Trimmed means for symptom trials with dropouts

Single-world intervention graphs for defining, identifying, and communicating estimands in clinical trials

Confusion often arises when attempting to articulate target estimand(s) of a clinical trial in plain language. We aim to rectify this confusion by using a type of causal graph called the Single-World Intervention Graph (SWIG) to provide a visual representation of the estimand that can be effectively communicated to interdisciplinary stakeholders. These graphs not only display estimands, but also illustrate the assumptions under which a causal estimand is identifiable by presenting the graphical relationships between the treatment, intercurrent events, and clinical outcomes. To demonstrate its usefulness in pharmaceutical research, we present examples of SWIGs for various intercurrent event strategies specified in the ICH E9(R1) addendum, as well as an example from a real-world clinical trial for chronic pain. code to generate all the SWIGs shown is this paper is made available. We advocate clinical trialists adopt the use of SWIGs in their estimand discussions during the planning stages of their studies.

EXCHANGE-2: investigating the efficacy of add-on plasma exchange as an adjunctive strategy against septic shock-a study protocol for a randomized, prospective, multicenter, open-label, controlled, parallel-group trial

BACKGROUND

Sepsis is as a life-threatening organ dysfunction caused by a dysregulated host response to an infection. The mortality of sepsis and particular of septic shock is very high. Treatment mostly focuses on infection control but a specific intervention that targets the underlying pathological host response is lacking to the present time. The investigators hypothesize that early therapeutic plasma exchange (TPE) will dampen the maladaptive host response by removing injurious mediators thereby limiting organ dysfunction and improving survival in patients with septic shock. Although small prospective studies demonstrated rapid hemodynamic stabilization under TPE, no adequately powered randomized clinical trial has investigated hard outcomes.

METHODS

This is a randomized, prospective, multicenter, open-label, controlled, parallel-group interventional trial to test the adjunctive effect of TPE in patients with early septic shock. Patients with a refractory (defined as norepinephrine (NE) ≥ 0.4 μg/kg/min ≥ 30 min OR NE 0.3 μg/kg/min + vasopressin) and early (shock onset < 24 h) septic shock will be included. The intervention is a standard TPE with donor fresh frozen plasma (1.2 × individual plasma volume) performed within 6 h after randomization and will be compared to a standard of care (SOC) control arm. The primary endpoint is 28 days mortality for which the power analysis revealed a group size of 137 / arm (n = 274) to demonstrate a benefit of 15%. The key secondary objective will be to compare the extent of organ failure indicated by mean SOFA over the first 7 days as well as organ support-free days until day 28 following randomization. Besides numerous biological secondary, safety endpoints such as incidence of bleeding, allergic reactions, transfusion associated lung injury, severe thrombocytopenia, and other severe adverse events will be assessed during the first 7 days. For exploratory scientific analyses, biomaterial will be acquired longitudinally and multiple predefined scientific subprojects are planned. This study is an investigator-initiated trial supported by the German Research Foundation (DFG, DA 1209/7-1), in which 26 different centers in Germany, Switzerland, and Austria will participate over a duration of 33 months.

DISCUSSION

This trial has substantial clinical relevance as it evaluates a promising adjunctive treatment option in refractory septic shock patients suffering from an extraordinary high mortality. A positive trial result could change the current standard of care for this septic subgroup. The results of this study will be disseminated through presentations at international congresses, workshops, and peer-reviewed publications.

TRIAL REGISTRATION

ClinicalTrials.gov NCT05726825 , Registered on 14 February 2023.

