Informing a Risk Prediction Model for Binary Outcomes with External Coefficient Information

• Activity Number: 501 - Biometrics Student Paper Awards 1
• Type: Topic Contributed
• Date/Time: Wednesday, August 2, 2017 : 10:30 AM to 12:15 PM
• Sponsor: Biometrics Section
• Author(s): Wenting Cheng* and Jeremy M. G. Taylor and Bhramar Mukherjee
• Companies: Department of Biostatistics, University of Michigan, Ann Arbor and University of Michigan and Department of Biostatistics, University of Michigan, Ann Arbor
• Keywords: Bayesian methods ; Constrained estimation ; Prediction models ; Logistic regression

Abstract

We consider a situation where there is rich historical data available for the coefficients and their standard errors in an established regression model describing Pr(Y = 1|X), from a large study. We would like to utilize this summary information for improving estimation and prediction in an expanded model of interest, Y|X, B. The additional variable B is a new biomarker, measured on a small number of subjects in a new dataset. We develop and evaluate several approaches for translating the external information into constraints on regression coefficients in Y|X, B. Borrowing from the measurement error literature we establish approximate relationship between the regression coefficients in the models Pr(Y = 1|X, ?), Pr(Y = 1|X, B, ?) and E(B|X, ?) for a Gaussian distribution of B. For binary B we propose an alternate expression. The simulation results comparing these methods indicate that historical information on Y|X can improve the efficiency of estimation and enhance the predictive power in the model Y|X, B. We illustrate our methodology by enhancing the High-grade Prostate Cancer Prevention Trial risk Calculator, with two biomarkers prostate cancer antigen 3 and TMPRSS2:ERG.