Deductive semiparametric estimation in Double-Sampling Designs with application to PEPFAR

Non-ignorable dropout is common in studies with long follow-up time, and it can bias study results unless handled carefully. A double-sampling design allocates additional resources to pursue a subsample of the dropouts and find out their outcomes, which can address potential biases due to non-ignorable dropout. It is desirable to construct semiparametric estimators for the double-sampling design because of their robustness properties. However, obtaining such semiparametric estimators remains a challenge due to the requirement of the analytic form of the efficient influence function (EIF), the derivation of which can be ad hoc and difficult for the double-sampling design. Recent work has shown how the derivation of EIF can be made deductive and computerizable using the functional derivative representation of the EIF in nonparametric models. This approach, however, requires deriving the mixture of a continuous distribution and a point mass, which can itself be challenging for complicated problems such as the double-sampling design. We propose semiparametric estimators for the survival probability in double-sampling designs by generalizing the deductive and computerizable estimation approach. In particular, we propose to build the semiparametric estimators based on a discretized support structure, which approximates the possibly continuous observed data distribution and circumvents the derivation of the mixture distribution. Our approach is deductive in the sense that it is expected to produce semiparametric locally efficient estimators within finite steps without knowledge of the EIF. We apply the proposed estimators to estimating the mortality rate in a double-sampling design component of the President's Emergency Plan for AIDS Relief (PEPFAR) program. We evaluate the impact of double-sampling selection criteria on the mortality rate estimates

Linear mixed models with endogenous covariates: modeling sequential treatment effects with application to a mobile health study

Mobile health is a rapidly developing field in which behavioral treatments are delivered to individuals via wearables or smartphones to facilitate health-related behavior change. Micro-randomized trials (MRT) are an experimental design for developing mobile health interventions. In an MRT the treatments are randomized numerous times for each individual over course of the trial. Along with assessing treatment effects, behavioral scientists aim to understand between-person heterogeneity in the treatment effect. A natural approach is the familiar linear mixed model. However, directly applying linear mixed models is problematic because potential moderators of the treatment effect are frequently endogenous---that is, may depend on prior treatment. We discuss model interpretation and biases that arise in the absence of additional assumptions when endogenous covariates are included in a linear mixed model. In particular, when there are endogenous covariates, the coefficients no longer have the customary marginal interpretation. However, these coefficients still have a conditional-on-the-random-effect interpretation. We provide an additional assumption that, if true, allows scientists to use standard software to fit linear mixed model with endogenous covariates, and person-specific predictions of effects can be provided. As an illustration, we assess the effect of activity suggestion in the HeartSteps MRT and analyze the between-person treatment effect heterogeneity

Semiparametric Estimation in Observational Studies and Randomized Trials

Researchers often seek robust inference for a parameter through semiparametric estimation. Semiparametric estimation is useful, for example, for survival analysis, for estimating growth parameters in longitudinal studies, and for estimating quantities under missing data, including treatment effects based on potential outcomes. In this dissertation we study semiparametric estimation from two design perspectives: observational studies and randomized trials. Traditional semiparametric estimation methods requires theoretical derivation of the efficient influence function, which can be a challenging and time-consuming task. To address this difficulty, we propose a new method, called ``deductive estimation'', for constructing semiparametric estimators for observational studies. The method is computerizable, meaning that it does not need theoretically deriving the functional form of the efficient influence function, and is guaranteed to produce semiparametric, locally efficient estimators even for complex parameters in nonparametric models. We apply the method to two designs: the two-phase design, and the double-sampling design. We demonstrate the method with a study on asthma care satisfaction and a study evaluating an HIV treatment in East Africa. In randomized trials, adjusting for baseline variables and short-term outcomes can lead to increased power and reduced sample size. We investigate the strengths and limitations of a semiparametric, locally efficient estimator compared to the standard unadjusted estimator in randomized trials context. We derive formulas for the precision gain from such covariate adjustment using semiparametric estimators for the average treatment effect, and give new results on what conditions lead to substantial power gains and sample size reductions. The theory is supported by two simulation studies: simulated group sequential trials based on data from the MISTIE Phase II trial, which is a trial of a new surgical intervention for stroke, and simulated adaptive enrichment trials based on data from the Alzheimer’s Disease Neuroimaging Initiative cohort study. Our results can be used in trial planning to predict the potential precision gain from covariate adjustment, which will translate to power gain or sample size reduction

Efficient and Globally Robust Causal Excursion Effect Estimation

Causal excursion effect (CEE) characterizes the effect of an intervention under policies that deviate from the experimental policy. It is widely used to study effect of time-varying interventions that have the potential to be frequently adaptive, such as those delivered through smartphones. We study the semiparametric efficient estimation of CEE and we derive a semiparametric efficiency bound for CEE with identity or log link functions under working assumptions. We propose a class of two-stage estimators that achieve the efficiency bound and are robust to misspecified nuisance models. In deriving the asymptotic property of the estimators, we establish a general theory for globally robust Z-estimators with either cross-fitted or non-cross-fitted nuisance parameters. We demonstrate substantial efficiency gain of the proposed estimator compared to existing ones through simulations and a real data application using the Drink Less micro-randomized trial

ADAPTIVE ENRICHMENT DESIGNS FOR RANDOMIZED TRIALS WITH DELAYED ENDPOINTS, USING LOCALLY EFFICIENT ESTIMATORS TO IMPROVE PRECISION

