Caprice 3-4
Informing a Risk Prediction Model for Binary Outcomes with External Coefficient Information (304799)
*Wenting Cheng, University of Michigan, Ann ArborJeremy Taylor, University of Michigan, Ann Arbor
Tian Gu, University of Michigan, Ann Arbor
Scott Tomlins, University of Michigan, Ann Arbor
Bhramar Mukherjee, University of Michigan, Ann Arbor
Keywords: Bayesian methods, Constrained estimation, Prediction models, Logistic regression
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, ß), 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.