We develop the scale transformed power prior for settings where historical and current data involve different data types, such as binary and continuous data, respectively. This situation arises often in clinical trials, for example, when historical data involve binary responses and the current data involve time-to-event or some other type of continuous or discrete outcome. The power prior proposed by Ibrahim and Chen (2000) does not address the issue of different data types. Herein, we develop a current type of power prior, which we call the scale transformed power prior (straPP). The straPP is constructed by transforming the power prior for the historical data by rescaling the parameter using a function of the Fisher information matrices for the historical and current data models, thereby shifting the scale of the parameter vector from that of the historical to that of the current data. Examples are presented to motivate the need for a scale transformation and simulation studies are presented to illustrate the performance advantages of the straPP over the power prior and other informative and non-informative priors. A real dataset from a clinical trial undertaken to study a novel transitional care model for stroke survivors is used to illustrate the methodology.
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Joseph G. Ibrahim is the Alumni Distinguished Professor of Biostatistics at the Department of Biostatistics in the University of North Carolina (Chapel Hill). He is also the Director of the Biostatistics Core at UNC's Lineberger Comprehensive Cancer Center. Professor Ibrahim is an elected member of the Institute of Mathematical Statistics, the International Statistics Institute, the American Statistical Association and the Royal Statistical Society. His research focuses on the analysis of clinical trials, Bayesian methods, missing data problems and cancer genomics and he is the originator of the popular method of prior elicitation known as the power prior.