A Causal Mediation Approach to Account for Interaction of Treatment and Intercurrent Events: Using Hypothetical Strategy.

Hypothetical strategy is a common strategy for handling intercurrent events (IEs). No current guideline or study considers treatment-IE interaction to target the estimand in any one IE-handling strategy. Based on the hypothetical strategy, we aimed to (1) assess the performance of three estimators with different considerations for the treatment-IE interaction in a simulation and (2) compare the estimation of these estimators in a real trial. Simulation data were generalized based on realistic clinical trials of Alzheimer's disease. The estimand of interest was the effect of treatment with no IE occurring under the hypothetical strategy. Three estimators, namely, G-estimation with and without interaction and IE-ignored estimation, were compared in scenarios where the treatment-IE interaction effect was set as -50% to 50% of the main effect. Bias was the key performance measure. The real case was derived from a randomized trial of methadone maintenance treatment. Only G-estimation with interaction exhibited unbiased estimations regardless of the existence, direction or magnitude of the treatment-IE interaction in those scenarios. Neglecting the interaction and ignoring the IE would introduce a bias as large as 0.093 and 0.241 (true value, -1.561) if the interaction effect existed. In the real case, compared with G-estimation with interaction, G-estimation without interaction and IE-ignored estimation increased the estimand of interest by 33.55% and 34.36%, respectively. This study highlights the importance of considering treatment-IE interaction in the estimand framework. In practice, it would be better to include the interaction in the estimator by default.

Distributional imputation for the analysis of censored recurrent events.

Longitudinal clinical trials for which recurrent events endpoints are of interest are commonly subject to missing event data. Primary analyses in such trials are often performed assuming events are missing at random, and sensitivity analyses are necessary to assess robustness of primary analysis conclusions to missing data assumptions. Control-based imputation is an attractive approach in superiority trials for imposing conservative assumptions on how data may be missing not at random. A popular approach to implementing control-based assumptions for recurrent events is multiple imputation (MI), but Rubin's variance estimator is often biased for the true sampling variability of the point estimator in the control-based setting. We propose distributional imputation (DI) with corresponding wild bootstrap variance estimation procedure for control-based sensitivity analyses of recurrent events. We apply control-based DI to a type I diabetes trial. In the application and simulation studies, DI produced more reasonable standard error estimates than MI with Rubin's combining rules in control-based sensitivity analyses of recurrent events.

Estimands in clinical trials of complex disease processes.

Clinical trials with random assignment of treatment provide evidence about causal effects of an experimental treatment compared to standard care. However, when disease processes involve multiple types of possibly semi-competing events, specification of target estimands and causal inferences can be challenging. Intercurrent events such as study withdrawal, the introduction of rescue medication, and death further complicate matters. There has been much discussion about these issues in recent years, but guidance remains ambiguous. Some recommended approaches are formulated in terms of hypothetical settings that have little bearing in the real world. We discuss issues in formulating estimands, beginning with intercurrent events in the context of a linear model and then move on to more complex disease history processes amenable to multistate modeling. We elucidate the meaning of estimands implicit in some recommended approaches for dealing with intercurrent events and highlight the disconnect between estimands formulated in terms of potential outcomes and the real world.

[Special issue PRO] A demonstration of estimands and sensitivity analyses for time-to-deterioration of patient reported outcomes.

In oncology trials, health-related quality of life (HRQoL), specifically patient-reported symptom burden and functional status, can support the interpretation of survival endpoints, such as progression-free survival. However, applying time-to-event endpoints to patient-reported outcomes (PRO) data is challenging. For example, in time-to-deterioration analyses clinical events such as disease progression are common in many settings and are often handled through censoring the patient at the time of occurrence; however, disease progression and HRQoL are often related leading to informative censoring. Special consideration to the definition of events and intercurrent events (ICEs) is necessary. In this work, we demonstrate time-to-deterioration of PRO estimands and sensitivity analyses to answer research questions using composite, hypothetical, and treatment policy strategies applied to a single endpoint of disease-related symptoms. Multiple imputation methods under both the missing-at-random and missing-not-at-random assumptions are used as sensitivity analyses of primary estimands. Hazard ratios ranged from 0.52 to 0.66 over all the estimands and sensitivity analyses modeling a robust treatment effect favoring the treatment in time to disease symptom deterioration or death. Differences in the estimands include how people who experience disease progression or discontinue the randomized treatment due to AEs are accounted for in the analysis. We use the estimand framework to define interpretable and principled approaches for different time-to-deterioration research questions and provide practical recommendations. Reporting the proportions of patient events and patient censoring by reason helps understand the mechanisms that drive the results, allowing for optimal interpretation.

