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.
Consider the setting where (i) individual‐level data are collected to build a regression model for the association between an event of interest and certain covariates, and (ii) some risk calculators predicting the risk of the event using less detailed covariates are available, possibly as algorithmic black boxes with little information available about how they were built. We propose a general empirical‐likelihood‐based framework to integrate the rich auxiliary information contained in the calculators into fitting the regression model, to make the estimation of regression parameters more efficient. Two methods are developed: one using working models to extract the calculator information and the other making a direct use of calculator predictions without working models. Theoretical and numerical investigations show that the calculator information can substantially reduce the variance of regression parameter estimation. As an application, we study the dependence of the risk of high‐grade prostate cancer on both conventional risk factors and newly identified molecular biomarkers by integrating information from the Prostate Biopsy Collaborative Group (PBCG) risk calculator, which was built based on conventional risk factors alone.
more » « less- NSF-PAR ID:
- 10411788
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Canadian Journal of Statistics
- Volume:
- 51
- Issue:
- 2
- ISSN:
- 0319-5724
- Page Range / eLocation ID:
- p. 355-374
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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