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In this paper, we develop a semiparametric sensitivity analysis approach designed to address unmeasured confounding in observational studies with time-to-event outcomes. We target estimation of the marginal distributions of potential outcomes under competing exposures using influence function-based techniques. We derived the non-parametric influence function for uncensored data and mapped the uncensored data influence function to the observed data influence function. Our methodology is motivated by and applied to an observational study evaluating the effectiveness of radical prostatectomy (RP) versus external beam radiotherapy with androgen deprivation (EBRT+AD) for the treatment of prostate cancer. We also present a simulation study to evaluate the statistical properties of our methodology., Comment: 19 pages, 2 tables, 4 figures

A Real-World Evidence (RWE) Scientific Working Group (SWG) of the American Statistical Association Biopharmaceutical Section (ASA BIOP) has been reviewing statistical considerations for the generation of RWE to support regulatory decision-making. As part of the effort, the working group is addressing estimands in RWE studies. Constructing the right estimand -- the target of estimation -- which reflects the research question and the study objective, is one of the key components in formulating a clinical study. ICH E9(R1) describes statistical principles for constructing estimands in clinical trials with a focus on five attributes -- population, treatment, endpoints, intercurrent events, and population-level summary. However, defining estimands for clinical studies using real-world data (RWD), i.e., RWE studies, requires additional considerations due to, for example, heterogeneity of study population, complexity of treatment regimes, different types and patterns of intercurrent events, and complexities in choosing study endpoints. This paper reviews the essential components of estimands and causal inference framework, discusses considerations in constructing estimands for RWE studies, highlights similarities and differences in traditional clinical trial and RWE study estimands, and provides a roadmap for choosing appropriate estimands for RWE studies.

An important strategy for identifying principal causal effects, which are often used in settings with noncompliance, is to invoke the principal ignorability (PI) assumption. As PI is untestable, it is important to gauge how sensitive effect estimates are to its violation. We focus on this task for the common one-sided noncompliance setting where there are two principal strata, compliers and noncompliers. Under PI, compliers and noncompliers share the same outcome-mean-given-covariates function under the control condition. For sensitivity analysis, we allow this function to differ between compliers and noncompliers in several ways, indexed by an odds ratio, a generalized odds ratio, a mean ratio, or a standardized mean difference sensitivity parameter. We tailor sensitivity analysis techniques (with any sensitivity parameter choice) to several types of PI-based main analysis methods, including outcome regression, influence function (IF) based and weighting methods. We illustrate the proposed sensitivity analyses using several outcome types from the JOBS II study. This application estimates nuisance functions parametrically -- for simplicity and accessibility. In addition, we establish rate conditions on nonparametric nuisance estimation for IF-based estimators to be asymptotically normal -- with a view to inform nonparametric inference.

Many trials are designed to collect outcomes at or around pre-specified times after randomization. In practice, there can be substantial variability in the times when participants are actually assessed. Such irregular assessment times pose a challenge to learning the effect of treatment since not all participants have outcome assessments at the times of interest. Furthermore, observed outcome values may not be representative of all participants' outcomes at a given time. This problem, known as informative assessment times, can arise if participants tend to have assessments when their outcomes are better (or worse) than at other times, or if participants with better outcomes tend to have more (or fewer) assessments. Methods have been developed that account for some types of informative assessment; however, since these methods rely on untestable assumptions, sensitivity analyses are needed. We develop a sensitivity analysis methodology by extending existing weighting methods. Our method accounts for the possibility that participants with worse outcomes at a given time are more (or less) likely than other participants to have an assessment at that time, even after controlling for variables observed earlier in the study. We apply our method to a randomized trial of low-income individuals with uncontrolled asthma. We illustrate implementation of our influence-function based estimation procedure in detail, and we derive the large-sample distribution of our estimator and evaluate its finite-sample performance., Comment: Revised to include more implementation details, including a tutorial implementing our estimator, and using a more flexible outcome modeling approach in the data analysis

Scharfstein et al. (2021) developed a sensitivity analysis model for analyzing randomized trials with repeatedly measured binary outcomes that are subject to nonmonotone missingness. Their approach becomes computationally intractable when the number of measurements is large (e.g., greater than 15). In this paper, we repair this problem by introducing mth-order Markovian restrictions. We establish identification results for the joint distribution of the binary outcomes by representing the model as a directed acyclic graph (DAG). We develop a novel estimation strategy for a smooth functional of the joint distrubution. We illustrate our methodology in the context of a randomized trial designed to evaluate a web-delivered psychosocial intervention to reduce substance use, assessed by evaluating abstinence twice weekly for 12 weeks, among patients entering outpatient addiction treatment.

Establishing cause-effect relationships from observational data often relies on untestable assumptions. It is crucial to know whether, and to what extent, the conclusions drawn from non-experimental studies are robust to potential unmeasured confounding. In this paper, we focus on the average causal effect (ACE) as our target of inference. We generalize the sensitivity analysis approach developed by Robins et al. (2000), Franks et al. (2020) and Zhou and Yao (2023. We use semiparametric theory to derive the non-parametric efficient influence function of the ACE, for fixed sensitivity parameters. We use this influence function to construct a one-step bias-corrected estimator of the ACE. Our estimator depends on semiparametric models for the distribution of the observed data; importantly, these models do not impose any restrictions on the values of sensitivity analysis parameters. We establish sufficient conditions ensuring that our estimator has root-n asymptotics. We use our methodology to evaluate the causal effect of smoking during pregnancy on birth weight. We also evaluate the performance of estimation procedure in a simulation study.

