Clinical trials that investigate interventions on physical activity often use accelerometers to measure step count at a very granular level, often in 5-second epochs. Participants typically wear the accelerometer for a week-long period at baseline, and for one or more week-long follow-up periods after the intervention. The data is usually aggregated to provide daily or weekly step counts for the primary analysis. Missing data are common as participants may not wear the device as per protocol. Approaches to handling missing data in the literature have largely defined missingness on the day level using a threshold on daily wear time, which leads to loss of information on the time of day when data are missing. We propose an approach to identifying and classifying missingness at the finer epoch-level, and then present two approaches to handling missingness. Firstly, we present a parametric approach which takes into account the number of missing epochs per day. Secondly, we describe a non-parametric approach to Multiple Imputation (MI) where missing periods during the day are replaced by donor data from the same person where possible, or data from a different person who is matched on demographic and physical activity-related variables. Our simulation studies comparing these approaches in a number of settings show that the non-parametric approach leads to estimates of the effect of treatment that are least biased while maintaining small standard errors. We illustrate the application of these different MI strategies to the analysis of the 2017 PACE-UP Trial. The proposed framework of classifying missingness and applying MI at the epoch-level is likely to be applicable to a number of different outcomes and data from other wearable devices.
Return-to-baseline is an important method to impute missing values or unobserved potential outcomes when certain hypothetical strategies are used to handle intercurrent events in clinical trials. Current return-to-baseline approaches seen in literature and in practice inflate the variability of the "complete" dataset after imputation and lead to biased mean estimators {when the probability of missingness depends on the observed baseline and/or postbaseline intermediate outcomes}. In this article, we first provide a set of criteria a return-to-baseline imputation method should satisfy. Under th…
We present a framework for generating multiple imputations for continuous data when the missing data mechanism is unknown. Imputations are generated from more than one imputation model in order to incorporate uncertainty regarding the missing data mechanism. Parameter estimates based on the different imputation models are combined using rules for nested multiple imputation. Through the use of simulation, we investigate the impact of missing data mechanism uncertainty on post-imputation inferences and show that incorporating this uncertainty can increase the coverage of parameter estimates. We …
Missing data is inevitable in longitudinal clinical trials. Conventionally, the missing at random assumption is assumed to handle missingness, which however is unverifiable empirically. Thus, sensitivity analysis is critically important to assess the robustness of the study conclusions against untestable assumptions. Toward this end, regulatory agencies often request using imputation models such as return-to-baseline, control-based, and washout imputation. Multiple imputation is popular in sensitivity analysis; however, it may be inefficient and result in an unsatisfying interval estimation by…
To select outcomes for clinical trials testing experimental therapies for Huntington disease, a fatal neurodegenerative disorder, analysts model how potential outcomes change over time. Yet, subjects with Huntington disease are often observed at different levels of disease progression. To account for these differences, analysts include time to clinical diagnosis as a covariate when modeling potential outcomes, but this covariate is often censored. One popular solution is imputation, whereby we impute censored values using predictions from a model of the censored covariate given other data, the…
Missing data is unavoidable in longitudinal clinical trials, and outcomes are not always normally distributed. In the presence of outliers or heavy-tailed distributions, the conventional multiple imputation with the mixed model with repeated measures analysis of the average treatment effect (ATE) based on the multivariate normal assumption may produce bias and power loss. Control-based imputation (CBI) is an approach for evaluating the treatment effect under the assumption that participants in both the test and control groups with missing outcome data have a similar outcome profile as those wi…
Data collected in clinical trials are often composed of multiple types of variables. For example, laboratory measurements and vital signs are longitudinal data of continuous or categorical variables, adverse events may be recurrent events, and death is a time-to-event variable. Missing data due to patients' discontinuation from the study or as a result of handling intercurrent events using a hypothetical strategy almost always occur during any clinical trial. Imputing these data with mixed types of variables simultaneously is a challenge that has not been studied extensively. In this article, …
Although approaches for handling missing data from longitudinal studies are well-developed when the patterns of missingness are monotone, fewer methods are available for non-monotone missingness. Moreover, the conventional missing at random (MAR) assumption -- a natural benchmark for monotone missingness -- does not model realistic beliefs about non-monotone missingness processes (Robins and Gill, 1997). This has provided the impetus for alternative non-monotone missing not at random (MNAR) mechanisms. The "no self-censoring" (NSC) model is such a mechanism and assumes the probability an outco…
