Pattern-mixture sensitivity analysis in longitudinaltrials with drop-out

e15003 Background: Stella Trial is a phase III, multinational, double-blind and randomized study to confirm clinical similarity between MB02 and EU-bevacizumab in patients with stage IIIB/IV no squamous NSCLC. 627 subjects with newly diagnosed or recurrent stage IIIb/IV NSCLC were randomized 1:1 to receive either MB02 or EU-bevacizumab plus chemotherapy (paclitaxel and carboplatin) every 3-week cycle for six cycles (week 18) followed by MB02/bevacizumab in blinded monotherapy until disease progression, treatment intolerance, death, patient withdrawal or end of study (w52). An approach targeting the MI of the continuous sum of target diameters (mm), and subsequent categorization of Overall Response (OR) was performed as sensitivity analysis for the assessment of the primary endpoint. Multiple Imputation (MI) has emerged as a credible method to assess the effects of missing data (MD), an inescapable problem with a potential ability to undermine research results' strength and validity in a clinical study, providing the user with a valuable toolset to sufficiently account for the varying types of MD and appropriately adjust the assumptions. Methods: The primary endpoint of the study was Objective Response Rate (ORR) at week 18 per an Independent Radiological Committee (IRC) in the Intention to treat set (ITT). The ORR was analysed with a Cochran-Mantel-Haenszel model, including the stratification factors of sex, smoking status, disease diagnosis and disease stage, comparing the stratified estimates risk difference (RD). In addition, these results were analysed implementing a pattern-mixture MI process accounting for missing at random (MAR) and missing not at random (MNAR) data based on the sum of target diameters in subjects without tumour response data or falling into the categories NonCR/NonPD or non-evaluable (NE). Results: The clinical equivalence of MB02 with EU-bevacizumab is demonstrated by the efficacy data provided through the primary endpoint and the MI sensitive analysis applied. The MI (MAR and MNAR) represents an added value that supports the biosimilarity of MB02 and EU-bevacizumab. The results for the primary analysis of the RD in ORR at w18 in the ITT set were entirely contained within the boundaries of predefined margins (±12): -4.02 [95% CI: -11.76 to 3.71]). Under MI, the ORR RD showed similarity at 95% CIs (-1.92; 95% CI: -10.02 to 6.19) and using the multiple imputations for subjects without tumour response data (missing, NonCR/NonPD or NE), the ORR RD was -2.22 with 95% CI of (-10.54 to 6.10) at w18 in the ITT. Conclusions: The clinical equivalence of MB02 with EU-bevacizumab is demonstrated by the efficacy data provided through the primary endpoint and the MI sensitive analysis applied. The MI (MAR and MNAR) represent an added value that supports the biosimilarity of MB02 and EU-bevacizumab. Clinical trial information: NCT03296163.

BackgroundMissing data are a common problem in prospective studies with a long follow-up, and the volume, pattern and reasons for missing data may be relevant when estimating the cost of illness. We aimed to evaluate the effects of different methods for dealing with missing longitudinal cost data and for costing caregiver time on total societal costs in Alzheimer’s disease (AD).MethodsGERAS is an 18-month observational study of costs associated with AD. Total societal costs included patient health and social care costs, and caregiver health and informal care costs. Missing data were classified as missing completely at random (MCAR), missing at random (MAR) or missing not at random (MNAR). Simulation datasets were generated from baseline data with 10–40 % missing total cost data for each missing data mechanism. Datasets were also simulated to reflect the missing cost data pattern at 18 months using MAR and MNAR assumptions. Naïve and multiple imputation (MI) methods were applied to each dataset and results compared with complete GERAS 18-month cost data. Opportunity and replacement cost approaches were used for caregiver time, which was costed with and without supervision included and with time for working caregivers only being costed.ResultsTotal costs were available for 99.4 % of 1497 patients at baseline. For MCAR datasets, naïve methods performed as well as MI methods. For MAR, MI methods performed better than naïve methods. All imputation approaches were poor for MNAR data. For all approaches, percentage bias increased with missing data volume. For datasets reflecting 18-month patterns, a combination of imputation methods provided more accurate cost estimates (e.g. bias: −1 % vs −6 % for single MI method), although different approaches to costing caregiver time had a greater impact on estimated costs (29–43 % increase over base case estimate).ConclusionsMethods used to impute missing cost data in AD will impact on accuracy of cost estimates although varying approaches to costing informal caregiver time has the greatest impact on total costs. Tailoring imputation methods to the reason for missing data will further our understanding of the best analytical approach for studies involving cost outcomes.Electronic supplementary materialThe online version of this article (doi:10.1186/s12874-016-0188-1) contains supplementary material, which is available to authorized users.

