Dual imputation model for incomplete longitudinal data.

Missing values are a practical issue in the analysis of longitudinal data. Multiple imputation (MI) is a well-known likelihood-based method that has optimal properties in terms of efficiency and consistency if the imputation model is correctly specified. Doubly robust (DR) weighing-based methods protect against misspecification bias if one of the models, but not necessarily both, for the data or the mechanism leading to missing data is correct. We propose a new imputation method that captures the simplicity of MI and protection from the DR method. This method integrates MI and DR to protect against misspecification of the imputation model under a missing at random assumption. Our method avoids analytical complications of missing data particularly in multivariate settings, and is easy to implement in standard statistical packages. Moreover, the proposed method works very well with an intermittent pattern of missingness when other DR methods can not be used. Simulation experiments show that the proposed approach achieves improved performance when one of the models is correct. The method is applied to data from the fireworks disaster study, a randomized clinical trial comparing therapies in disaster-exposed children. We conclude that the new method increases the robustness of imputations.

[1]  J. Schafer.  Multiple Imputation in Multivariate Problems When the Imputation and Analysis Models Differ , 2003 .

[2]  John Van Hoewyk,et al.  A multivariate technique for multiply imputing missing values using a sequence of regression models , 2001 .

[3]  Roderick J. A. Little,et al.  Statistical Analysis with Missing Data: Little/Statistical Analysis with Missing Data , 2002 .

[4]  Geert Molenberghs,et al.  EVERY MISSING NOT AT RANDOM MODEL HAS GOT A MISSING AT RANDOM COUNTERPART WITH EQUAL FIT , 2008 .

[5]  John B Carlin,et al.  Multiple imputation for missing data: fully conditional specification versus multivariate normal imputation. , 2010, American journal of epidemiology.

[6]  M. Kenward.  Selection models for repeated measurements with non-random dropout: an illustration of sensitivity. , 1998, Statistics in medicine.

[7]  Marie Davidian,et al.  Improved Doubly Robust Estimation When Data Are Monotonely Coarsened, with Application to Longitudinal Studies with Dropout , 2011, Biometrics.

[8]  Lihong Qi,et al.  A comparison of multiple imputation and fully augmented weighted estimators for Cox regression with missing covariates , 2010, Statistics in medicine.

[9]  M. Kenward,et al.  Analysis of Incomplete Data Using Inverse Probability Weighting and Doubly Robust Estimators , 2010 .

[10]  Patrick Royston,et al.  Multiple imputation using chained equations: Issues and guidance for practice , 2011, Statistics in medicine.

[11]  M. Davidian,et al.  Improving efficiency and robustness of the doubly robust estimator for a population mean with incomplete data , 2009, Biometrika.

[12]  J. Robins,et al.  Doubly Robust Estimation in Missing Data and Causal Inference Models , 2005, Biometrics.

[13]  M. Kenward,et al.  A comparison of multiple imputation and doubly robust estimation for analyses with missing data , 2006 .

[14]  Stef van Buuren,et al.  Multiple imputation of discrete and continuous data by fully conditional specification , 2007 .

[15]  A. Gelman,et al.  ON THE STATIONARY DISTRIBUTION OF ITERATIVE IMPUTATIONS , 2010, 1012.2902.

[16]  W. G. Cochran.  The effectiveness of adjustment by subclassification in removing bias in observational studies. , 1968, Biometrics.

[17]  Guangyu Zhang,et al.  Extensions of the Penalized Spline of Propensity Prediction Method of Imputation , 2009, Biometrics.

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

[19]  A. Rotnitzky.  Inverse probability weighted methods , 2008 .

[20]  Michael G. Kenward,et al.  A method for increasing the robustness of multiple imputation , 2012, Comput. Stat. Data Anal..

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

[22]  Hyonggin An,et al.  Robust Model-Based Inference for Incomplete Data via Penalized Spline Propensity Prediction , 2008, Commun. Stat. Simul. Comput..

[23]  R. Little,et al.  A comparative study of doubly robust estimators of the mean with missing data , 2011 .

[24]  M. Kenward,et al.  Informative dropout in longitudinal data analysis (with discussion) , 1994 .

[25]  J. Robins,et al.  Sensitivity Analysis for Selection bias and unmeasured Confounding in missing Data and Causal inference models , 2000 .

[26]  Joseph Kang,et al.  Demystifying Double Robustness: A Comparison of Alternative Strategies for Estimating a Population Mean from Incomplete Data , 2007, 0804.2958.

[27]  D. Rubin,et al.  Fully conditional specification in multivariate imputation , 2006 .

[28]  Joseph L Schafer,et al.  Analysis of Incomplete Multivariate Data , 1997 .

[29]  J. Schafer,et al.  Missing data: our view of the state of the art. , 2002, Psychological methods.

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

[31]  Peter J. Diggle,et al.  Informative dropout in longitudinal data analysis. , 1994 .

[32]  Joseph L Schafer,et al.  Robustness of a multivariate normal approximation for imputation of incomplete binary data , 2007, Statistics in medicine.

[33]  J. Robins,et al.  Adjusting for Nonignorable Drop-Out Using Semiparametric Nonresponse Models , 1999 .

[34]  Stef van Buuren,et al.  Flexible Imputation of Missing Data , 2012 .

[35]  L. Frank,et al.  Combining the complete-data and nonresponse models for drawing imputations under MAR , 2012 .

[36]  Ricky Greenwald,et al.  A randomised comparison of cognitive behavioural therapy (CBT) and eye movement desensitisation and reprocessing (EMDR) in disaster-exposed children , 2011, European journal of psychotraumatology.

[37]  Hakan Demirtas,et al.  Plausibility of multivariate normality assumption when multiply imputing non-Gaussian continuous outcomes: a simulation assessment , 2008 .

[38]  T. Shakespeare,et al.  Observational Studies , 2003 .

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

[40]  S. van Buuren.  Multiple imputation of discrete and continuous data by fully conditional specification , 2007, Statistical methods in medical research.

[41]  M. Kenward,et al.  Informative Drop‐Out in Longitudinal Data Analysis , 1994 .

[42]  H. Boshuizen,et al.  Multiple imputation of missing blood pressure covariates in survival analysis. , 1999, Statistics in medicine.

[43]  J. Robins,et al.  Comment: Performance of Double-Robust Estimators When “Inverse Probability” Weights Are Highly Variable , 2007, 0804.2965.

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