CITIES: Clinical trials with intercurrent events simulator.

Although clinical trials are often designed with randomization and well-controlled protocols, complications will inevitably arise in the presence of intercurrent events (ICEs) such as treatment discontinuation. These can lead to missing outcome data and possibly confounding causal inference when the missingness is a function of a latent stratification of patients defined by intermediate outcomes. The pharmaceutical industry has been focused on developing new methods that can yield pertinent causal inferences in trials with ICEs. However, it is difficult to compare the properties of different methods developed in this endeavor as real-life clinical trial data cannot be easily shared to provide benchmark data sets. Furthermore, different methods consider distinct assumptions for the underlying data-generating mechanisms, and simulation studies often are customized to specific situations or methods. We develop a novel, general simulation model and corresponding Shiny application in R for clinical trials with ICEs, aptly named the Clinical Trials with Intercurrent Events Simulator (CITIES). It is formulated under the Rubin Causal Model where the considered treatment effects account for ICEs in clinical trials with repeated measures. CITIES facilitates the effective generation of data that resemble real-life clinical trials with respect to their reported summary statistics, without requiring the use of the original trial data. We illustrate the utility of CITIES via two case studies involving real-life clinical trials that demonstrate how CITIES provides a comprehensive tool for practitioners in the pharmaceutical industry to compare methods for the analysis of clinical trials with ICEs on identical, benchmark settings that resemble real-life trials.

Multistate models as a framework for estimand specification in clinical trials of complex processes.

Intensity-based multistate models provide a useful framework for characterizing disease processes, the introduction of interventions, loss to followup, and other complications arising in the conduct of randomized trials studying complex life history processes. Within this framework we discuss the issues involved in the specification of estimands and show the limiting values of common estimators of marginal process features based on cumulative incidence function regression models. When intercurrent events arise we stress the need to carefully define the target estimand and the importance of avoiding targets of inference that are not interpretable in the real world. This has implications for analyses, but also the design of clinical trials where protocols may help in the interpretation of estimands based on marginal features.

Defining estimands in clinical trials: A unified procedure.

The ICH E9 (R1) addendum proposes five strategies to define estimands by addressing intercurrent events. However, mathematical forms of these targeted quantities are lacking, which might lead to discordance between statisticians who estimate these quantities and clinicians, drug sponsors, and regulators who interpret them. To improve the concordance, we provide a unified four-step procedure for constructing the mathematical estimands. We apply the procedure for each strategy to derive the mathematical estimands and compare the five strategies in practical interpretations, data collection, and analytical methods. Finally, we show that the procedure can help ease tasks of defining estimands in settings with multiple types of intercurrent events using two real clinical trials.

The net benefit for time-to-event outcome in oncology clinical trials with treatment switching.

BACKGROUND: The net benefit is an effect measure for any type of endpoint, including the time-to-event outcome, and can provide intuitive and clinically meaningful interpretation. It is defined as the probability of a randomly selected subject from the experimental arm surviving by at least a clinically relevant time longer than a randomly selected subject from the control arm. In oncology clinical trials, an intercurrent event such as treatment switching is common, which potentially causes informative censoring; nevertheless, conventional methods for the net benefit are not able to deal with it. In this study, we proposed a new estimator using the inverse probability of censoring weighting (IPCW) method and illustrated an oncology clinical trial with treatment switching (the SHIVA study) to apply the proposed method under the estimand framework. METHODS: The net benefit can be estimated using the survival functions of each treatment group. The proposed estimator was based on the survival functions estimated by the inverse probability of the censoring weighting method that can handle covariate-dependent censoring. The simulation study was undertaken to evaluate the operating characteristics of the proposed estimator under several scenarios; we varied the shapes of the survival curves, treatment effect, covariates effect on censoring, proportion of the censoring, threshold of the net benefit, and sample size. We also applied conventional methods (the scoring rules by Péron or Gehan) and the proposed method to the SHIVA study. RESULTS: Our simulation study showed that the proposed estimator provided less biased results under the covariate-dependent censoring than existing estimators. When applying the proposed method to the SHIVA study, we were able to estimate the net benefit by incorporating the information of the covariates with different estimand strategies to address the intercurrent event of the treatment switching. However, the estimates of the proposed method and those of the aforementioned conventional methods were similar under the hypothetical strategy. CONCLUSIONS: We proposed a new estimator of the net benefit that can include covariates to account for the possibly informative censoring. We also provided an illustrative analysis of the proposed method for the oncology clinical trial with treatment switching using the estimand framework. Our proposed new estimator is suitable for handling the intercurrent events that can potentially cause covariate-dependent censoring.