Multiple imputation (MI) is a powerful statistical method for handling missing data. Standard implementations of MI are valid under the unverifiable assumption of missing at random (MAR), which is often implausible in practice. The delta-adjustment method, implemented within the MI framework, can be used to perform sensitivity analyses that assess the impact of departures from the MAR assumption on the final inference. This method requires specification of unknown sensitivity parameter(s) (termed as delta(s)). We illustrate the application of the delta-adjustment method using data from the Longitudinal Study of Australian Children, where the epidemiological question is to estimate the association between exposure to maternal emotional distress at age 4–5 years and total (social, emotional, and behavioural) difficulties at age 8–9 years. We elicited the sensitivity parameters for the outcome (????????) and exposure (????????) variables from a panel of experts. The elicited quantile judgements from each expert were converted into a suitable parametric probability distribution and combined using the linear pooling method. We then applied MI under MAR followed by sensitivity analyses under missing not at random (MNAR) using the delta-adjustment method. We present results from sensitivity analyses that used different percentile values of the pooled distributions for the delta parameters for ???????? and ????????, and demonstrate that twofold increases in the magnitude of the association between maternal distress and total difficulties are only observed for large departures from MAR.

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

<title>Abstract</title> <bold>Background:</bold> Functional attrition (non-response) of Patient-Reported Outcomes (PROs) and Quality of Life (QoL) deterioration are common and non-random in oncology trials. While functional attrition is informative, it is often treated as simple missing data, which biases the interpretation of QoL trajectories and prediction models. <bold>Objectives and Methods:</bold> This study aimed (1) To examine prognostic factors of transitions between active participation, functional attrition, and death using multinomial models and (2) To evaluate how different methods of dealing with missing data affect the reliability of QoL deterioration prediction models. A discrete-state modeling framework was used to analyze transitions between active participation, functional attrition, and death in advanced cancer patients. QoL decline was then predicted using LASSO, Random Forest, and XGBoost algorithms, while Inverse Probability of Completion Weighting (IPCW) under a conditional Missing At Random (MAR) assumption was systematically compared against Multiple Imputation by Chained Equations (MICE). At the end, we examined robustness to deviations from MAR through delta-adjusted Missing Not At Random (MNAR) sensitivity analyses. <bold>Results:</bold> Functional attrition accumulated more rapidly than death within the first 12 weeks, confirming its high prevalence and distinct determinants. Lower educational attainment was associated with functional attrition, whereas poor performance status and depressive symptoms primarily predicted mortality. Among predictive models, LASSO combined with MICE achieved the best performance (median AUC = 0.671 [IQR 0.136]), reflecting the modest predictability of dynamic PRO outcomes when relying on baseline covariates. Methodological comparison demonstrated superior discrimination and substantially improved calibration for MICE relative to IPCW, with IPCW models showing marked miscalibration. These findings remained stable across MNAR sensitivity scenarios. <bold>Conclusion:</bold> By modeling the functional attrition as a distinct state, we revealed its specific socio-demographic determinants and clarified how covariate profiles shape patient trajectories <bold>.</bold> For QoL prediction under conditional MAR, MICE yields more stable and better-calibrated models than IPCW. Robustness across MNAR scenarios supports the methodological validity of these conclusions and highlights the importance of principled handling of informative non-response in longitudinal PRO research.

Randomized clinical trials with outcome measured longitudinally are frequently analyzed using either random effect models or generalized estimating equations. Both approaches assume that the dropout mechanism is missing at random (MAR) or missing completely at random (MCAR). We propose a Bayesian pattern-mixture model to incorporate missingness mechanisms that might be missing not at random (MNAR), where the distribution of the outcome measure at the follow-up time , conditional on the prior history, differs across the patterns of missing data. We then perform sensitivity analysis on estimates of the parameters of interest. The sensitivity parameters relate the distribution of the outcome of interest between subjects from a missing-data pattern at time with that of the observed subjects at time . The large number of the sensitivity parameters is reduced by treating them as random with a prior distribution having some pre-specified mean and variance, which are varied to explore the sensitivity of inferences. The missing at random (MAR) mechanism is a special case of the proposed model, allowing a sensitivity analysis of deviations from MAR. The proposed approach is applied to data from the Trial of Preventing Hypertension.

Conventional approaches for handling missingness in substance use disorder trials commonly rely upon a single deterministic "worst value" imputation that posits a perfect relationship between missingness and drug use ("missing value = presumed drug use"); this yields biased estimates of treatment effects and their standard errors. Instead, deterministic imputations should be replaced by probabilistic versions that encode researchers prior beliefs that those with missing data are more likely to be using drugs at those occasions. Motivated by this problem, we present a method for handling non-monotone missing binary data in longitudinal studies. Specifically, we consider a joint model that combines a not missing at random (NMAR) selection model with a generalized linear mixed model for longitudinal binary data. The selection model links the distribution of a missing outcome to the corresponding distribution of the outcome for those observed at that occasion via a fixed and known sensitivity parameter. The mixed model for longitudinal binary data assumes the random effects have bridge distributions; the latter yields regression parameters that have both subject-specific and marginal interpretations. This approach is completely transparent about what is being assumed about missing data and can be used as the basis for sensitivity analysis.