Results from clinical trials can be susceptible to bias if investigators choose their analysis approach after seeing trial data, as this can allow them to perform multiple analyses and then choose the method that provides the most favourable result (commonly referred to as 'p-hacking'). Pre-specification of the planned analysis approach is essential to help reduce such bias, as it ensures analytical methods are chosen in advance of seeing the trial data. However, pre-specification is only effective if done in a way that does not allow p-hacking. For example, investigators may pre-specify a cer…
Reference based multiple imputation methods have become popular for handling missing data in randomised clinical trials. Rubin's variance estimator is well known to be biased compared to the reference based imputation estimator's true repeated sampling variance. Somewhat surprisingly given the increasingly popularity of these methods, there has been relatively little debate in the literature as to whether Rubin's variance estimator or alternative (smaller) variance estimators targeting the repeated sampling variance are more appropriate. We review the arguments made on both sides of this debat…
Parkinson's disease (PD) is a chronic, degenerative neurological disorder. PD cannot be prevented, slowed or cured as of today but highly effective symptomatic treatments are available. We consider relevant estimands and treatment effect estimators for randomized trials of a novel treatment which aims to slow down disease progression versus placebo in early, untreated PD. A commonly used endpoint in PD trials is the MDS-Unified Parkinson's Disease Rating Scale (MDS-UPDRS), which is longitudinally assessed at scheduled visits. The most important intercurrent events (ICEs) which affect the inter…
Bayesian analysis of the causal reference-based model for missing data in clinical trials, accommodating partially observed post-intercurrent event data
In many clinical trials, outcomes of interest include binary-valued endpoints. It is not uncommon that a binary-valued outcome is dichotomized from a continuous outcome at a threshold of clinical interest. To reach the objective, common approaches include (a) fitting the generalized linear mixed model (GLMM) to the dichotomized longitudinal binary outcome and (b) imputation method (MI): imputing the missing values in the continuous outcome, dichotomizing it into a binary outcome, and then fitting the generalized linear model for the "complete" data. We conducted comprehensive simulation studie…
An efficient monotone data augmentation (MDA) algorithm is proposed for missing data imputation for incomplete multivariate nonnormal data that may contain variables of different types, and are modeled by a sequence of regression models including the linear, binary logistic, multinomial logistic, proportional odds, Poisson, negative binomial, skew-normal, skew-t regressions or a mixture of these models. The MDA algorithm is applied to the sensitivity analyses of longitudinal trials with nonignorable dropout using the controlled pattern imputations that assume the treatment effect reduces or di…
When data are collected subject to a detection limit, observations below the detection limit may be considered censored. In addition, the domain of such observations may be restricted; for example, values may be required to be non-negative. We propose a regression method for censored observations that also accounts for domain restriction. The method finds maximum likelihood estimates assuming an underlying truncated normal distribution. We show that our method, tcensReg, outperforms other methods commonly used for data with detection limits such as Tobit regression and single imputation of the…
Trial-based cost-effectiveness analyses (CEAs) are an important source of evidence in the assessment of health interventions. In these studies, cost and effectiveness outcomes are commonly measured at multiple time points, but some observations may be missing. Restricting the analysis to the participants with complete data can lead to biased and inefficient estimates. Methods, such as multiple imputation, have been recommended as they make better use of the data available and are valid under less restrictive Missing At Random (MAR) assumption. Linear mixed effects models (LMMs) offer a simple …
Clinical trials with longitudinal outcomes typically include missing data due to missed assessments or structural missingness of outcomes after intercurrent events handled with a hypothetical strategy. Approaches based on Bayesian random multiple imputation and Rubin's rule for pooling results across multiple imputed datasets are increasingly used in order to align the analysis of these trials with the targeted estimand. We propose and justify deterministic conditional mean imputation combined with the jackknife for inference as an alternative approach. The method is applicable to imputations …
In clinical trials, mixed effects models for repeated measures (MMRM) and pattern mixture models (PMM) are often used to analyze longitudinal continuous outcomes. We describe a simple missing data imputation algorithm for the MMRM that can be easily implemented in standard statistical software packages such as SAS PROC MI. We explore the relationship of the missing data distribution in the control-based and delta-adjusted PMMs with that in the MMRM, and suggest an efficient imputation algorithm for these PMMs. The unobserved values in PMMs can be imputed by subtracting the mean difference in t…
