Sensitivity analysis of incomplete longitudinal data departing from the missing at random assumption: Methodology and application in a clinical trial with drop-outs

Statistical analyses of longitudinal data with drop-outs based on direct likelihood, and using all the available data, provide unbiased and fully efficient estimates under some assumptions about the drop-out mechanism. Unfortunately, these assumptions can never be tested from the data. Thus, sensitivity analyses should be routinely performed to assess the robustness of inferences to departures from these assumptions. However, each specific scientific context requires different considerations when setting up such an analysis, no standard method exists and this is still an active area of research. We propose a flexible procedure to perform sensitivity analyses when dealing with continuous outcomes, which are described by a linear mixed model in an initial likelihood analysis. The methodology relies on the pattern-mixture model factorisation of the full data likelihood and was validated in a simulation study. The approach was prompted by a randomised clinical trial for sleep-maintenance insomnia treatment. This case study illustrated the practical value of our approach and underlined the need for sensitivity analyses when analysing data with drop-outs: some of the conclusions from the initial analysis were shown to be reliable, while others were found to be fragile and strongly dependent on modelling assumptions. R code for implementation is provided.

[1]  Roderick J. A. Little,et al.  A Class of Pattern-Mixture Models for Normal Incomplete Data , 1994 .

[2]  Bohdana Ratitch,et al.  Missing data in clinical trials: from clinical assumptions to statistical analysis using pattern mixture models , 2013, Pharmaceutical statistics.

[3]  Xiao-Li Meng,et al.  Multiple-Imputation Inferences with Uncongenial Sources of Input , 1994 .

[4]  D. Rubin,et al.  Large-sample significance levels from multiply imputed data using moment-based statistics and an F reference distribution , 1991 .

[5]  Geert Molenberghs,et al.  Pattern‐mixture models with proper time dependence , 2003 .

[6]  R. A. Leibler,et al.  On Information and Sufficiency , 1951 .

[7]  Stef van Buuren,et al.  MICE: Multivariate Imputation by Chained Equations in R , 2011 .

[8]  Joseph W. Hogan,et al.  Comments on: Missing data methods in longitudinal studies: a review , 2009 .

[9]  Michel Chavance,et al.  Sensitivity analysis of longitudinal normal data with drop‐outs , 2004, Statistics in medicine.

[10]  Roch Giorgi,et al.  Sensitivity analysis when data are missing not-at-random. , 2011, Epidemiology.

[11]  R Little,et al.  Intent-to-treat analysis for longitudinal studies with drop-outs. , 1996, Biometrics.

[12]  Tadayoshi Fushiki.  Bootstrap prediction and Bayesian prediction under misspecified models , 2005 .

[13]  J. Robins,et al.  Inference for imputation estimators , 2000 .

[14]  Geert Molenberghs,et al.  Missing Data in Clinical Studies , 2007 .

[15]  Joseph L Schafer,et al.  On the performance of random‐coefficient pattern‐mixture models for non‐ignorable drop‐out , 2003, Statistics in medicine.

[16]  D B Rubin,et al.  Multiple imputation in health-care databases: an overview and some applications. , 1991, Statistics in medicine.

[17]  R. Little.  Pattern-Mixture Models for Multivariate Incomplete Data , 1993 .

[18]  H. White.  Maximum Likelihood Estimation of Misspecified Models , 1982 .

[19]  Geert Molenberghs,et al.  Monotone missing data and pattern‐mixture models , 1998 .

[20]  I. White,et al.  Eliciting and using expert opinions about dropout bias in randomized controlled trials , 2007, Clinical trials.

[21]  D. Rubin.  INFERENCE AND MISSING DATA , 1975 .

[22]  J. LaFountain.  Inc. , 2013, American Art.

[23]  Michel Chavance,et al.  Sensitivity analysis of longitudinal binary data with non-monotone missing values. , 2004, Biostatistics.

[24]  Joseph G. Ibrahim,et al.  Missing data methods in longitudinal studies: a review , 2009 .

[25]  James Stephen Marron,et al.  Discussion of nonparametric and semiparametric regression , 2004 .

[26]  Michael J. Daniels,et al.  Comments on: Missing data methods in longitudinal studies: a review , 2009 .

[27]  Geert Molenberghs,et al.  Strategies to fit pattern-mixture models. , 2002, Biostatistics.

[28]  D. Bates.  Penalized least squares versus generalized least squares representations of linear mixed models , 2014 .

[29]  Michael G. Kenward,et al.  Missing Data in Clinical Trials - A Practical Guide , 2007 .

[30]  Donald B. Rubin,et al.  Performing likelihood ratio tests with multiply-imputed data sets , 1992 .

[31]  Michael G. Kenward,et al.  Discussion of two important missing data issues , 2004 .

[32]  D. Rubin,et al.  Statistical Analysis with Missing Data , 1988 .

[33]  Roger A. Sugden,et al.  Multiple Imputation for Nonresponse in Surveys , 1988 .

[34]  M. Kenward,et al.  Every missingness not at random model has a missingness at random counterpart with equal fit , 2008 .

[35]  J W Hogan,et al.  Reparameterizing the Pattern Mixture Model for Sensitivity Analyses Under Informative Dropout , 2000, Biometrics.

[36]  Brian Sullivan,et al.  Missing data: Discussion points from the PSI missing data expert group , 2010, Pharmaceutical statistics.