Mixed-Model Imputation of Cost Data for Early Discontinuers from a Randomized Clinical Trial
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0092-8615/99 Copyright 0 1999 Drug Information Association Inc.
MIXED-MODEL IMPUTATION OF COST DATA FOR EARLY DISCONTINUERS FROM A RANDOMIZED CLINICAL TRIAL ROBERTL. OBENCHAIN, PHD Senior Research Scientist, Statistics and Mathematical Sciences
BRYANM. JOHNSTONE, PHD Research Scientist, USA Health Outcomes Evaluation Lilly Research Laboratories, Lilly Corporate Center, Indianapolis, Indiana
For studies with appreciable attrition in which one expects not only differences between individual patients but also time trends in repeated measures, a “sophisticatedly simple ” approach to imputation of missing values is illustrated. A linear model having random patient intercept and slope terms as well as jixed effects for treatment, investigator; time, and interactions between both treatment-investigator and treatment-time is used. In contrast to a purely fixed effects approach, mixed-model estimation then optimally shrinks patient-specific differences toward zero. This shrinkage moves the predictions for each patient toward the average time line for the corresponding investigator and treatment. Using a variety of sensitivity analyses, it is established that imputation of missing values using these mixed-model predictions provides a “benchmark” lower limit for cost differences between treatments. To illustrate concepts, supplementary analyses of selected cost and effectiveness outcomes from a randomized, double-blind trial of olanzapine versus haloperidol for the treatment of schizophrenia are presented. Key Words: Mixed linear models; Single and multiple imputation; Variance component heterogeneity; “Time-is-money” survival curves; Bootstrap inference in cost-effectiveness
INTRODUCTION
new missing-data analysis concepts (11-14), and the evolution of statistical software (15STARTING WITH THE WORK of Laird and Ware (1). mixed-models have been 19), mixed-models have become convenient widely used for analysis of repeated mea- and highly realistic tools for imputation of missing data. sures in studies subject to attrition. Thanks The authors’ approach to the analysis of to recent advances and applications (2-lo), healthcare costs is ideal for situations where repeated measures show obvious time trends. Presented at the DIA Annual Symposium “Global Sta- In these situations, it is preferable to avoid tistical Challenges and Strategies in the Pharmaceutical imputing missing values by “carrying forIndustry,” March 15-17, 1998, Hilton Head, South Car- ward” a patient’s average cost or hisher last olina. nonmissing value. Patients who discontinue Reprint address: Robert L. Obenchain, PhD,Senior early from a clinical trial may represent exResearch Scientist, Statistics and Mathematical Scitremes on costs or clinical measures. Carryences, Lilly Research Laboratories, Lilly Corporate Center, Indianapolis, IN 46285-1850. ing extreme values forward over a lengthy 191
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trial may create statistical “outliers” that distort averages, yielding estimates that are numerically unreasonable. Thus, the authors “log-predict-exp-smear” met
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