Chapter 14 - Methods for handling missing data

Dropout is a common complication in longitudinal studies, especially since the distinction between missing not at random (MNAR) and missing at random (MAR) dropout is intractable. Consequently, one starts with an analysis that is valid under MAR and then performs a sensitivity analysis by considering MNAR departures from it. To this end, specific classes of joint models, such as pattern-mixture models (PMMs) and selection models (SeMs), have been proposed. On the contrary, shared-parameter models (SPMs) have received less attention, possibly because they do not embody a characterization of MAR. A few approaches to achieve MAR in SPMs exist, but are difficult to implement in existing software. In this article, we focus on SPMs for incomplete longitudinal and time-to-dropout data and propose an alternative characterization of MAR by exploiting the conditional independence assumption, under which outcome and missingness are independent given a set of random effects. By doing so, the censoring distribution can be utilized to cover a wide range of assumptions for the missing data mechanism on the subject-specific level. This approach offers substantial advantages over its counterparts and can be easily implemented in existing software. More specifically, it offers flexibility over the assumption for the missing data generating mechanism that governs dropout by allowing subject-specific perturbations of the censoring distribution, whereas in PMMs and SeMs dropout is considered MNAR strictly.

In longitudinal studies, missing data are ubiquitous. This article made a comparison of three model-based techniques for handling different types of missing data (i.e., missing at random (MAR)-based maximum likelihood (ML) approach, missing not at random (MNAR)-based Diggle–Kenward (DK) selection model and MNAR-based pattern mixture (PM) model) in longitudinal studies through a Monte Carlo simulation study. Two influential factors were considered: the dropout rates (5%, 10%, 20%, and 40%) and the sample sizes (100, 300, 500, and 1000) under MAR and MNAR missingness mechanisms respectively. The results indicated that the model selection was a crucial issue when researchers were dealing with missing data in longitudinal studies because under MNAR mechanism, DK method outperformed MAR-based ML approach, but PM method performed worse than MAR-based method did. The differences of the parameter estimation among three methods became more significant as the sample size and the dropout rate increased.

In the analyses of incomplete longitudinal clinical trial data, there has been a shift, away from simple ad hoc methods that are valid only if the data are missing completely at random (MCAR), to more principled (likelihood-based or Bayesian) ignorable analyses, which are valid under the less restrictive missing at random (MAR) assumption. The availability of the necessary standard statistical software allows for such analyses in practice. Although the possibility of data missing not at random (MNAR) cannot be ruled out, it is argued that analyses valid under MNAR are not well suited for the primary analysis in clinical trials. Therefore, rather than either forgetting about or blindly shifting to an MNAR framework, the optimal place for MNAR analyses is within a sensitivity analysis context. Such analyses can be used, for example, to assess how sensitive results from an ignorable analysis are to possible departures from MAR and how much results are affected by influential observations. In this article, we apply the local influence sensitivity tool (Verbeke et al., 2001) to a longitudinal depression trial, thereby applying it to continuous outcomes from clinical trials.

Missing data are frequently encountered in various disciplines and can be divided into three categories: missing completely at random (MCAR), missing at random (MAR), and missing not at random (MNAR). Valid statistical approaches to missing data depend crucially on correct identification of the underlying missingness mechanism. Although the problem of testing whether this mechanism is MCAR or MAR has been extensively studied, there has been very little research on testing MAR versus MNAR. A critical challenge that is faced when dealing with this problem is the issue of model identification under MNAR. In this paper, under a logistic model for the missing probability, we develop two score tests for the problem of whether the missingness mechanism is MAR or MNAR under a parametric model and a semiparametric location model on the regression function. The implementation of the score tests circumvents the identification issue as it requires only parameter estimation under the null MAR assumption. Our simulations and analysis of human immunodeficiency virus data show that the score tests have well-controlled type I errors and desirable powers.

