Informing a risk prediction model for binary outcomes with external coefficient information

Wenting Cheng, Jeremy M. G. Taylor, Tian Gu, Scott A. Tomlins and Bhramar Mukherjee

Journal of the Royal Statistical Society Series C, 2019, vol. 68, issue 1, 121-139

Abstract: We consider a situation where rich historical data are available for the coefficients and their standard errors in an established regression model describing the association between a binary outcome variable Y and a set of predicting factors 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 data set. We develop and evaluate several approaches for translating the external information into constraints on regression coefficients in a logistic regression model of Y|X,B. Borrowing from the measurement error literature we establish an approximate relationship between the regression coefficients in the models Pr(Y=1|X,β), Pr(Y=1|X,B,γ) and E(B|X,θ) for a Gaussian distribution of B. For binary B we propose an alternative expression. The simulation results comparing these methods indicate that historical information on Pr(Y=1|X,β) can improve the efficiency of estimation and enhance the predictive power in the regression model of interest Pr(Y=1|X,B,γ). We illustrate our methodology by enhancing the high grade prostate cancer prevention trial risk calculator, with two new biomarkers: prostate cancer antigen 3 and TMPRSS2:ERG.

Date: 2019
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