Sensitivity analyses for the principal ignorability assumption using multiple imputation

In the context of clinical trials, there is interest in the treatment effect for subpopulations of patients defined by intercurrent events, namely disease-related events occurring after treatment initiation that affect either the interpretation or the existence of endpoints. With the principal stratum strategy, the ICH E9(R1) guideline introduces a formal framework in drug development for defining treatment effects in such subpopulations. Statistical estimation of the treatment effect can be performed based on the principal ignorability assumption using multiple imputation approaches. Principal ignorability is a conditional independence assumption that cannot be directly verified; therefore, it is crucial to evaluate the robustness of results to deviations from this assumption. As a sensitivity analysis, we propose a joint model that multiply imputes the principal stratum membership and the outcome variable while allowing different levels of violation of the principal ignorability assumption. We illustrate with a simulation study that the joint imputation model-based approaches are superior to naive subpopulation analyses. Motivated by an oncology clinical trial, we implement the sensitivity analysis on a time-to-event outcome to assess the treatment effect in the subpopulation of patients who discontinued due to adverse events using a synthetic dataset. Finally, we explore the potential usage and provide interpretation of such analyses in clinical settings, as well as possible extension of such models in more general cases.     

Statistical methods for handling missing data to align with treatment policy strategy

The International Council for Harmonization (ICH) E9(R1) addendum recommends choosing an appropriate estimand based on the study objectives in advance of trial design. One defining attribute of an estimand is the intercurrent event, specifically what is considered an intercurrent event and how it should be handled. The primary objective of a clinical study is usually to assess a product's effectiveness and safety based on the planned treatment regimen instead of the actual treatment received. The estimand using the treatment policy strategy, which collects and analyzes data regardless of the occurrence of intercurrent events, is usually utilized. In this article, we explain how missing data can be handled using the treatment policy strategy from the authors' viewpoint in connection with antihyperglycemic product development programs. The article discusses five statistical methods to impute missing data occurring after intercurrent events. All five methods are applied within the framework of the treatment policy strategy. The article compares the five methods via Markov Chain Monte Carlo simulations and showcases how three of these five methods have been applied to estimate the treatment effects published in the labels for three antihyperglycemic agents currently on the market.     

Strategies for composite estimands in confirmatory clinical trials: Examples from trials in nasal polyps and steroid reduction

The draft addendum to the ICH E9 regulatory guideline asks for explicit definition of the treatment effect to be estimated in clinical trials. The draft guideline also introduces the concept of intercurrent events to describe events that occur post‐randomisation that may affect efficacy assessment. Composite estimands allow incorporation of intercurrent events in the definition of the endpoint. A common example of an intercurrent event is discontinuation of randomised treatment and use of a composite strategy would assess treatment effect based on a variable that combines the outcome variable of interest with discontinuation of randomised treatment. Use of a composite estimand may avoid the need for imputation which would be required by a treatment policy estimand. The draft guideline gives the example of a binary approach for specifying a composite estimand. When the variable is measured on a non‐binary scale, other options are available where the intercurrent event is given an extreme unfavourable value, for example comparison of median values or analysis based on categories of response. This paper reviews approaches to deriving a composite estimand and contrasts the use of this estimand to the treatment policy estimand. The benefits of using each strategy are discussed and examples of the use of the different approaches are given for a clinical trial in nasal polyposis and a steroid reduction trial in severe asthma.     

Defining estimands for efficacy assessment in single arm phase 1b or phase 2 clinical trials in oncology early development

The addendum of the ICH E9 guideline on the statistical principles for clinical trials introduced the estimand framework. The framework is designed to strengthen the dialog between different stakeholders, to introduce greater clarity in the clinical trial objectives and to provide alignment between the estimand and statistical analysis. Estimand framework related publications thus far have mainly focused on randomized clinical trials. The intention of the Early Development Estimand Nexus (EDEN), a task force of the cross-industry Oncology Estimand Working Group ( www.oncoestimand.org ), is to apply it to single arms Phase 1b or Phase 2 trials designed to detect a treatment-related efficacy signal, typically measured by objective response rate. Key recommendations regarding the estimand attributes include that in a single arm early clinical trial, the treatment attribute should start when the first dose is received by the participant. Focusing on the estimation of an absolute effect, the population-level summary measure should reflect only the property used for the estimation. Another major component introduced in the ICH E9 addendum is the definition of intercurrent events and the associated possible ways to handle them. Different strategies reflect different clinical questions of interest that can be answered based on the journeys an individual subject can take during a trial. We provide detailed strategy recommendations for intercurrent events typically seen in early-stage oncology. We highlight where implicit assumptions should be made transparent as whenever follow-up is suspended, a while-on-treatment strategy is implied.     

