We consider a situation where there is rich historical data 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 dataset. 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 alternate 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.

中文翻译：

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使用外部系数信息为二元结果提供风险预测模型。

在大型研究中，我们考虑了在建立的回归模型中有丰富的历史数据可用于系数及其标准误差的情况，该回归模型描述了二进制结果变量Y与一组预测因子X之间的关联。我们想利用此摘要信息来改进感兴趣的扩展模型Y |中的估计和预测。X，B。附加变量B是新的生物标志物，是在新数据集中的少量受试者上测得的。我们开发并评估了几种将外部信息转换为约束条件的逻辑回归模型中回归系数约束的方法。从测量误差文献中借用，我们建立了模型Pr（Y = 1 | X，β），Pr（Y = 1 | X，B，γ）和E（B | X，θ）表示B的高斯分布。对于二进制B，我们提出了一个替换表达式。对比这些方法的仿真结果表明，有关Pr（Y = 1 | X，β）的历史信息可以提高估计效率并增强目标回归模型Pr（Y = 1 | X，B，γ）的预测能力。我们通过使用两种新的生物标志物前列腺癌抗原3和TMPRSS2：ERG增强高级前列腺癌预防试验风险计算器来说明我们的方法。