Using principal stratification in analysis of clinical trials

The ICH E9(R1) addendum (2019) proposed principal stratification (PS) as one of five strategies for dealing with intercurrent events. Therefore, understanding the strengths, limitations, and assumptions of PS is important for the broad community of clinical trialists. Many approaches have been developed under the general framework of PS in different areas of research, including experimental and observational studies. These diverse applications have utilized a diverse set of tools and assumptions. Thus, need exists to present these approaches in a unifying manner. The goal of this tutorial is threefold. First, we provide a coherent and unifying description of PS. Second, we emphasize that estimation of effects within PS relies on strong assumptions and we thoroughly examine the consequences of these assumptions to understand in which situations certain assumptions are reasonable. Finally, we provide an overview of a variety of key methods for PS analysis and use a real clinical trial example to illustrate them. Examples of code for implementation of some of these approaches are given in Supplemental Materials.

A hybrid return to baseline imputation method to incorporate MAR and MNAR dropout missingness

Missing data are inevitable in longitudinal clinical trials due to intercurrent events (ICEs) such as treatment interruption or premature discontinuation for different reasons. Missing at random (MAR) assumption is usually unverifiable and sensitivity analyses are often requested under missing not at random (MNAR) assumption. Return to baseline (RTB) imputation is a commonly used MNAR method. In practice, not all dropout missingness can be assumed MNAR. For example, missingness or dropouts due to COVID-19 can be reasonably assumed MAR. Therefore, traditional RTB is not applicable when there is both MAR and MNAR dropout missingness. Here we propose a hybrid strategy for RTB imputation which can handle missing data due to MAR and MNAR dropouts at the same time. Standard multiple imputation approach is proposed and an analytic likelihood based approach is derived to improve efficiency.

Impute the missing data using retrieved dropouts

Background

In the past few decades various methods have been proposed to handle missing data of clinical studies, so as to assess the robustness of primary results. Some of the methods are based on the assumption of missing at random (MAR) which assumes subjects who discontinue the treatment will maintain the treatment effect after discontinuation. The agency, however, has expressed concern over methods based on this overly optimistic assumption, because it hardly holds for subjects discontinuing the investigational drug. Although in recent years a good number of sensitivity analyses based on missing not at random (MNAR) assumptions have been proposed, some use very conservative assumption on which it might be hard for sponsors and regulators to reach common ground.

Methods

Here we propose a multiple imputation method targeting at “treatment policy” estimand based on the MNAR assumption. This method can be used as the primary analysis, in addition to serving as a sensitivity analysis. It imputes missing data using information from retrieved dropouts defined as subjects who remain in the study despite occurrence of intercurrent events. Then imputed data long with completers and retrieved dropouts are analyzed altogether and finally multiple results are summarized into a single estimate. According to definition in ICH E9 (R1), this proposed approach fully aligns with the treatment policy estimand but its assumption is much more realistic and reasonable.

Results

Our approach has well controlled type I error rate with no loss of power. As expected, the effect size estimates take into account any dilution effect contributed by retrieved dropouts, conforming to the MNAR assumption.

Conclusions

Although multiple imputation approaches are always used as sensitivity analyses, this multiple imputation approach can be used as primary analysis for trials with sufficient retrieved dropouts or trials designed to collect retrieved dropouts.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12874-022-01509-9.

Sensitivity to missing not at random dropout in clinical trials: Use and interpretation of the trimmed means estimator

Outcome values in randomized controlled trials (RCTs) may be missing not at random (MNAR), if patients with extreme outcome values are more likely to drop out (eg, due to perceived ineffectiveness of treatment, or adverse effects). In such scenarios, estimates from complete case analysis (CCA) and multiple imputation (MI) will be biased. We investigate the use of the trimmed means (TM) estimator for the case of univariable missingness in one continuous outcome. The TM estimator operates by setting missing values to the most extreme value, and then “trimming” away equal fractions of both groups, estimating the treatment effect using the remaining data. The TM estimator relies on two assumptions, which we term the “strong MNAR” and “location shift” assumptions. We derive formulae for the TM estimator bias resulting from the violation of these assumptions for normally distributed outcomes. We propose an adjusted TM estimator, which relaxes the location shift assumption and detail how our bias formulae can be used to establish the direction of bias of CCA and TM estimates, to inform sensitivity analyses. The TM approach is illustrated in a sensitivity analysis of the CoBalT RCT of cognitive behavioral therapy (CBT) in 469 individuals with 46 months follow‐up. Results were consistent with a beneficial CBT treatment effect, with MI estimates closer to the null and TM estimates further from the null than the CCA estimate. We propose using the TM estimator as a sensitivity analysis for data where extreme outcome value dropout is plausible.

