Synthesis of clinical prediction models under different sets of covariates with one individual patient data.

Daisuke Yoneoka,Manami Inoue,Norie Sawada,Masayuki Henmi

doi:10.1186/s12874-015-0087-x

Abstract

BackgroundRecently, increased development of clinical prediction models has been reported in the medical literature. However, evidence synthesis methodologies for these prediction models have not been sufficiently studied, especially for practical situations such as a meta-analyses where only aggregated summaries of important predictors are available. Also, in general, the covariate sets involved in the prediction models are not common across studies. As in ordinary model misspecification problems, dropping relevant covariates would raise potentially serious biases to the prediction models, and consequently to the synthesized results.MethodsWe developed synthesizing methods for logistic clinical prediction models with possibly different sets of covariates. In order to aggregate the regression coefficient estimates from different prediction models, we adopted a generalized least squares approach with non-linear terms (a sort of generalization of multivariate meta-analysis). Firstly, we evaluated omitted variable biases in this approach. Then, under an assumption of homogeneity of studies, we developed bias-corrected estimating procedures for regression coefficients of the synthesized prediction models.ResultsNumerical evaluations with simulations showed that our approach resulted in smaller biases and more precise estimates compared with conventional methods, which use only studies with common covariates or which utilize a mean imputation method for omitted coefficients. These methods were also applied to a series of Japanese epidemiologic studies on the incidence of a stroke.ConclusionsOur proposed methods adequately correct the biases due to different sets of covariates between studies, and would provide precise estimates compared with the conventional approach. If the assumption of homogeneity within studies is plausible, this methodology would be useful for incorporating prior published information into the construction of new prediction models.

Highlights

Increased development of clinical prediction models has been reported in the medical literature
We show that our method is asymptotically more efficient than the conventional approach applying multivariate meta-analysis, by using studies with common covariate sets and the previously proposed approach of Debray et al [6]
In order to improve this situation, we propose a new method for synthesis of logistic regression coefficients under different sets of covariates

Summary

Introduction

Increased development of clinical prediction models has been reported in the medical literature. In general, each published prediction model is developed using different sets of covariates [7,8,9,10], and dropping relevant covariates would raise potentially serious biases to the prediction models, as in ordinary model misspecification problems To tackle this problem, the Fibrinogen Studies Collaboration [11] proposed a multivariate meta-analysis approach to borrow strength from partially adjusted results by using individual patient data (IPD), and Riley et al [12] demonstrated the approach in practice. Instead of using every IPD record, Debray et al [6] considered a method that uses the reported summary statistics with one set of IPD They adopted an adhoc approach utilizing mean or zero imputations for the missing coefficient estimates to straightforwardly apply the multivariate meta-analysis method [6]. Debray’s approach is a simple implementation strategy, it should raise substantial biases to the synthesized results because the interpretation of the coefficients depends on which covariates are included in each regression model

Methods

Discussion

Conclusion