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Marie Davidian

Publications and source records attributed to Marie Davidian.

15 recordsLinked to original sources
arXiv2025

Independent increments and group sequential tests

Widely used methods and software for group sequential tests of a null hypothesis of no treatment difference that allow for early stopping of a clinical trial depend primarily on the fact that sequentially-computed test statistics have the independent increments property. However, there are many practical situations where the sequentially-computed test statistics do not possess this property. Key examples are in trials where the primary outcome is a time to an event but where the assumption of proportional hazards is likely violated, motivating consideration of treatment effects such as the difference in restricted mean survival time or the use of approaches that are alternatives to the familiar logrank test, in which case the associated test statistics may not possess independent increments. We show that, regardless of the covariance structure of sequentially-computed test statistics, one can always derive linear combinations of these test statistics sequentially that do have the independent increments property. We also describe how to best choose these linear combinations to target specific alternative hypotheses, such as proportional or non-proportional hazards or log odds alternatives. We thus derive new, sequentially-computed test statistics that not only have the independent increments property, supporting straightforward use of existing methods and software, but that also have greater power against target alternative hypotheses than do procedures based on the original test statistics, regardless of whether or not the original statistics have the independent increments property. We illustrate with two examples.

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arXiv2025

Bayesian adaptive randomization in the I-SPY2 sequential multiple assignment randomized trial

The I-SPY2 phase 2 clinical trial is a long-running platform trial that evaluates neoadjuvant treatments for locally advanced breast cancer, assigning subjects to novel agents using response-adaptive randomization. Recently, I-SPY2 was reconfigured as a sequential multiple assignment randomized trial (SMART), with up to three stages of therapy. At the first stage, a subject is assigned to a tumor-subtype-specific therapy. If the subject fails to show a satisfactory response to the initial therapy, the subject is assigned to a second subtype-specific therapy, and receives a third, rescue therapy if response is still not achieved. The I-SPY2 SMART thus evaluates entire treatment regimes that recommend therapies at every stage if needed. The transition of I-SPY2 to a SMART required development of a response-adaptive randomization scheme that updates randomization probabilities at each stage, aligned with the goal of maximizing the number of subjects who achieve a pathological complete response (pCR). We present the details of our novel approach, which uses Thompson sampling to update randomization probabilities based on the posterior probability that treatments are part of the optimal regime. Empirical studies that demonstrate that it improves within-trial regime-specific pCR rates and recommends optimal regimes at rates similar to uniform, nonadaptive randomization.

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arXiv2024

Optimal treatment strategies for prioritized outcomes

Dynamic treatment regimes formalize precision medicine as a sequence of decision rules, one for each stage of clinical intervention, that map current patient information to a recommended intervention. Optimal regimes are typically defined as maximizing some functional of a scalar outcome's distribution, e.g., the distribution's mean or median. However, in many clinical applications, there are multiple outcomes of interest. We consider the problem of estimating an optimal regime when there are multiple outcomes that are ordered by priority but which cannot be readily combined by domain experts into a meaningful single scalar outcome. We propose a definition of optimality in this setting and show that an optimal regime with respect to this definition leads to maximal mean utility under a large class of utility functions. Furthermore, we use inverse reinforcement learning to identify a composite outcome that most closely aligns with our definition within a pre-specified class. Simulation experiments and an application to data from a sequential multiple assignment randomized trial (SMART) on HIV/STI prevention illustrate the usefulness of the proposed approach.