Connecting Instrumental Variable methods for causal inference to the Estimand Framework

Causal inference methods are gaining increasing prominence in pharmaceutical drug development in light of the recently published addendum on estimands and sensitivity analysis in clinical trials to the E9 guideline of the International Council for Harmonisation. The E9 addendum emphasises the need to account for post-randomization or 'intercurrent' events that can potentially influence the interpretation of a treatment effect estimate at a trial's conclusion. Instrumental Variables (IV) methods have been used extensively in economics, epidemiology, and academic clinical studies for 'causal inference,' but less so in the pharmaceutical industry setting until now. In this tutorial article we review the basic tools for causal inference, including graphical diagrams and potential outcomes, as well as several conceptual frameworks that an IV analysis can sit within. We discuss in detail how to map these approaches to the Treatment Policy, Principal Stratum and Hypothetical 'estimand strategies' introduced in the E9 addendum, and provide details of their implementation using standard regression models. Specific attention is given to discussing the assumptions each estimation strategy relies on in order to be consistent, the extent to which they can be empirically tested and sensitivity analyses in which specific assumptions can be relaxed. We finish by applying the methods described to simulated data closely matching two recent pharmaceutical trials to further motivate and clarify the ideas.

Identifying treatment effects using trimmed means when data are missing not at random

Patients often discontinue from a clinical trial because their health condition is not improving or they cannot tolerate the assigned treatment. Consequently, the observed clinical outcomes in the trial are likely better on average than if every patient had completed the trial. If these differences between trial completers and non-completers cannot be explained by the observed data, then the study outcomes are missing not at random (MNAR). One way to overcome this problem-the trimmed means approach for missing data due to study discontinuation-sets missing values as the worst observed outcome and then trims away a fraction of the distribution from each treatment arm before calculating differences in treatment efficacy (Permutt T, Li F. Trimmed means for symptom trials with dropouts. Pharm Stat. 2017;16(1):20-28). In this paper, we derive sufficient and necessary conditions for when this approach can identify the average population treatment effect. Simulation studies show the trimmed means approach's ability to effectively estimate treatment efficacy when data are MNAR and missingness due to study discontinuation is strongly associated with an unfavorable outcome, but trimmed means fail when data are missing at random. If the reasons for study discontinuation in a clinical trial are known, analysts can improve estimates with a combination of multiple imputation and the trimmed means approach when the assumptions of each hold. We compare the methodology to existing approaches using data from a clinical trial for chronic pain. An R package trim implements the method. When the assumptions are justifiable, using trimmed means can help identify treatment effects notwithstanding MNAR data.

Estimands and missing data in clinical trials of chronic pain treatments: advances in design and analysis

In clinical trials of treatments for chronic pain, the percentage of participants who withdraw early can be as high as 50%. Major reasons for early withdrawal in these studies include perceived lack of efficacy and adverse events. Commonly used strategies for accommodating missing data include last observation carried forward, baseline observation carried forward, and more principled methods such as mixed-model repeated-measures and multiple imputation. All these methods require strong and untestable assumptions concerning the conditional distribution of outcomes after dropout, given the observed data. We review recent developments in statistical methods for handling missing data in clinical trials, including implications of the increased emphasis being placed on precise formulation of the study objectives and the estimand (treatment effect to be estimated) of interest. A flexible method that seems to be well suited for the analysis of chronic pain clinical trials is control-based imputation, which allows a variety of assumptions to be made concerning the conditional distribution of postdropout outcomes that can be tailored to the estimand of interest. These assumptions can depend, for example, on the stated reasons for dropout. We illustrate these methods using data from 4 clinical trials of pregabalin for the treatment of painful diabetic peripheral neuropathy and postherpetic neuralgia. When planning chronic pain clinical trials, careful consideration of the trial objectives should determine the definition of the trial estimand, which in turn should inform methods used to accommodate missing data in the statistical analysis.

