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Background: Count data collected in substance abuse research often come with an excess of “zeroes,” which are typically handled using zero-inflated regression models. However, there is a need to consider the design aspects of those studies before using such a statistical model to ascertain the sources of zeroes. Objectives: We sought to illustrate hurdle models as alternatives to zero-inflated models to validate a two-stage decision-making process in situations of “excess zeroes.” Methods: We use data from a study of 45 cocaine-dependent subjects where the primary scientific question was to evaluate whether study participation influences drug-seeking behavior. The outcome, “the frequency (count) of cocaine use days per week,” is bounded (ranging from 0 to 7). We fit and compare binomial, Poisson, negative binomial, and the hurdle version of these models to study the effect of gender, age, time, and study participation on cocaine use. Results: The hurdle binomial model provides the best fit. Gender and time are not predictive of use. Higher odds of use versus no use are associated with age; however once use is experienced, odds of further use decrease with increase in age. Participation was associated with higher odds of no-cocaine use; once there is use, participation reduced the odds of further use. Conclusion: Age and study participation are significantly predictive of cocaine-use behavior. Scientific Significance: The two-stage decision process as modeled by a hurdle binomial model (appropriate for bounded count data with excess zeroes) provides interesting insights into the study of covariate effects on count responses of substance use, when all enrolled subjects are believed to be “at-risk” of use.

Tooth loss from periodontal disease is a major public health burden in the United States. Standard clinical practice is to recommend a dental visit every six months; however, this practice is not evidence-based, and poor dental outcomes and increasing dental insurance premiums indicate room for improvement. We consider a tailored approach that recommends recall time based on patient characteristics and medical history to minimize disease progression without increasing resource expenditures. We formalize this method as a dynamic treatment regime which comprises a sequence of decisions, one per stage of intervention, that follow a decision rule which maps current patient information to a recommendation for their next visit time. The dynamics of periodontal health, visit frequency, and patient compliance are complex, yet the estimated optimal regime must be interpretable to domain experts if it is to be integrated into clinical practice. We combine nonparametric Bayesian dynamics modeling with policy-search algorithms to estimate the optimal dynamic treatment regime within an interpretable class of regimes. Both simulation experiments and application to a rich database of electronic dental records from the HealthPartners HMO shows that our proposed method leads to better dental health without increasing the average recommended recall time relative to competing methods. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

Periodontal disease (PD) progression is often quantified by clinical attachment level (CAL) defined as the distance down a tooth's root that is detached from the surrounding bone. Measured at six locations per tooth throughout the mouth (excluding the molars), it gives rise to a dependent data setup. These data are often reduced to a one-number summary, such as the whole-mouth average or the number of observations greater than a threshold, to be used as the response in a regression to identify important covariates related to the current state of a subject's periodontal health. Rather than a simple one-number summary, we set forward to analyze all available CAL data for each subject, exploiting the presence of spatial dependence, nonstationarity, and nonnormality. Also, many subjects have a considerable proportion of missing teeth, which cannot be considered missing at random because PD is the leading cause of adult tooth loss. Under a Bayesian paradigm, we propose a nonparametric flexible spatial (joint) model of observed CAL and the location of missing tooth via kernel convolution methods, incorporating the aforementioned features of CAL data under a unified framework. Application of this methodology to a dataset recording the periodontal health of an African-American population, as well as simulation studies reveal the gain in model fit and inference, and provides a new perspective into unraveling covariate–response relationships in the presence of complexities posed by these data.