Abstract
Statistical models are simple mathematical rules derived from empirical data describing the association between an outcome and several explanatory variables. In a typical modeling situation statistical analysis often involves a large number of potential explanatory variables and frequently only partial subject-matter knowledge is available. Therefore, selecting the most suitable variables for a model in an objective and practical manner is usually a non-trivial task. We briefly revisit the purposeful variable selection procedure suggested by Hosmer and Lemeshow which combines significance and change-in-estimate criteria for variable selection and critically discuss the change-in-estimate criterion. We show that using a significance-based threshold for the change-in-estimate criterion reduces to a simple significance-based selection of variables, as if the change-in-estimate criterion is not considered at all. Various extensions to the purposeful variable selection procedure are suggested. We propose to use backward elimination augmented with a standardized change-in-estimate criterion on the quantity of interest usually reported and interpreted in a model for variable selection. Augmented backward elimination has been implemented in a SAS macro for linear, logistic and Cox proportional hazards regression. The algorithm and its implementation were evaluated by means of a simulation study. Augmented backward elimination tends to select larger models than backward elimination and approximates the unselected model up to negligible differences in point estimates of the regression coefficients. On average, regression coefficients obtained after applying augmented backward elimination were less biased relative to the coefficients of correctly specified models than after backward elimination. In summary, we propose augmented backward elimination as a reproducible variable selection algorithm that gives the analyst more flexibility in adopting model selection to a specific statistical modeling situation.
Highlights
Statistical modeling is concerned with finding a simple general rule to describe the dependency of an outcome on several explanatory variables
While the full results of our simulation study are contained in a Technical Report [14], the relative behavior of modeling by augmented backward elimination (ABE), backward elimination (BE) or by applying no variable selection can already be understood from the results selected for Table 1
In biomedical research we are often confronted with complex statistical modeling problems involving a large number of potential explanatory variables and only restricted prior knowledge about their relationships
Summary
Statistical modeling is concerned with finding a simple general rule to describe the dependency of an outcome on several explanatory variables. Such rules may be simple linear combinations, or more complex formulas involving product and non-linear terms. They should be valid, i.e., provide predictions with acceptable accuracy. They should be practically useful, i.e., a model should allow to derive conclusions such as ‘how large is the expected change in the outcome if one of the explanatory variables changes by one unit’. In a typical modeling situation the analyst is often confronted with a large number of potential explanatory variables, and selecting the most suitable ones for a model is usually a non-trivial task
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