Distribution-free models for longitudinal count responses with overdispersion and structural zeros.

Overdispersion and structural zeros are two major manifestations of departure from the Poisson assumption when modeling count responses using Poisson log-linear regression. As noted in a large body of literature, ignoring such departures could yield bias and lead to wrong conclusions. Different approaches have been developed to tackle these two major problems. This paper reviews available methods for dealing with overdispersion and structural zeroes within a longitudinal data setting and proposes a distribution-free modeling approach to address the limitations of these methods by utilizing a new class of functional response methods.

This approach is illustrated first with simulated data, and then with real study data from the National Drug Abuse Treatment Clinical Trials Network protocol CTN-0018 (“Reducing HIV/STD Risk Behaviors : A Research Study for Men in Drug Abuse Treatment”). The examples demonstrate that the proposed approach works well for longitudinal data under both complete and missing data settings, as well as for samples with a sample size as small as 50.

Related protocols: CTN-0018