The use of twins designs to address causal questions is becoming increasingly popular. A standard assumption is that there is no interference between twins---that is, no twin's exposure has a causal impact on their co-twin's outcome. However, there may be settings in which this assumption would not hold, and this would (1) impact the causal interpretation of parameters obtained by commonly used existing methods; (2) change which effects are of greatest interest; and (3) impact the conditions under which we may estimate these effects. We explore these issues, and we derive semi-parametric efficient estimators for causal effects in the presence of interference between twins. Using data from the Minnesota Twin Family Study, we apply our estimators to assess whether twins' consumption of alcohol in early adolescence may have a causal impact on their co-twins' substance use later in life.

In a comprehensive cohort study of two competing treatments (say, A and B), clinically eligible individuals are first asked to enroll in a randomized trial and, if they refuse, are then asked to enroll in a parallel observational study in which they can choose treatment according to their own preference. We consider estimation of two estimands: (1) comprehensive cohort causal effect -- the difference in mean potential outcomes had all patients in the comprehensive cohort received treatment A vs. treatment B and (2) randomized trial causal effect -- the difference in mean potential outcomes had all patients enrolled in the randomized trial received treatment A vs. treatment B. For each estimand, we consider inference under various sets of unconfoundedness assumptions and construct semiparametric efficient and robust estimators. These estimators depend on nuisance functions, which we estimate, for illustrative purposes, using generalized additive models. Using the theory of sample splitting, we establish the asymptotic properties of our proposed estimators. We also illustrate our methodology using data from the Bypass Angioplasty Revascularization Investigation (BARI) randomized trial and observational registry to evaluate the effect of percutaneous transluminal coronary balloon angioplasty versus coronary artery bypass grafting on 5-year mortality. To evaluate the finite sample performance of our estimators, we use the BARI dataset as the basis of a realistic simulation study., Comment: 34 pages, 1 figure, 3 tables

While generic drugs offer a cost-effective alternative to brand name drugs, regulators need a method to assess therapeutic equivalence in a post market setting. We develop such a method in the context of assessing the therapeutic equivalence of immediate release (IM) venlafaxine, based on a large insurance claims dataset provided by OptumLabs\textsuperscript{\textregistered}. To properly address this question, our methodology must deal with issues of non-adherence, secular trends in health outcomes, and lack of treatment overlap due to sharp uptake of the generic once it becomes available. We define, identify (under assumptions) and estimate (using G-computation) a causal effect for a time-to-event outcome by extending regression discontinuity to survival curves. We do not find evidence for a lack of therapeutic equivalence of brand and generic IM venlafaxine.

We develop a Bayesian nonparametric (BNP) approach to evaluate the causal effect of treatment in a randomized trial where a nonterminal event may be censored by a terminal event, but not vice versa (i.e., semi-competing risks). Based on the idea of principal stratification, we define a novel estimand for the causal effect of treatment on the nonterminal event. We introduce identification assumptions, indexed by a sensitivity parameter, and show how to draw inference using our BNP approach. We conduct simulation studies and illustrate our methodology using data from a brain cancer trial.

The treatment effect in a specific subgroup is often of interest in randomized clinical trials. When the subgroup is characterized by the absence of certain post-randomization events, a naive analysis on the subset of patients without these events may be misleading. The principal stratification framework allows one to define an appropriate causal estimand in such settings. Statistical inference for the principal stratum estimand hinges on scientifically justified assumptions, which can be included with Bayesian methods through prior distributions. Our motivating example is a large randomized placebo-controlled trial of siponimod in patients with secondary progressive multiple sclerosis. The primary objective of this trial was to demonstrate the efficacy of siponimod relative to placebo in delaying disability progression for the whole study population. However, the treatment effect in the subgroup of patients who would not relapse during the trial is relevant from both a scientific and regulatory perspective. Assessing this subgroup treatment effect is challenging as there is strong evidence that siponimod reduces relapses. Aligned with the draft regulatory guidance ICH E9(R1), we describe in detail the scientific question of interest, the principal stratum estimand, the corresponding analysis method for binary endpoints and sensitivity analyses., Comment: 16 pages, 2 figures

In randomized studies evaluating treatments for tuberculosis (TB), individuals are scheduled to be routinely evaluated for the presence of TB using sputum cultures. One important endpoint in such studies is the time of culture conversion, the first visit at which a patient's sputum culture is negative and remains negative. This article addresses how to draw inference about treatment effects when sputum cultures are intermittently missing on some patients. We discuss inference under a novel benchmark assumption and under a class of assumptions indexed by a treatment-specific sensitivity parameter that quantify departures from the benchmark assumption. We motivate and illustrate our approach using data from a randomized trial comparing the effectiveness of two treatments for adult TB patients in Brazil., Comment: Published at http://dx.doi.org/10.1214/15-AOAS860 in the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)

We address estimation of intervention effects in experimental designs in which (a) interventions are assigned at the cluster level; (b) clusters are selected to form pairs, matched on observed characteristics; and (c) intervention is assigned to one cluster at random within each pair. One goal of policy interest is to estimate the average outcome if all clusters in all pairs are assigned control versus if all clusters in all pairs are assigned to intervention. In such designs, inference that ignores individual level covariates can be imprecise because cluster-level assignment can leave substantial imbalance in the covariate distribution between experimental arms within each pair. However, most existing methods that adjust for covariates have estimands that are not of policy interest. We propose a methodology that explicitly balances the observed covariates among clusters in a pair, and retains the original estimand of interest. We demonstrate our approach through the evaluation of the Guided Care program., Comment: 27 pages, 3 figures, 3 tables