Testing the Adequacy of a Spline Model to Correlated Binary Data

• Activity Number: 364
• Type: Contributed
• Date/Time: Wednesday, August 14, 2002 : 2:00 PM to 3:50 PM
• Sponsor: Biopharmaceutical Section*
• Author(s): George Hurley*+ and Jorge Morel
• Affiliation(s): Procter and Gamble Co., Inc. and Procter & Gamble Company
• Keywords: Goodness-of-fit test ; Splines ; Logistic Regression ; Generalized Estimating Equations (GEE)

Abstract

Two clinical trials were conducted to investigate the efficacy of a therapeutic heatwrap device (ThermaCare (TM)). In each study, subjects were randomized to one of several groups including heatwrap and oral placebo. After initial dosing, pain relief was rated on a six-point scale each hour for 8 hours and also at 24 hours; clinically relevant pain relief (CRPR) was defined as any rating marked in the top four categories. It was of interest to determine if the heatwrap, had a significantly higher incidence of CRPR at each time point than oral placebo. In analyzing these data, the Generalized Estimating Equations (GEE) techniques of Liang and Zeger (1986) were implemented to take into account the correlated nature of the Bernoulli responses. The GEE methodology is robust to the choice of the working correlation matrix, but requires a proper specification of the mean of the model. Using spline techniques, several logistic regression models were fit. We propose an asymptotic Chi-square statistic to evaluate the goodness of fit of these models. Under the most appropriate models, it is shown that the heatwrap increases the odds of obtaining CRPR over the oral placebo.