Censored survival data are common in clinical trial studies. We propose a unified framework for sensitivity analysis to censoring at random in survival data using multiple imputation and martingale, called SMIM. The proposed framework adopts the δ-adjusted and control-based models, indexed by the sensitivity parameter, entailing censoring at random and a wide collection of censoring not at random assumptions. Also, it targets for a broad class of treatment effect estimands defined as functionals of treatment-specific survival functions, taking into account of missing data due to censoring. Mul…
We focus on the problem of generalizing a causal effect estimated on a randomized controlled trial (RCT) to a target population described by a set of covariates from observational data. Available methods such as inverse propensity sampling weighting are not designed to handle missing values, which are however common in both data sources. In addition to coupling the assumptions for causal effect identifiability and for the missing values mechanism and to defining appropriate estimation strategies, one difficulty is to consider the specific structure of the data with two sources and treatment an…
Randomized controlled trials are considered the gold standard to evaluate the treatment effect (estimand) for efficacy and safety. According to the recent International Council on Harmonisation (ICH)-E9 addendum (R1), intercurrent events (ICEs) need to be considered when defining an estimand, and principal stratum is one of the five strategies to handle ICEs. Qu et al. (2020, Statistics in Biopharmaceutical Research 12:1-18) proposed estimators for the adherer average causal effect (AdACE) for estimating the treatment difference for those who adhere to one or both treatments based on the causa…
Public policy-makers use cost-effectiveness analyses (CEA) to decide which health and social care interventions to provide. Appropriate methods have not been developed for handling missing data in complex settings, such as for CEA that use data from cluster randomised trials (CRTs). We present a multilevel multiple imputation (MI) approach that recognises when missing data have a hierarchical structure, and is compatible with the bivariate multilevel models used to report cost-effectiveness. We contrast the multilevel MI approach with single-level MI and complete case analysis in a CEA alongsi…
Missing observations are common in cluster randomised trials. Approaches taken to handling such missing data include: complete case analysis, single-level multiple imputation that ignores the clustering, multiple imputation with a fixed effect for each cluster and multilevel multiple imputation. We conducted a simulation study to assess the performance of these approaches, in terms of confidence interval coverage and empirical bias in the estimated treatment effects. Missing-at-random clustered data scenarios were simulated following a full-factorial design. An Analysis of Variance was carried…
We propose a copula based method to handle missing values in multivariate data of mixed types in multilevel data sets. Building upon the extended rank likelihood of \cite{hoff2007extending} and the multinomial probit model, our model is a latent variable model which is able to capture the relationship among variables of different types as well as accounting for the clustering structure. We fit the model by approximating the posterior distribution of the parameters and the missing values through a Gibbs sampling scheme. We use the multiple imputation procedure to incorporate the uncertainty due…
Causal inference from observational data can be viewed as a missing data problem arising from a hypothetical population-scale randomized trial matched to the observational study. This links a target trial protocol with a corresponding generative predictive model for inference, providing a complete framework for transparent communication of causal assumptions and statistical uncertainty on treatment effects, without the need for counterfactuals. The intuitive foundation for the work is that a whole population randomized trial would provide answers to any observable causal question with certaint…
Non-adherence to assigned treatment is common in randomised controlled trials (RCTs). Recently, there has been an increased interest in estimating causal effects of treatment received, for example the so-called local average treatment effect (LATE). Instrumental variables (IV) methods can be used for identification, with estimation proceeding either via fully parametric mixture models or two-stage least squares (TSLS). TSLS is popular but can be problematic for binary outcomes where the estimand of interest is a causal odds ratio. Mixture models are rarely used in practice, perhaps because of …
Missing outcomes are a commonly occurring problem for cluster randomised trials, which can lead to biased and inefficient inference if ignored or handled inappropriately. Two approaches for analysing such trials are cluster-level analysis and individual-level analysis. In this study, we assessed the performance of unadjusted cluster-level analysis, baseline covariate adjusted cluster-level analysis, random effects logistic regression (RELR) and generalised estimating equations (GEE) when binary outcomes are missing under a baseline covariate dependent missingness mechanism. Missing outcomes we…
Attrition is a common occurrence in cluster randomised trials (CRTs) which leads to missing outcome data. Two approaches for analysing such trials are cluster-level analysis and individual-level analysis. This paper compares the performance of unadjusted cluster-level analysis, baseline covariate adjusted cluster-level analysis and linear mixed model (LMM) analysis, under baseline covariate dependent missingness (CDM) in continuous outcomes, in terms of bias, average estimated standard error and coverage probability. The methods of complete case analysis (CCA) and multiple imputation (MI) are …