Estimand framework: Are we asking the right questions? A case study in the solid tumor setting

The estimand framework requires a precise definition of the clinical question of interest (the estimand) as different ways of accounting for “intercurrent” events post randomization may result in different scientific questions. The initiation of subsequent therapy is common in oncology clinical trials and is considered an intercurrent event if the start of such therapy occurs prior to a recurrence or progression event. Three possible ways to account for this intercurrent event in the analysis are to censor at initiation, consider recurrence or progression events (including death) that occur before and after the initiation of subsequent therapy, or consider the start of subsequent therapy as an event in and of itself. The new estimand framework clarifies that these analyses address different questions (“does the drug delay recurrence if no patient had received subsequent therapy?” vs “does the drug delay recurrence with or without subsequent therapy?” vs “does the drug delay recurrence or start of subsequent therapy?”). The framework facilitates discussions during clinical trial planning and design to ensure alignment between the key question of interest, the analysis, and interpretation. This article is a result of a cross-industry collaboration to connect the International Council for Harmonisation E9 addendum concepts to applications. Data from previously reported randomized phase 3 studies in the renal cell carcinoma setting are used to consider common intercurrent events in solid tumor studies, and to illustrate different scientific questions and the consequences of the estimand choice for study design, data collection, analysis, and interpretation.     

Estimation of Causal Effects in Latent Strata with an Encouragement for Response

We consider a new approach to deal with non ignorable non response on an outcome variable, in a causal inference framework. Assuming that a binary instrumental variable for non response is available, we provide a likelihood-based approach to identify and estimate heterogeneous causal effects of a binary treatment on specific latent subgroups of units, named principal strata, defined by the non response behavior under each level of the treatment and of the instrument. We show that, within each stratum, non response is ignorable and respondents can be properly compared by treatment status. In order to assess our method and its robustness when the usually invoked assumptions are relaxed or misspecified, we simulate data to resemble a real experiment conducted on a panel survey which compares different methods of reducing panel attrition.     

Estimating Causal Effects in Trials Involving Multi-Treatment Arms Subject to Non-compliance: A Bayesian framework

Data analysis for randomized trials including multi-treatment arms is often complicated by subjects who do not comply with their treatment assignment. We discuss here methods of estimating treatment efficacy for randomized trials involving multi-treatment arms subject to non-compliance. One treatment effect of interest in the presence of non-compliance is the complier average causal effect (CACE) (Angrist et al. 1996), which is defined as the treatment effect for subjects who would comply regardless of the assigned treatment. Following the idea of principal stratification (Frangakis & Rubin 2002), we define principal compliance (Little et al. 2009) in trials with three treatment arms, extend CACE and define causal estimands of interest in this setting. In addition, we discuss structural assumptions needed for estimation of causal effects and the identifiability problem inherent in this setting from both a Bayesian and a classical statistical perspective. We propose a likelihood-based framework that models potential outcomes in this setting and a Bayes procedure for statistical inference. We compare our method with a method of moments approach proposed by Cheng & Small (2006) using a hypothetical data set, and further illustrate our approach with an application to a behavioral intervention study (Janevic et al. 2003).     

Did the Military Interventions in the Mexican Drug War Increase Violence?