Handling intercurrent events and missing data in non-inferiority trials using the estimand framework: A tuberculosis case study.

INTRODUCTION: The ICH E9 addendum outlining the estimand framework for clinical trials was published in 2019 but provides limited guidance around how to handle intercurrent events for non-inferiority studies. Once an estimand is defined, it is also unclear how to deal with missing values using principled analyses for non-inferiority studies. METHODS: Using a tuberculosis clinical trial as a case study, we propose a primary estimand, and an additional estimand suitable for non-inferiority studies. For estimation, multiple imputation methods that align with the estimands for both primary and sensitivity analysis are proposed. We demonstrate estimation methods using the twofold fully conditional specification multiple imputation algorithm and then extend and use reference-based multiple imputation for a binary outcome to target the relevant estimands, proposing sensitivity analyses under each. We compare the results from using these multiple imputation methods with those from the original study. RESULTS: Consistent with the ICH E9 addendum, estimands can be constructed for a non-inferiority trial which improves on the per-protocol/intention-to-treat-type analysis population previously advocated, involving respectively a hypothetical or treatment policy strategy to handle relevant intercurrent events. Results from using the 'twofold' multiple imputation approach to estimate the primary hypothetical estimand, and using reference-based methods for an additional treatment policy estimand, including sensitivity analyses to handle the missing data, were consistent with the original study's reported per-protocol and intention-to-treat analysis in failing to demonstrate non-inferiority. CONCLUSIONS: Using carefully constructed estimands and appropriate primary and sensitivity estimators, using all the information available, results in a more principled and statistically rigorous approach to analysis. Doing so provides an accurate interpretation of the estimand.

Application of estimand framework in ICH E9 (R1) to safety evaluation.

Defining the right question of interest is important to a clinical study. ICH E9 (R1) introduces the framework of an estimand and its five attributes, which provide a basis for connecting different components of a study with its clinical questions. Most of the applications of the estimand framework focus on efficacy instead of safety assessment. In this paper, we expand the estimand framework into the safety evaluation and compare/contrast the similarity and differences between safety and efficacy estimand. Furthermore, we present and discuss applications of a safety estimand to oncology trials and pooled data analyses. At last, we also discuss the potential usage of safety estimand to handle the impacts of COVID-19 pandemic on safety assessment.

Application of estimand framework in ICH E9 (R1) to vaccine trials.

Over the past decades, the primary interest in vaccine efficacy or immunogenicity evaluation mostly focuses on the biological effect of immunization in complying with the vaccination schedule in a targeted population. The safety questions, which are essential for vaccines as they are generally given to large healthy populations, need to be clearly defined to reflect the risk assessment of interest. ICH E9 (R1) provides a structured framework to clarify the clinical questions and formulate the treatment effect as an estimand. This paper applies the estimand framework to vaccine clinical trials on common clinical questions regarding efficacy, immunogenicity, and safety.

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.

Translating questions to estimands in randomized clinical trials with intercurrent events.

Intercurrent (post-treatment) events occur frequently in randomized trials, and investigators often express interest in treatment effects that suitably take account of these events. Contrasts that naively condition on intercurrent events do not have a straight-forward causal interpretation, and the practical relevance of other commonly used approaches is debated. In this work, we discuss how to formulate and choose an estimand, beyond the marginal intention-to-treat effect, from the point of view of a decision maker and drug developer. In particular, we argue that careful articulation of a practically useful research question should either reflect decision making at this point in time or future drug development. Indeed, a substantially interesting estimand is simply a formalization of the (plain English) description of a research question. A common feature of estimands that are practically useful is that they correspond to possibly hypothetical but well-defined interventions in identifiable (sub)populations. To illustrate our points, we consider five examples that were recently used to motivate consideration of principal stratum estimands in clinical trials. In all of these examples, we propose alternative causal estimands, such as conditional effects, sequential regime effects, and separable effects, that correspond to explicit research questions of substantial interest.