Essential statistical principles of clinical trials of pain treatments

This article presents an overview of fundamental statistical principles of clinical trials of pain treatments. Statistical considerations relevant to phase 2 proof of concept and phase 3 confirmatory randomized trials investigating efficacy and safety are discussed, including (1) research design; (2) endpoints and analyses; (3) sample size determination and statistical power; (4) missing data and trial estimands; (5) data monitoring and interim analyses; and (6) interpretation of results. Although clinical trials of pharmacologic treatments are emphasized, the key issues raised by these trials are also directly applicable to clinical trials of other types of treatments, including biologics, devices, nonpharmacologic therapies (eg, physical therapy and cognitive-behavior therapy), and complementary and integrative health interventions.

The attributable estimand: A new approach to account for intercurrent events

The term "intercurrent events" has recently been used to describe events in clinical trials that may complicate the definition and calculation of the treatment effect estimand. This paper focuses on the use of an attributable estimand to address intercurrent events. Those events that are considered to be adversely related to randomized treatment (eg, discontinuation due to adverse events or lack of efficacy) are considered attributable and handled with a composite estimand strategy, while a hypothetical estimand strategy is used for intercurrent events not considered to be related to randomized treatment (eg, unrelated adverse events). We explore several options for how to implement this approach and compare them to hypothetical "efficacy" and treatment policy estimand strategies through a series of simulation studies whose design is inspired by recent trials in chronic obstructive pulmonary disease (COPD), and we illustrate through an analysis of a recently completed COPD trial.

A constructive critique of the draft ICH E9 Addendum

In this article, I review the key elements of the proposed International Council for Harmonisation of Technical Requirements for Pharmaceuticals for Human Use E9 Addendum, present a constructive critique, and provide recommendations of how it can be improved. To highlight ideas, I present a case study involving a confirmatory trial for a chronic pain medication.

Analytical approaches and estimands to take account of missing patient-reported data in longitudinal studies

Patient-reported outcomes, such as quality of life, functioning, and symptoms, are used widely in therapeutic and behavioral trials and are increasingly used in drug development to represent the patient voice. Missing patient reported data is common and can undermine the validity of results reporting by reducing power, biasing estimates, and ultimately reducing confidence in the results. In this paper, we review statistically principled approaches for handling missing patient-reported outcome data and introduce the idea of estimands in the context of behavioral trials. Specifically, we outline a plan that considers missing data at each stage of research: design, data collection, analysis, and reporting. The design stage includes processes to prevent missing data, define the estimand, and specify primary and sensitivity analyses. The analytic strategy considering missing data depends on the estimand. Reviewed approaches include maximum likelihood-based models, multiple imputation, generalized estimating equations, and responder analysis. We outline sensitivity analyses to assess the robustness of the primary analysis results when data are missing. We also describe ad-hoc methods, including approaches to avoid. Last, we demonstrate methods using data from a behavioral intervention, where the primary outcome was self-reported cognition.

Defining treatment effects: A regulatory perspective

The proposed addendum to the International Conference on Harmonization document, Statistical Principles for Clinical Trials, can be read in two ways. There is a new framework for talking about estimands, but is it about fitting present methods into the framework? Or is it about changing methods? My answer: some of each. Where different methods are needed, there are challenging problems in estimating some desirable estimands, but there may also be desirable estimands that can be estimated easily and robustly.

Defining Treatment Effects: A Primer for Nonstatisticians

It would often be of interest to know the effect of a drug compared to control in people who take the drug. However, different people will likely take the drug and the control. Thus, comparing takers of the drug to takers of the control does not yield a drug effect. Drug effects in drug takers can be estimated, but first they must be carefully defined.

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.