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arXiv2024

A Generalized Logrank-type Test for Comparison of Treatment Regimes in Sequential Multiple Assignment Randomized Trials

The sequential multiple assignment randomized trial (SMART) is the ideal study design for the evaluation of multistage treatment regimes, which comprise sequential decision rules that recommend treatments for a patient at each of a series of decision points based on their evolving characteristics. A common goal is to compare the set of so-called embedded regimes represented in the design on the basis of a primary outcome of interest. In the study of chronic diseases and disorders, this outcome is often a time to an event, and a goal is to compare the distributions of the time-to-event outcome associated with each regime in the set. We present a general statistical framework in which we develop a logrank-type test for comparison of the survival distributions associated with regimes within a specified set based on the data from a SMART with an arbitrary number of stages that allows incorporation of covariate information to enhance efficiency and can also be used with data from an observational study. The framework provides clarification of the assumptions required to yield a principled test procedure, and the proposed test subsumes or offers an improved alternative to existing methods. We demonstrate performance of the methods in a suite of simulation studies. The methods are applied to a SMART in patients with acute promyelocytic leukemia.

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arXiv2024

Adaptive Randomization Methods for Sequential Multiple Assignment Randomized Trials (SMARTs) via Thompson Sampling

Response-adaptive randomization (RAR) has been studied extensively in conventional, single-stage clinical trials, where it has been shown to yield ethical and statistical benefits, especially in trials with many treatment arms. However, RAR and its potential benefits are understudied in sequential multiple assignment randomized trials (SMARTs), which are the gold-standard trial design for evaluation of multi-stage treatment regimes. We propose a suite of RAR algorithms for SMARTs based on Thompson Sampling (TS), a widely used RAR method in single-stage trials in which treatment randomization probabilities are aligned with the estimated probability that the treatment is optimal. We focus on two common objectives in SMARTs: (i) comparison of the regimes embedded in the trial, and (ii) estimation of an optimal embedded regime. We develop valid post-study inferential procedures for treatment regimes under the proposed algorithms. This is nontrivial, as (even in single-stage settings) RAR can lead to nonnormal limiting distributions of estimators. Our algorithms are the first for RAR in multi-stage trials that account for nonregularity in the estimand. Empirical studies based on real-world SMARTs show that TS can improve in-trial subject outcomes without sacrificing efficiency for post-trial comparisons.

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arXiv2022

Interim Monitoring of Sequential Multiple Assignment Randomized Trials Using Partial Information

The sequential multiple assignment randomized trial (SMART) is the gold standard trial design to generate data for the evaluation of multi-stage treatment regimes. As with conventional (single-stage) randomized clinical trials, interim monitoring allows early stopping; however, there are few methods for principled interim analysis in SMARTs. Because SMARTs involve multiple stages of treatment, a key challenge is that not all enrolled participants will have progressed through all treatment stages at the time of an interim analysis. Wu et al. (2021) propose basing interim analyses on an estimator for the mean outcome under a given regime that uses data only from participants who have completed all treatment stages. We propose an estimator for the mean outcome under a given regime that gains efficiency by using partial information from enrolled participants regardless of their progression through treatment stages. Using the asymptotic distribution of this estimator, we derive associated Pocock and O'Brien-Fleming testing procedures for early stopping. In simulation experiments, the estimator controls type I error and achieves nominal power while reducing expected sample size relative to the method of Wu et al. (2021). We present an illustrative application of the proposed estimator based on a recent SMART evaluating behavioral pain interventions for breast cancer patients.

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arXiv2022

Group sequential methods for interim monitoring of randomized clinical trials with time-lagged outcome

The primary analysis in two-arm clinical trials usually involves inference on a scalar treatment effect parameter; e.g., depending on the outcome, the difference of treatment-specific means, risk difference, risk ratio, or odds ratio. Most clinical trials are monitored for the possibility of early stopping. Because ordinarily the outcome on any given subject can be ascertained only after some time lag, at the time of an interim analysis, among the subjects already enrolled, the outcome is known for only a subset and is effectively censored for those who have not been enrolled sufficiently long for it to be observed. Typically, the interim analysis is based only on the data from subjects for whom the outcome has been ascertained. A goal of an interim analysis is to stop the trial as soon as the evidence is strong enough to do so, suggesting that the analysis ideally should make the most efficient use of all available data, thus including information on censoring as well as other baseline and time-dependent covariates in a principled way. A general group sequential framework is proposed for clinical trials with a time-lagged outcome. Treatment effect estimators that take account of censoring and incorporate covariate information at an interim analysis are derived using semiparametric theory and are demonstrated to lead to stronger evidence for early stopping than standard approaches. The associated test statistics are shown to have the independent increments structure, so that standard software can be used to obtain stopping boundaries.