Adaptive enrichment designs involve preplanned rules for modifying enrollment criteria based on accrued data in an ongoing trial. For example, enrollment of a subpopulation where there is sufficient evidence of treatment efficacy, futility, or harm could be stopped, while enrollment for the remaining subpopulations is continued. Most existing methods for constructing adaptive enrichment designs are limited to situations where patient outcomes are observed soon after enrollment. This is a major barrier to the use of such designs in practice, since for many diseases the outcome of most clinical importance does not occur shortly after enrollment. We propose a new class of adaptive enrichment designs for delayed endpoints. At each analysis, semiparametric, locally efficient estimators leverage information in baseline variables and short-term outcomes to improve precision. This can reduce the sample size required to achieve a desired power. We propose new multiple testing procedures tailored to this problem, which we prove to strongly control the family-wise Type I error rate, asymptotically. These methods are illustrated through simulations of a trial for a new surgical intervention for stroke

Incorporating nonparametric methods for estimating causal excursion effects in mobile health with zero-inflated count outcomes

In the domain of mobile health, tailoring interventions for real-time delivery is of paramount importance. Micro-randomized trials have emerged as the "gold-standard" methodology for developing such interventions. Analyzing data from these trials provides insights into the efficacy of interventions and the potential moderation by specific covariates. The "causal excursion effect", a novel class of causal estimand, addresses these inquiries, backed by current semiparametric inference techniques. Yet, existing methods mainly focus on continuous or binary data, leaving count data largely unexplored. The current work is motivated by the Drink Less micro-randomized trial from the UK, which focuses on a zero-inflated proximal outcome, the number of screen views in the subsequent hour following the intervention decision point. In the current paper, we revisit the concept of causal excursion effects, specifically for zero-inflated count outcomes, and introduce novel estimation approaches that incorporate nonparametric techniques. Bidirectional asymptotics are derived for the proposed estimators. Through extensive simulation studies, we evaluate the performance of the proposed estimators. As an illustration, we also employ the proposed methods to the Drink Less trial data.Comment: 37pages,2 figure

Deductive Derivation and Computerization of Compatible Semiparametric Efficient Estimation

Researchers often seek robust inference for a parameter through semiparametric estimation. Efficient semiparametric estimation currently requires theoretical derivation of the efficient influence function (EIF), which can be a challenging and time-consuming task. If this task can be computerized, it can save dramatic human effort, which can be transferred, for example, to the design of new studies. Although the EIF is, in principle, a derivative, simple numerical differentiation to calculate the EIF by a computer masks the EIF\u27s functional dependence on the parameter of interest. For this reason, the standard approach to obtaining the EIF has been the theoretical construction of the space of scores under all possible parametric submodels. This process currently depends on the correctness of conjectures about these spaces, and the correct verification of such conjectures. The correct guessing of such conjectures, though successful in some problems, is a nondeductive process, i.e., is not guaranteed to succeed (e.g., is not computerizable), and the verification of conjectures is generally susceptible to mistakes. We propose a method that can deductively produce semiparametric locally efficient estimators. The proposed method is computerizable, meaning that it does not need either conjecturing for, or otherwise theoretically deriving the functional form of the EIF, and is guaranteed to produce the result. The method is demonstared through an example

COMPARISON OF ADAPTIVE RANDOMIZED TRIAL DESIGNS FOR TIME-TO-EVENT OUTCOMES THAT EXPAND VERSUS RESTRICT ENROLLMENT CRITERIA, TO TEST NON-INFERIORITY

Adaptive enrichment designs involve preplanned rules for modifying patient enrollment criteria based on data accrued in an ongoing trial. These designs may be useful when it is suspected that a subpopulation, e.g., defined by a biomarker or risk score measured at baseline, may benefit more from treatment than the complementary subpopulation. We compare two types of such designs, for the case of two subpopulations that partition the overall population. The first type starts by enrolling the subpopulation where it is suspected the new treatment is most likely to work, and then may expand inclusion criteria if there is early evidence of a treatment benefit. The second type starts by enrolling from the overall population and then may selectively restrict enrollment if sufficient evidence accrues that the treatment is not benefiting a subpopulation. We construct two-stage designs of each type that guarantee strong control of the familywise Type I error rate, asymptotically. We then compare performance of the designs from each type under different scenarios; the scenarios mimic key features of a completed non-inferiority trial of HIV treatments. Performance criteria include power, sample size, Type I error, estimator bias, and confidence inteval coverage probability

The Micro-Randomized Trial for Developing Digital Interventions: Data Analysis Methods

Although there is much excitement surrounding the use of mobile and wearable technology for the purposes of delivering interventions as people go through their day-to-day lives, data analysis methods for constructing and optimizing digital interventions lag behind. Here, we elucidate data analysis methods for primary and secondary analyses of micro-randomized trials (MRTs), an experimental design to optimize digital just-in-time adaptive interventions. We provide a definition of causal "excursion" effects suitable for use in digital intervention development. We introduce the weighted and centered least-squares (WCLS) estimator which provides consistent causal excursion effect estimators for digital interventions from MRT data. We describe how the WCLS estimator along with associated test statistics can be obtained using standard statistical software such as SAS or R. Throughout we use HeartSteps, an MRT designed to increase physical activity among sedentary individuals, to illustrate potential primary and secondary analyses