An imputation strategy for incomplete longitudinal ordinal data

A new quasi-imputation strategy for correlated ordinal responses is proposed by borrowing ideas from random number generation. The essential idea is collapsing ordinal levels to binary ones and converting correlated binary outcomes to multivariate normal outcomes in a sensible way so that re-conversion to the binary and then ordinal scale, after conducting multiple imputation, yields the original marginal distributions and correlations. This conversion process ensures that the correlations are transformed reasonably, which in turn allows us to take advantage of well-developed imputation techniques for Gaussian outcomes. We use the phrase 'quasi' because the original observations are not guaranteed to be preserved. We present an application using a data set from psychiatric research. We conclude that the proposed method may be a promising tool for handling incomplete longitudinal or clustered ordinal outcomes.

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

[2]  D. Rubin.  Formalizing Subjective Notions about the Effect of Nonrespondents in Sample Surveys , 1977 .

[3]  H. Demirtas.  A method for multivariate ordinal data generation given marginal distributions and correlations , 2006 .

[4]  Roderick J. A. Little,et al.  Statistical Analysis with Missing Data , 1988 .

[5]  J M Taylor,et al.  Multiple Imputation and Posterior Simulation for Multivariate Missing Data in Longitudinal Studies , 2000, Biometrics.

[6]  D. Rubin.  Multiple Imputation After 18+ Years , 1996 .

[7]  G. Molenberghs,et al.  Linear Mixed Models for Longitudinal Data , 2001 .

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

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

[10]  M. Piedmonte,et al.  A Method for Generating High-Dimensional Multivariate Binary Variates , 1991 .

[11]  J. Schafer,et al.  Computational Strategies for Multivariate Linear Mixed-Effects Models With Missing Values , 2002 .

[12]  D. Hedeker,et al.  A random-effects ordinal regression model for multilevel analysis. , 1994, Biometrics.

[13]  Joseph L. Schafer,et al.  Multiple imputation with PAN. , 2001 .

[14]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[15]  Stef van Buuren,et al.  Imputation of missing categorical data by maximizing internal consistency , 1992 .

[16]  Hakan Demirtas.  Simulation driven inferences for multiply imputed longitudinal datasets , 2004 .

[17]  W. Wong,et al.  The calculation of posterior distributions by data augmentation , 1987 .

[18]  Hakan Demirtas,et al.  Multiple imputation under Bayesianly smoothed pattern‐mixture models for non‐ignorable drop‐out , 2005, Statistics in medicine.

[19]  Søren Feodor Nielsen,et al.  1. Statistical Analysis with Missing Data (2nd edn). Roderick J. Little and Donald B. Rubin, John Wiley & Sons, New York, 2002. No. of pages: xv+381. ISBN: 0‐471‐18386‐5 , 2004 .

[20]  Donald Hedeker,et al.  Gaussianization-based quasi-imputation and expansion strategies for incomplete correlated binary responses. , 2007, Statistics in medicine.

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