We analyze publicly available data to estimate the causal effects of military interventions on the homicide rates in certain problematic regions in Mexico. We use the Rubin causal model to compare the post-intervention homicide rate in each intervened region to the hypothetical homicide rate for that same year had the military intervention not taken place. Because the effect of a military intervention is not confined to the municipality subject to the intervention, a nonstandard definition of units is necessary to estimate the causal effect of the intervention under the standard no-interference assumption of stable-unit treatment value assumption (SUTVA). Donor pools are created for each missing potential outcome under no intervention, thereby allowing for the estimation of unit-level causal effects. A multiple imputation approach accounts for uncertainty about the missing potential outcomes.     

Defining estimands using a mix of strategies to handle intercurrent events in clinical trials

Randomized controlled trials (RCTs) are the gold standard for evaluation of the efficacy and safety of investigational interventions. If every patient in an RCT were to adhere to the randomized treatment, one could simply analyze the complete data to infer the treatment effect. However, intercurrent events (ICEs) including the use of concomitant medication for unsatisfactory efficacy, treatment discontinuation due to adverse events, or lack of efficacy may lead to interventions that deviate from the original treatment assignment. Therefore, defining the appropriate estimand (the appropriate parameter to be estimated) based on the primary objective of the study is critical prior to determining the statistical analysis method and analyzing the data. The International Council for Harmonisation (ICH) E9 (R1), adopted on November 20, 2019, provided five strategies to define the estimand: treatment policy, hypothetical, composite variable, while on treatment, and principal stratum. In this article, we propose an estimand using a mix of strategies in handling ICEs. This estimand is an average of the “null” treatment difference for those with ICEs potentially related to safety and the treatment difference for the other patients if they would complete the assigned treatments. Two examples from clinical trials evaluating antidiabetes treatments are provided to illustrate the estimation of this proposed estimand and to compare it with the estimates for estimands using hypothetical and treatment policy strategies in handling ICEs.     

Sensitivity analyses for partially observed recurrent event data

Recurrent events involve the occurrences of the same type of event repeatedly over time and are commonly encountered in longitudinal studies. Examples include seizures in epileptic studies or occurrence of cancer tumors. In such studies, interest lies in the number of events that occur over a fixed period of time. One considerable challenge in analyzing such data arises when a large proportion of patients discontinues before the end of the study, for example, because of adverse events, leading to partially observed data. In this situation, data are often modeled using a negative binomial distribution with time‐in‐study as offset. Such an analysis assumes that data are missing at random (MAR). As we cannot test the adequacy of MAR, sensitivity analyses that assess the robustness of conclusions across a range of different assumptions need to be performed. Sophisticated sensitivity analyses for continuous data are being frequently performed. However, this is less the case for recurrent event or count data. We will present a flexible approach to perform clinically interpretable sensitivity analyses for recurrent event data. Our approach fits into the framework of reference‐based imputations, where information from reference arms can be borrowed to impute post‐discontinuation data. Different assumptions about the future behavior of dropouts dependent on reasons for dropout and received treatment can be made. The imputation model is based on a flexible model that allows for time‐varying baseline intensities. We assess the performance in a simulation study and provide an illustration with a clinical trial in patients who suffer from bladder cancer. Copyright © 2015 John Wiley & Sons, Ltd.     

THE POTENTIAL FOR BIAS IN PRINCIPAL CAUSAL EFFECT ESTIMATION WHEN TREATMENT RECEIVED DEPENDS ON A KEY COVARIATE

Motivated by a potential-outcomes perspective, the idea of principal stratification has been widely recognized for its relevance in settings susceptible to posttreatment selection bias such as randomized clinical trials where treatment received can differ from treatment assigned. In one such setting, we address subtleties involved in inference for causal effects when using a key covariate to predict membership in latent principal strata. We show that when treatment received can differ from treatment assigned in both study arms, incorporating a stratum-predictive covariate can make estimates of the "complier average causal effect" (CACE) derive from observations in the two treatment arms with different covariate distributions. Adopting a Bayesian perspective and using Markov chain Monte Carlo for computation, we develop posterior checks that characterize the extent to which incorporating the pretreatment covariate endangers estimation of the CACE. We apply the method to analyze a clinical trial comparing two treatments for jaw fractures in which the study protocol allowed surgeons to overrule both possible randomized treatment assignments based on their clinical judgment and the data contained a key covariate (injury severity) predictive of treatment received.     

