Weighted Random Regression Models and Dropouts
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Weighted Random Regression Models and Dropouts U
Chul Ahm, PhD Department oflnternal Medicine, University of Texas Medical School, Houston, Texas
Sin-Ho Jung, PhD Department of Biostatistics and Bioinformatics, Duke University. Durham, North Carolina Seung-Ho Kong, PhD Department of Statistics, Ewha Womans University, Seoul, Korea
Key Words Weighted random regression; Dropouts; Simulation Correspondence Address Chul Ahn. PhD, Department oflnternal Medicine, UTHouston Medical School, 6431 Fannin Street, MSB I . 122. Houston, TX 77030 (e-mail: [email protected]).
In studies with repeated measurements, one of the popular primary interests is the comparison of the rates of change in a response variable between groups. The random regression model (RRM)has been offered as a potential solution to statistical problems posed ty dropouts in clinical tials. Howevq the power of RRM tests for differences in rates of change can be seriously reduced due to dropouts. We examine the effect of dropouts on the power of RRM tests for testing differences in the rates of change between two groups through simulation. We exam-
INTRODUCTION The hypothesis of primary interest in doubleblind trials concerns the difference between patterns or magnitudes of change from baseline. A simple approach to analyze data from this type of study is to summarize each subject’soutcome with a single summary statistic. With this method, each subject’s measurements are transformed into a single statistic, which will be tested for the equality of parameters among the study groups. Examples of summary statistics include the difference between the baseline and the final measurements, the least-squares slope, and the final outcome. The slope is often used to assess treatment effects in trials where the goal is to slow progression of degenerative disorders. For example, in the Intermittent Positive Pressure Breathing Trial (IPPBT) (l),the progression of lung function over time was compared by investigating differences in the means of individual estimated slopes between treatment groups. In this trial, the patients were followed closely for at least 2.5 years, most were followed for three years or until they died or withdrew from the study. The two-stage RRM fits a least squares linear regression equation in stage 1 for calculation of subject-specific regression coefficients, and
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ine the performanceof weighted random regression models, which assign equal weights to subjects, equal weights to measurements, and optimal weights that minimize the variance of the regression coefficient. We perform the simulation study to evaluate the performance of the above three weighting schemes using type 1 errors and the power in repeated measurements data as affected by different dropout mechanisms such as random dropouts and treatmentdependent dropouts.
then evaluates the significance of the difference between group means on the regression coefficients using analysis of variance (ANOVA) tests. Overall et al. (2), Overall (3), and Ahn et al. (4) examine the imp
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