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arXiv2021

Estimation of the odds ratio in a proportional odds model with censored time-lagged outcome in a randomized clinical trial

In many randomized clinical trials of therapeutics for COVID-19, the primary outcome is an ordinal categorical variable, and interest focuses on the odds ratio (active agent vs. control) under the assumption of a proportional odds model. Although at the final analysis the outcome will be determined for all subjects, at an interim analysis, the status of some participants may not yet be determined, e.g., because ascertainment of the outcome may not be possible until some pre-specified follow-up time. Accordingly, the outcome from these subjects can be viewed as censored. A valid interim analysis can be based on data only from those subjects with full follow up; however, this approach is inefficient, as it does not exploit additional information that may be available on those for whom the outcome is not yet available at the time of the interim analysis. Appealing to the theory of semiparametrics, we propose an estimator for the odds ratio in a proportional odds model with censored, time-lagged categorical outcome that incorporates additional baseline and time-dependent covariate information and demonstrate that it can result in considerable gains in efficiency relative to simpler approaches. A byproduct of the approach is a covariate-adjusted estimator for the odds ratio based on the full data that would be available at a final analysis.

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arXiv2021

Estimating Vaccine Efficacy Over Time After a Randomized Study is Unblinded

The COVID-19 pandemic due to the novel coronavirus SARS CoV-2 has inspired remarkable breakthroughs in development of vaccines against the virus and the launch of several phase 3 vaccine trials in Summer 2020 to evaluate vaccine efficacy (VE). Trials of vaccine candidates using mRNA delivery systems developed by Pfizer-BioNTech and Moderna have shown substantial VEs of 94-95%, leading the US Food and Drug Administration to issue Emergency Use Authorizations and subsequent widespread administration of the vaccines. As the trials continue, a key issue is the possibility that VE may wane over time. Ethical considerations dictate that all trial participants be unblinded and those randomized to placebo be offered vaccine, leading to trial protocol amendments specifying unblinding strategies. Crossover of placebo subjects to vaccine complicates inference on waning of VE. We focus on the particular features of the Moderna trial and propose a statistical framework based on a potential outcomes formulation within which we develop methods for inference on whether or not VE wanes over time and estimation of VE at any post-vaccination time. The framework clarifies assumptions made regarding individual- and population-level phenomena and acknowledges the possibility that subjects who are more or less likely to become infected may be crossed over to vaccine differentially over time. The principles of the framework can be adapted straightforwardly to other trials.

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arXiv2019

Sample Size Calculations for SMARTs

Sequential Multiple Assignment Randomized Trials (SMARTs) are considered the gold standard for estimation and evaluation of treatment regimes. SMARTs are typically sized to ensure sufficient power for a simple comparison, e.g., the comparison of two fixed treatment sequences. Estimation of an optimal treatment regime is conducted as part of a secondary and hypothesis-generating analysis with formal evaluation of the estimated optimal regime deferred to a follow-up trial. However, running a follow-up trial to evaluate an estimated optimal treatment regime is costly and time-consuming; furthermore, the estimated optimal regime that is to be evaluated in such a follow-up trial may be far from optimal if the original trial was underpowered for estimation of an optimal regime. We derive sample size procedures for a SMART that ensure: (i) sufficient power for comparing the optimal treatment regime with standard of care; and (ii) the estimated optimal regime is within a given tolerance of the true optimal regime with high-probability. We establish asymptotic validity of the proposed procedures and demonstrate their finite sample performance in a series of simulation experiments.

