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Nelson DB, Noorbaloochi S. Graphical Diagnostic Methods for Generalized Linear Models and Proportional Hazards Models. Presented at: VA HSR&D / QUERI National Meeting; 2015 Jul 8; Philadelphia, PA.
Objectives: Statistical inference in the medical research used to inform VA policy decisions, healthcare initiatives, and patient care frequently requires use of complex regression models. Model diagnostics therefore are critically important to establish the appropriateness and validity of the models. The objective of this research was to develop a graphical methodology for assessing the fit of generalized linear models and proportional hazards survival models yielding graphs that are more readily interpretable than those from current residual based graphical methods. Methods: We demonstrate that predictors and outcomes considered in these regression analyses are independent conditional on the regression function. We use this simple result to develop the theory and methodology for regression model diagnostics based on comparing the fitted regression model to local nonparametric regression models. We evaluate the performance of the developed diagnostic methodology in a series of simulation studies and in application to existing well known medical datasets and compare the performance of the developed methodology to existing methods. Results: The diagnostic plots generated using this methodology perform similarly to residual plots for linear regression analyses and do not exhibit the complicating features present in existing residual based methods stemming from the consideration of discrete outcomes. Simulation studies and application of this method to existing data sets indicate that the method either performs comparably to existing methods or detects problems with model specification missed by the currently available methods. Implications: This methodology provides a useful approach to assessing the fit of these regression models that complements existing methods and in some cases performs better than existing methods. Impacts: These diagnostic plots will lead to improved reliability of the models used in VA research and increased reliability of the inferences drawn from these research projects.
