PRM190 - Extension of the hosmer-lemeshow goodness of fit statistic to linear models with repeated measurements

Abstract

PRM190 EXTENSION OF THE HOSMER-LEMESHOW GOODNESS OF FIT STATISTIC TO LINEAR MODELS WITH REPEATED MEASUREMENTS Li R1, Su Z2, Mendelsohn A2, Gemmen E1 1Quintiles Outcome, Rockville, MD, USA, 2Quintiles Outcome, Cambridge, MA, USA OBJECTIVES: Studies of health outcomes commonly involve binary measures, assessed multiple times. Although generalized linear mixed (GLIMMIX) models are well suited for analyzing these data, there does not exist a formal statistic to assess the goodness of fit (GOF) for GLIMMIX models. We developed an extension of the Hosmer-Lemeshow GOF test used for logistic regression that can be applied to GLIMMIX models. METHODS: The correlation among repeated measurements of the binary outcome variable was accounted for by a random effect in the GLIMMIX model. The principles of Hosmer-Lemeshow method were followed. The linear unbiased estimate of dependent variables were transformed to the original probability, sorted from least to largest, and divided into deciles. A Chi-square statistic and corresponding p-value with eight degrees of freedom, was calculated based upon the expected and observed numbers among deciles. The proposed GOF test was validated by a simulation study with 1000 runs generated from logistic regression models with and without random effects. The results were compared with the Hosmer-Lemeshow GOF test in situations where the latter is appropriate. The proposed method was used in the analysis of a comparative effectiveness (CE) study of ophthalmologic treatments for openangle glaucoma patients. RESULTS: When there was no random effect, the proposed GOF test results from the GLIMMIX procedure were almost identical to those of Hosmer-Lemeshow GOF test from the logistic procedure. With a random effect built in a correctly specified model, the goodness of fit rejection rate was 5.1%, which is close to the nominal level 5%. The proposed test did not indicate lack of fit for the regression models in the CE study. CONCLUSIONS: The proposed GOF test provides an assessment of model fit for models with binary outcomes and repeated measurements for predictor variables.