CAUSAL EFFECTS OF TREATMENTS FOR INFORMATIVE MISSING DATA DUE TO PROGRESSION/DEATH

In longitudinal clinical trials, when outcome variables at later time points are only defined for patients who survive to those times, the evaluation of the causal effect of treatment is complicated. In this paper, we describe an approach that can be used to obtain the causal effect of three treatment arms with ordinal outcomes in the presence of death using a principal stratification approach. We introduce a set of flexible assumptions to identify the causal effect and implement a sensitivity analysis for non-identifiable assumptions which we parameterize parsimoniously. Methods are illustrated on quality of life data from a recent colorectal cancer clinical trial.     

Estimands in hematologic oncology trials

The estimand framework included in the addendum to the ICH E9 guideline facilitates discussions to ensure alignment between the key question of interest, the analysis, and interpretation. Therapeutic knowledge and drug mechanism play a crucial role in determining the strategy and defining the estimand for clinical trial designs. Clinical trials in patients with hematological malignancies often present unique challenges for trial design due to complexity of treatment options and existence of potential curative but highly risky procedures, for example, stem cell transplant or treatment sequence across different phases (induction, consolidation, maintenance). Here, we illustrate how to apply the estimand framework in hematological clinical trials and how the estimand framework can address potential difficulties in trial result interpretation. This paper is a result of a cross-industry collaboration to connect the International Conference on Harmonisation (ICH) E9 addendum concepts to applications. Three randomized phase 3 trials will be used to consider common challenges including intercurrent events in hematologic oncology trials to illustrate different scientific questions and the consequences of the estimand choice for trial design, data collection, analysis, and interpretation. Template language for describing estimand in both study protocols and statistical analysis plans is suggested for statisticians' reference.     

Estimating percentile-specific treatment effects in counterfactual models: a case-study of micronutrient supplementation, birth weight and infant mortality

Summary.  Clinical trials of micronutrient supplementation are aimed at reducing the risk of infant mortality by increasing birth weight. Because infant mortality is greatest among the low birth weight (LBW) infants (2500 g or under), an effective intervention increases the birth weight among the smallest babies. The paper defines population and counterfactual parameters for estimating the treatment effects on birth weight and on survival as functions of the percentiles of the birth weight distribution. We use a Bayesian approach with data augmentation to approximate the posterior distributions of the parameters, taking into account uncertainty that is associated with the imputation of the counterfactuals. This approach is particularly suitable for exploring the sensitivity of the results to unverifiable modelling assumptions and other prior beliefs. We estimate that the average causal effect of the treatment on birth weight is 72 g (95% posterior regions 33–110 g) and that this causal effect is largest among the LBW infants. Posterior inferences about average causal effects of the treatment on birth weight are robust to modelling assumptions. However, inferences about causal effects for babies at the tails of the birth weight distribution can be highly sensitive to the unverifiable assumption about the correl-ation between the observed and the counterfactuals birth weights. Among the LBW infants who have a large causal effect of the treatment on birth weight, we estimate that a baby receiving the treatment has 5% less chance of death than if the same baby had received the control. Among the LBW infants, we found weak evidence supporting an additional beneficial effect of the treatment on mortality independent of birth weight.     

Signed directed acyclic graphs for causal inference

Summary.  Formal rules governing signed edges on causal directed acyclic graphs are described and it is shown how these rules can be useful in reasoning about causality. Specifically, the notions of a monotonic effect, a weak monotonic effect and a signed edge are introduced. Results are developed relating these monotonic effects and signed edges to the sign of the causal effect of an intervention in the presence of intermediate variables. The incorporation of signed edges in the directed acyclic graph causal framework furthermore allows for the development of rules governing the relationship between monotonic effects and the sign of the covariance between two variables. It is shown that when certain assumptions about monotonic effects can be made then these results can be used to draw conclusions about the presence of causal effects even when data are missing on confounding variables.     