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arXiv2016

Interpretable Dynamic Treatment Regimes

Precision medicine is currently a topic of great interest in clinical and intervention science. One way to formalize precision medicine is through a treatment regime, which is a sequence of decision rules, one per stage of clinical intervention, that map up-to-date patient information to a recommended treatment. An optimal treatment regime is defined as maximizing the mean of some cumulative clinical outcome if applied to a population of interest. It is well-known that even under simple generative models an optimal treatment regime can be a highly nonlinear function of patient information. Consequently, a focal point of recent methodological research has been the development of flexible models for estimating optimal treatment regimes. However, in many settings, estimation of an optimal treatment regime is an exploratory analysis intended to generate new hypotheses for subsequent research and not to directly dictate treatment to new patients. In such settings, an estimated treatment regime that is interpretable in a domain context may be of greater value than an unintelligible treatment regime built using "black-box" estimation methods. We propose an estimator of an optimal treatment regime composed of a sequence of decision rules, each expressible as a list of "if-then" statements that can be presented as either a paragraph or as a simple flowchart that is immediately interpretable to domain experts. The discreteness of these lists precludes smooth, i.e., gradient-based, methods of estimation and leads to non-standard asymptotics. Nevertheless, we provide a computationally efficient estimation algorithm, prove consistency of the proposed estimator, and derive rates of convergence. We illustrate the proposed methods using a series of simulation examples and application to data from a sequential clinical trial on bipolar disorder.

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arXiv2015

Using Decision Lists to Construct Interpretable and Parsimonious Treatment Regimes

A treatment regime formalizes personalized medicine as a function from individual patient characteristics to a recommended treatment. A high-quality treatment regime can improve patient outcomes while reducing cost, resource consumption, and treatment burden. Thus, there is tremendous interest in estimating treatment regimes from observational and randomized studies. However, the development of treatment regimes for application in clinical practice requires the long-term, joint effort of statisticians and clinical scientists. In this collaborative process, the statistician must integrate clinical science into the statistical models underlying a treatment regime and the clinician must scrutinize the estimated treatment regime for scientific validity. To facilitate meaningful information exchange, it is important that estimated treatment regimes be interpretable in a subject-matter context. We propose a simple, yet flexible class of treatment regimes whose members are representable as a short list of if-then statements. Regimes in this class are immediately interpretable and are therefore an appealing choice for broad application in practice. We derive a robust estimator of the optimal regime within this class and demonstrate its finite sample performance using simulation experiments. The proposed method is illustrated with data from two clinical trials.

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arXiv2015

$Q$- and $A$-Learning Methods for Estimating Optimal Dynamic Treatment Regimes

In clinical practice, physicians make a series of treatment decisions over the course of a patient's disease based on his/her baseline and evolving characteristics. A dynamic treatment regime is a set of sequential decision rules that operationalizes this process. Each rule corresponds to a decision point and dictates the next treatment action based on the accrued information. Using existing data, a key goal is estimating the optimal regime, that, if followed by the patient population, would yield the most favorable outcome on average. Q- and A-learning are two main approaches for this purpose. We provide a detailed account of these methods, study their performance, and illustrate them using data from a depression study.

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arXiv2014

On Estimation of Optimal Treatment Regimes For Maximizing t-Year Survival Probability

A treatment regime is a deterministic function that dictates personalized treatment based on patients' individual prognostic information. There is a fast-growing interest in finding optimal treatment regimes to maximize expected long-term clinical outcomes of patients for complex diseases, such as cancer and AIDS. For many clinical studies with survival time as a primary endpoint, a main goal is to maximize patients' survival probabilities given treatments. In this article, we first propose two nonparametric estimators for survival function of patients following a given treatment regime. Then, we derive the estimation of the optimal treatment regime based on a value-based searching algorithm within a set of treatment regimes indexed by parameters. The asymptotic properties of the proposed estimators for survival probabilities under derived optimal treatment regimes are established under suitable regularity conditions. Simulations are conducted to evaluate the numerical performance of the proposed estimators under various scenarios. An application to an AIDS clinical trial data is also given to illustrate the methods.

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