonstrated in both simulations and a clinical data example.

Estimating individualized treatment rules for multicategory type 2 diabetes treatments using electronic health records.

In this article, we propose a general framework to learn optimal treatment rules for type 2 diabetes (T2D) patients using electronic health records (EHRs). We first propose a joint modeling approach to characterize patient's pretreatment conditions using longitudinal markers from EHRs. The estimation accounts for informative measurement times using inverse-intensity weighting methods. The predicted latent processes in the joint model are used to divide patients into a finite of subgroups and, within each group, patients share similar health profiles in EHRs. Within each patient group, we estimate optimal individualized treatment rules by extending a matched learning method to handle multicategory treatments using a one-versus-one approach. Each matched learning for two treatments is implemented by a weighted support vector machine with matched pairs of patients. We apply our method to estimate optimal treatment rules for T2D patients in a large sample of EHRs from the Ohio State University Wexner Medical Center. We demonstrate the utility of our method to select the optimal treatments from four classes of drugs and achieve a better control of glycated hemoglobin than any one-size-fits-all rules.

Individualized treatment rules under stochastic treatment cost constraints.

Estimation and evaluation of individualized treatment rules have been studied extensively, but real-world treatment resource constraints have received limited attention in existing methods. We investigate a setting in which treatment is intervened upon based on covariates to optimize the mean counterfactual outcome under treatment cost constraints when the treatment cost is random. In a particularly interesting special case, an instrumental variable corresponding to encouragement to treatment is intervened upon with constraints on the proportion receiving treatment. For such settings, we first develop a method to estimate optimal individualized treatment rules. We further construct an asymptotically efficient plug-in estimator of the corresponding average treatment effect relative to a given reference rule.

Model selection for survival individualized treatment rules using the jackknife estimator

BackgroundPrecision medicine is an emerging field that involves the selection of treatments based on patients’ individual prognostic data. It is formalized through the identification of individualized treatment rules (ITRs) that maximize a clinical outcome. When the type of outcome is time-to-event, the correct handling of censoring is crucial for estimating reliable optimal ITRs.MethodsWe propose a jackknife estimator of the value function to allow for right-censored data for a binary treatment. The jackknife estimator or leave-one-out-cross-validation approach can be used to estimate the value function and select optimal ITRs using existing machine learning methods. We address the issue of censoring in survival data by introducing an inverse probability of censoring weighted (IPCW) adjustment in the expression of the jackknife estimator of the value function. In this paper, we estimate the optimal ITR by using random survival forest (RSF) and Cox proportional hazards model (COX). We use a Z-test to compare the optimal ITRs learned by RSF and COX with the zero-order model (or one-size-fits-all). Through simulation studies, we investigate the asymptotic properties and the performance of our proposed estimator under different censoring rates. We illustrate our proposed method on a phase III clinical trial of non-small cell lung cancer data.ResultsOur simulations show that COX outperforms RSF for small sample sizes. As sample sizes increase, the performance of RSF improves, in particular when the expected log failure time is not linear in the covariates. The estimator is fairly normally distributed across different combinations of simulation scenarios and censoring rates. When applied to a non-small-cell lung cancer data set, our method determines the zero-order model (ZOM) as the best performing model. This finding highlights the possibility that tailoring may not be needed for this cancer data set.ConclusionThe jackknife approach for estimating the value function in the presence of right-censored data shows satisfactory performance when there is small to moderate censoring. Winsorizing the upper and lower percentiles of the estimated survival weights for computing the IPCWs stabilizes the estimator.

Transfer Learning of Individualized Treatment Rules from Experimental to Real-World Data

Individualized treatment effect lies at the heart of precision medicine. Interpretable individualized treatment rules (ITRs) are desirable for clinicians or policymakers due to their intuitive appeal and transparency. The gold-standard approach to estimating the ITRs is randomized experiments, where subjects are randomized to different treatment groups and the confounding bias is minimized to the extent possible. However, experimental studies are limited in external validity because of their selection restrictions, and therefore the underlying study population is not representative of the target real-world population. Conventional learning methods of optimal interpretable ITRs for a target population based only on experimental data are biased. On the other hand, real-world data (RWD) are becoming popular and provide a representative sample of the target population. To learn the generalizable optimal interpretable ITRs, we propose an integrative transfer learning method based on weighting schemes to calibrate the covariate distribution of the experiment to that of the RWD. Theoretically, we establish the risk consistency for the proposed ITR estimator. Empirically, we evaluate the finite-sample performance of the transfer learner through simulations and apply it to a real data application of a job training program. Supplementary materials for this article are available online.