EXTENSION OF THE HOSMER-LEMESHOW GOODNESS OF FIT STATISTIC TO LINEAR MODELS WITH REPEATED MEASUREMENTS

Author(s)

Li R*1;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 open-angle 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.

Conference/Value in Health Info

2013-05, ISPOR 2013, New Orleans, LA, USA

Value in Health, Vol. 16, No. 3 (May 2013)

Code

PRM190

Topic

Methodological & Statistical Research

Topic Subcategory

Confounding, Selection Bias Correction, Causal Inference

Disease

Multiple Diseases

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