Sequential modeling for a class of reference-based imputation methods in clinical trials with quantitative or binary outcomes.

We consider treatment effect estimation in a randomized clinical trial with longitudinally measured quantitative or categorical outcomes. To handle missing data, we usually assume missing at random and then conduct sensitivity analysis for missing not at random. In the literature, several reference-based imputation methods, including "jump to reference" (J2R) and "copy reference" (CR), have been commonly used for conducting sensitivity analysis. J2R assumes the mean effect profile of patients who discontinue the investigative treatment jumps to that of the patients in the reference group after discontinuation, while CR assumes the conditional mean effect profile given the status prior to the time of discontinuation copies that of the patients in the reference group after discontinuation. In this article, we propose a novel, wide class of reference-based imputation methods for conducting sensitivity analysis, which includes J2R and CR as two extreme ends. The framework is motivated by the thought that the investigative treatment may have no, partially, or fully carried-over effect after deviation from the assigned treatment (eg, discontinue the assigned treatment or change to a different treatment). Further, we show that the proposed reference-based imputation methods can be implemented through sequential modeling. This property ensures that the methods can be applied to clinical trials with either quantitative or categorical outcomes. We use both causal-inference arguments and numerical examples to demonstrate the performance of the proposed methods.

How measurements affected by medication use are reported and handled in observational research: A literature review.

PURPOSE: In epidemiological research, measurements affected by medication, for example, blood pressure lowered by antihypertensives, are common. Different ways of handling medication are required depending on the research questions and whether the affected measurement is the exposure, the outcome, or a confounder. This study aimed to review handling of medication use in observational research. METHODS: PubMed was searched for etiological studies published between 2015 and 2019 in 15 high-ranked journals from cardiology, diabetes, and epidemiology. We selected studies that analyzed blood pressure, glucose, or lipid measurements (whether exposure, outcome or confounder) by linear or logistic regression. Two reviewers independently recorded how medication use was handled and assessed whether the methods used were in accordance with the research aim. We reported the methods used per variable category (exposure, outcome, confounder). RESULTS: A total of 127 articles were included. Most studies did not perform any method to account for medication use (exposure 58%, outcome 53%, and confounder 45%). Restriction (exposure 22%, outcome 23%, and confounders 10%), or adjusting for medication use using a binary indicator were also used frequently (exposure: 18%, outcome: 19%, confounder: 45%). No advanced methods were applied. In 60% of studies, the methods' validity could not be judged due to ambiguous reporting of the research aim. Invalid approaches were used in 28% of the studies, mostly when the affected variable was the outcome (36%). CONCLUSION: Many studies ambiguously stated the research aim and used invalid methods to handle medication use. Researchers should consider a valid methodological approach based on their research question.

Rethinking intercurrent events in defining estimands for tuberculosis trials.

