Comparison of methods for modelling a count outcome with excess zeros: application to Activities of Daily Living (ADL-s)

Background Count outcomes are commonly encountered in many epidemiology applications, and are often characterised by a large proportion of zeros. Although linear or logistic regression models have often been used to analyse count outcomes, the resulting estimates are likely to be inefficient, inconsistent or biased.

Methods Data were taken from the first wave of the English Longitudinal Study of Ageing (ELSA). The main outcome measure is difficulty (ranging from 0 to 6) with ‘Activities of Daily Living (ADL-s)’, such as dressing, walking across a room, bathing, eating, getting in and out of bed and using the toilet. Four regression models specifically developed for count outcomes were fitted to the data: Poisson, negative binomial (NB), zero-inflated Poisson (ZIP) and zero-inflated negative binomial (ZINB). The models were compared using the Likelihood Ratio (LR) test of overdispersion, the Vuong test and graphical methods.

Results The plots of predictions showed that overall, the ZINB model fit best. Although the ZINB and the ZIP models showed similar fit, the LR test provided strong evidence that the ZINB had improved fit over the ZIP. Increasing difficulties with ADL-s were associated with fair/poor self-reported health, limiting longstanding illness and physical inactivity. The probability of not having any difficulty with ADL-s decreases with a limiting longstanding illness, increasing age, no education, fair/poor self-reported health and with not living with a partner.

Conclusion Models specifically developed for count outcomes with excess zeros such as ZINB can provide better insights into the investigation of the factors associated with the difficulties with ADL-s.