Missing data due to loss to follow-up or intercurrent events are unintended, but unfortunately inevitable in clinical trials. Since the true values of missing data are never known, it is necessary to assess the impact of untestable and unavoidable assumptions about any unobserved data in sensitivity analysis. This tutorial provides an overview of controlled multiple imputation (MI) techniques and a practical guide to their use for sensitivity analysis of trials with missing continuous outcome data. These include δ- and reference-based MI procedures. In δ-based imputation, an offset term, δ, is typically added to the expected value of the missing data to assess the impact of unobserved participants having a worse or better response than those observed. Reference-based imputation draws imputed values with some reference to observed data in other groups of the trial, typically in other treatment arms. We illustrate the accessibility of these methods using data from a pediatric eczema trial and a chronic headache trial and provide Stata code to facilitate adoption. We discuss issues surrounding the choice of δ in δ-based sensitivity analysis. We also review the debate on variance estimation within reference-based analysis and justify the use of Rubin's variance estimator in this setting, since as we further elaborate on within, it provides information anchored inference.

Missing data are nearly always a problem in research, and missing values represent a serious threat to the validity of inferences drawn from findings. Increasingly, social science researchers are turning to multiple imputation to handle missing data. Multiple imputation, in which missing values are replaced by values repeatedly drawn from conditional probability distributions, is an appropriate method for handling missing data when values are not missing completely at random. However, use of this method requires developing an imputation model from the observed data. This is typically a rigorous and time-consuming process. To encourage wider adoption of multiple imputation in social work research, a simple framework for designing imputation models is presented. The framework and its ability to generate unbiased estimates are demonstrated in a simulation study. KEY WORDS: missing data; multiple imputation; nonresponse ********** Missing data are ubiquitous in social research, and missingness or nonresponse can represent a threat to the validity of inferences because of undue effects on efficiency, power, and parameter bias (Shadish, Cook, & Campbell, 2002). Social work researchers are now addressing missing data in a more rigorous manner. Recently, Saunders et al. (2006) and Choi, Golder, Gillmore, and Morrison (2005) described important data imputation methods and dispelled misunderstandings regarding popular imputation methods, such as mean substitution. Recent advances in analytic methods, such as multiple imputation (MI), are taking hold in social work research. With MI, missing values are replaced with values repeatedly drawn from simulated conditional probability distributions (Schafer, 1997), thus creating multiple versions of the data set. Each version of the data set is analyzed according to the data analysis model, and the multiple results are combined into point estimates (Rubin, 1996). A critical task in MI is to devise an imputation model (Allison, 2002) or missing data model (Graham, Olchowski, & Gilreath, 2007), which involves specifying the measures that are putatively associated with the missing values. Although this process adds additional steps, the specification of an imputation model and the creation of multiple data sets can produce less-biased estimates in the presence of missing data across a wide variety of data analysis techniques (Schafer, 1997). Besides MI, there are many other methods for addressing missing data (Schafer, 1999; Schafer & Graham, 2002). An equally rigorous method known as direct or full information maximum likelihood (FIML) estimation can produce unbiased estimates and correct standard errors in the presence of missing data. When the number of imputations is sufficiently large, identical missing data models will produce the same estimates under MI and FIML (Graham et al., 2007). Unlike MI, FIML is limited to maximum likelihood analytic techniques and the missing data model must be included in the analysis model. Although we focus on MI, the steps we describe for developing an imputation model are equally appropriate for use in the missing data model for FIML. On the basis of the MI literature, this article describes a framework for developing an imputation model for use with any free or commercial software package that performs MI. BRIEF REVIEW OF MISSING DATA CONCEPTS Generally, both MI and a broad range of missing data issues have received ample attention in the applied literature (Graham et al., 2007). We briefly discuss the three types of distributions that describe the randomness of nonresponse given that this property has consequences for the development of an imputation model. For a discussion of general missing data concepts that are not critical to understanding our discussion of imputation model development, we refer readers to Schafer and Graham (2002). Distribution of Nonresponse The probability distribution of nonresponse--more frequently referred to as the missing data or nonresponse mechanism (Rubin, 1976)--is both an important factor in the decision to impute with MI and a context for the development of an imputation model. …

We analytically derive the fixed-effects estimates in unconditional linear growth curve models by typical linear mixed-effects modelling (TLME) and by a pattern-mixture (PM) approach with random-slope-dependent two-missing-pattern missing not at random (MNAR) longitudinal data. Results showed that when the missingness mechanism is random-slope-dependent MNAR, TLME estimates of both the mean intercept and mean slope are biased because of incorrect weights used in the estimation. More specifically, the estimate of the mean slope is biased towards the mean slope for completers, whereas the estimate of the mean intercept is biased towards the opposite direction as compared to the estimate of the mean slope. We also discuss why the PM approach can provide unbiased fixed-effects estimates for random-coefficients-dependent MNAR data but does not work well for missing at random or outcome-dependent MNAR data. A small simulation study was conducted to illustrate the results and to compare results from TLME and PM. Results from an empirical data analysis showed that the conceptual finding can be generalized to other real conditions even when some assumptions for the analytical derivation cannot be met. Implications from the analytical and empirical results were discussed and sensitivity analysis was suggested for longitudinal data analysis with missing data.