BACKGROUND/AIMS: Tuberculosis remains one of the leading causes of death from an infectious disease globally. Both choices of outcome definitions and approaches to handling events happening post-randomisation can change the treatment effect being estimated, but these are often inconsistently described, thus inhibiting clear interpretation and comparison across trials. METHODS: Starting from the ICH E9(R1) addendum's definition of an estimand, we use our experience of conducting large Phase III tuberculosis treatment trials and our understanding of the estimand framework to identify the key decisions regarding how different event types are handled in the primary outcome definition, and the important points that should be considered in making such decisions. A key issue is the handling of intercurrent (i.e. post-randomisation) events (ICEs) which affect interpretation of or preclude measurement of the intended final outcome. We consider common ICEs including treatment changes and treatment extension, poor adherence to randomised treatment, re-infection with a new strain of tuberculosis which is different from the original infection, and death. We use two completed tuberculosis trials (REMoxTB and STREAM Stage 1) as illustrative examples. These trials tested non-inferiority of new tuberculosis treatment regimens versus a control regimen. The primary outcome was a binary composite endpoint, 'favourable' or 'unfavourable', which was constructed from several components. RESULTS: We propose the following improvements in handling the above-mentioned ICEs and loss to follow-up (a post-randomisation event that is not in itself an ICE). First, changes to allocated regimens should not necessarily be viewed as an unfavourable outcome; from the patient perspective, the potential harms associated with a change in the regimen should instead be directly quantified. Second, handling poor adherence to randomised treatment using a per-protocol analysis does not necessarily target a clear estimand; instead, it would be desirable to develop ways to estimate the treatment effects more relevant to programmatic settings. Third, re-infection with a new strain of tuberculosis could be handled with different strategies, depending on whether the outcome of interest is the ability to attain culture negativity from infection with any strain of tuberculosis, or specifically the presenting strain of tuberculosis. Fourth, where possible, death could be separated into tuberculosis-related and non-tuberculosis-related and handled using appropriate strategies. Finally, although some losses to follow-up would result in early treatment discontinuation, patients lost to follow-up before the end of the trial should not always be classified as having an unfavourable outcome. Instead, loss to follow-up should be separated from not completing the treatment, which is an ICE and may be considered as an unfavourable outcome. CONCLUSION: The estimand framework clarifies many issues in tuberculosis trials but also challenges trialists to justify and improve their outcome definitions. Future trialists should consider all the above points in defining their outcomes.

A novel estimand to adjust for rescue treatment in randomized clinical trials.

The interpretation of randomized clinical trial results is often complicated by intercurrent events. For instance, rescue medication is sometimes given to patients in response to worsening of their disease, either in addition to the randomized treatment or in its place. The use of such medication complicates the interpretation of the intention-to-treat analysis. In view of this, we propose a novel estimand defined as the intention-to-treat effect that would have been observed, had patients on the active arm been switched to rescue medication if and only if they would have been switched when randomized to control. This enables us to disentangle the treatment effect from the effect of rescue medication on a patient's outcome, while tempering the strong extrapolations that are typically needed when inferring what the intention-to-treat effect would have been in the absence of rescue medication. We propose a novel inverse probability weighting method for estimating this effect in settings where the decision to initiate rescue medication is made at one prespecified time point. This estimator relies on specific untestable assumptions, in view of which we propose a sensitivity analysis. We use the method for the analysis of a clinical trial conducted by Janssen Pharmaceuticals, in which patients with type 2 diabetes mellitus can switch to rescue medication for ethical reasons. Monte Carlo simulations confirm that the proposed estimator is unbiased in moderate sample sizes.

Estimands in practice: Bridging the gap between study objectives and statistical analysis.

The International Council for Harmonisation (ICH) guideline E9 Statistical Principles for Clinical Trials (1) was issued in 1998. In October 2014, an addendum to ICH E9 was proposed on statistical principles relating to estimands and sensitivity analyses. The final version of the addendum to ICH E9 (R1) (2) was issued in November 2019. This virtual edition of Pharmaceutical Statistics takes a closer look at some of the progress that has been made since 2018 when implementing the estimand framework within clinical research. The articles discussed in this virtual issue are not new, but a compilation from previous issues. This specific article will act as a refresher for those not familiar with the topic and discuss the ABCs of estimands and their proposed deployment for improving the quality of clinical research. An overview of the more recent Pharmaceutical Statistics articles on estimands will be provided, signifying areas where progress have been made. The articles should be considered as contributions to the ongoing discussions rather than the final word. Finally, a personal perspective on the estimand success story and remaining challenges with proposed solutions will be discussed.

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.

Implementation of tripartite estimands using adherence causal estimators under the causal inference framework.

Intercurrent events (ICEs) and missing values are inevitable in clinical trials of any size and duration, making it difficult to assess the treatment effect for all patients in randomized clinical trials. Defining the appropriate estimand that is relevant to the clinical research question is the first step in analyzing data. The tripartite estimands, which evaluate the treatment differences in the proportion of patients with ICEs due to adverse events, the proportion of patients with ICEs due to lack of efficacy, and the primary efficacy outcome for those who can adhere to study treatment under the causal inference framework, are of interest to many stakeholders in understanding the totality of treatment effects. In this manuscript, we discuss the details of how to estimate tripartite estimands based on a causal inference framework and how to interpret tripartite estimates through a phase 3 clinical study evaluating a basal insulin treatment for patients with type 1 diabetes.