Single Distribution, Two-Part, and Two-Component Finite Mixture Models for Predicting Smoking-Related Indirect Costs In Us Working Adults

OBJECTIVES: Indirect costs data typically include a high proportion of zeros that cannot be adequately modeled with a single distribution.The current study examined predicted total costs associated with work impairments using different models applicable to such distributions. METHODS: Data on employed US adults (18-64 years old) were analyzed from the 2013 National Health and Wellness Survey Self-report was used to define smoking status (never smoked, quit, attempting to quit, and currently smoke) as a predictor. Costs due to work productivity loss were derived from Work Productivity and Activity Impairment questionnaire-based measures on percentage absenteeism and presenteeism, and calculated using weekly wages by age and sex from the US Bureau of Labor Statistics (2014). Given excessive zeros (60%) in the cost data, two-part (first part logit, second part negative binomial [NB]) and two-component finite mixture (first component constant, second component truncated NB) models were used to predict costs as a function of smoking status, controlling for respondent demographics and health characteristics. Model fit statistics (Akaike and Bayesian Information Criterion [AIC and BIC, respectively] and mean squared error [MSE]) were compared with those from a single-distribution generalized linear model (GLM) with NB distribution, which is also suited to highly skewed, count-like distributions. RESULTS: Among 36,883 working adults, the two-part model had the best fit statistics (AIC=359159; BIC=35935S) compared with the mixture (AIC=394788; BIC= 395001) and the GLM (AIC=391201; BIC=391312) models, and also the smallest MSE (105454117 compared with 105482560 and 21486386573, respectively). Overestimation of costs among those with zero cost was greatest in the single-distribution GLM (average predicted costs=$5306.76) compared with those from two-part ($5293.13) and mixture ($5293.04) models. CONCLUSIONS: In a broadly representative US population of working adults, two-part modeling was found to better represent high zero-skewed indirect cost data compared with two-component finite mixture and single-distribution models.