Estimating efficacy in a proposed randomized trial with initial and later non-compliance

Summary.  A controversial topic in obstetrics is the effect of walking on the probability of Caesarean section among women in labour. A major reason for the controversy is the presence of non-compliance that complicates the estimation of efficacy, the effect of treatment received on outcome. The intent-to-treat method does not estimate efficacy, and estimates of efficacy that are based directly on treatment received may be biased because they are not protected by randomization. However, when non-compliance occurs immediately after randomization, the use of a potential outcomes model with reasonable assumptions has made it possible to estimate efficacy and still to retain the benefits of randomization to avoid selection bias. In this obstetrics application, non-compliance occurs initially and later in one arm. Consequently some parameters cannot be uniquely estimated without making strong assumptions. This difficulty is circumvented by a new study design involving an additional randomization group and a novel potential outcomes model (principal stratification).     

Bayesian regression model for recurrent event data with event-varying covariate effects and event effect

In the course of hypertension, cardiovascular disease events (e.g. stroke, heart failure) occur frequently and recurrently. The scientific interest in such study may lie in the estimation of treatment effect while accounting for the correlation among event times. The correlation among recurrent event times comes from two sources: subject-specific heterogeneity (e.g. varied lifestyles, genetic variations, and other unmeasurable effects) and event dependence (i.e. event incidences may change the risk of future recurrent events). Moreover, event incidences may change the disease progression so that there may exist event-varying covariate effects (the covariate effects may change after each event) and event effect (the effect of prior events on the future events). In this article, we propose a Bayesian regression model that not only accommodates correlation among recurrent events from both sources, but also explicitly characterizes the event-varying covariate effects and event effect. This model is especially useful in quantifying how the incidences of events change the effects of covariates and risk of future events. We compare the proposed model with several commonly used recurrent event models and apply our model to the motivating lipid-lowering trial (LLT) component of the Antihypertensive and Lipid-Lowering Treatment to Prevent Heart Attack Trial (ALLHAT) (ALLHAT-LLT).     

Using recurrent time-to-event models with multinomial outcomes to generate toxicity profiles

Most clinical studies, which investigate the impact of therapy simultaneously, record the frequency of adverse events in order to monitor safety of the intervention. Study reports typically summarise adverse event data by tabulating the frequencies of the worst grade experienced but provide no details of the temporal profiles of specific types of adverse events. Such 'toxicity profiles' are potentially important tools in disease management and in the assessment of newer therapies including targeted treatments and immunotherapy where different types of toxicity may be more common at various times during long-term drug exposure. Toxicity profiles of commonly experienced adverse events occurring due to exposure to long-term treatment could assist in evaluating the costs of the health care benefits of therapy. We show how to generate toxicity profiles using an adaptation of the ordinal time-to-event model comprising of a two-step process, involving estimation of the multinomial response probabilities using multinomial logistic regression and combining these with recurrent time to event hazard estimates to produce cumulative event probabilities for each of the multinomial adverse event response categories. Such a model permits the simultaneous assessment of the risk of events over time and provides cumulative risk probabilities for each type of adverse event response. The method can be applied more generally by using different models to estimate outcome/response probabilities. The method is illustrated by developing toxicity profiles for three distinct types of adverse events associated with two treatment regimens for patients with advanced breast cancer.     

Blinded assessment of treatment effects for survival endpoint in an ongoing trial

Many assumptions, including assumptions regarding treatment effects, are made at the design stage of a clinical trial for power and sample size calculations. It is desirable to check these assumptions during the trial by using blinded data. Methods for sample size re‐estimation based on blinded data analyses have been proposed for normal and binary endpoints. However, there is a debate that no reliable estimate of the treatment effect can be obtained in a typical clinical trial situation. In this paper, we consider the case of a survival endpoint and investigate the feasibility of estimating the treatment effect in an ongoing trial without unblinding. We incorporate information of a surrogate endpoint and investigate three estimation procedures, including a classification method and two expectation–maximization (EM) algorithms. Simulations and a clinical trial example are used to assess the performance of the procedures. Our studies show that the expectation–maximization algorithms highly depend on the initial estimates of the model parameters. Despite utilization of a surrogate endpoint, all three methods have large variations in the treatment effect estimates and hence fail to provide a precise conclusion about the treatment effect. Copyright © 2012 John Wiley & Sons, Ltd.