Efficient Computation of Reduced Regression Models

We consider settings where it is of interest to fit and assess regression submodels that arise as various explanatory variables are excluded from a larger regression model. The larger model is referred to as the full model; the submodels are the reduced models. We show that a computationally efficient approximation to the regression estimates under any reduced model can be obtained from a simple weighted least squares (WLS) approach based on the estimated regression parameters and covariance matrix from the full model. This WLS approach can be considered an extension to unbiased estimating equations of a first-order Taylor series approach proposed by Lawless and Singhal. Using data from the 2010 Nationwide Inpatient Sample (NIS), a 20% weighted, stratified, cluster sample of approximately 8 million hospital stays from approximately 1000 hospitals, we illustrate the WLS approach when fitting interval censored regression models to estimate the effect of type of surgery (robotic versus nonrobotic surgery) on hospital length-of-stay while adjusting for three sets of covariates: patient-level characteristics, hospital characteristics, and zip-code level characteristics. Ordinarily, standard fitting of the reduced models to the NIS data takes approximately 10 hours; using the proposed WLS approach, the reduced models take seconds to fit.