Journal of Biometrics & Biostatistics

Combining Prediction Models in a Linear Way: Results of Numeric Simulation

Abstract

Alexander Goldfarb-Rumyantzev and Ning Dong

Background: Using standard expressions for logistic regression and proportional hazard models and data from published outcome studies might allow generating prediction models and risk stratification tools in a more streamline fashion. However it might require combining the models, adding or removing predictors. The feasibility of this approach has been examined here. Methods: The outcome of this simulation study is mortality. The simulation exercise was based on the imaginary population of 20,000 subjects whose mortality was completely determined by five variables in the specified logistic regression model. In the first simulation exercise using “full model”, we evaluated the option of combining the results of two separate studies (studies A and B) each based on subset of the population. In the second simulation exercise studies A and B were based on limited number of predictors. Each simulation was repeated 50 times. Results: Both simulation exercises demonstrated the robustness of the model and feasibility of adding or removing predictors to/from the model. We also compared the results of linear model to the more complex exponential model using all five predictors. In subjects with lower risk indicator the outcome of linear model is similar to the outcome of the logistic regression model and to the true outcome rate, however it underestimates the risk in the high-risk groups. On the other hand, logistic regression model is accurate compared to actual outcomes. This confirms our hypothesis that dropping or adding variables should not distort the prediction in any noticeable way. Conclusions: Simple linear combination of prediction models, adding or removing predictors do not cause distortion of the model and predictions remain robust. Prediction of linear model is similar to exponential model, except the former underestimate the outcome in the high risk groups.