Modeling zero‐modified count and semicontinuous data in health services research Part 1: background and overview

Abstract

Health services data often contain a high proportion of zeros. In studies examining patient hospitalization rates, for instance, many patients will have no hospitalizations, resulting in a count of zero. When the number of zeros is greater or less than expected under a standard count model, the data are said to be zero modified relative to the standard model. A similar phenomenon arises with semicontinuous data, which are characterized by a spike at zero followed by a continuous distribution with positive support. When analyzing zero-modified count and semicontinuous data, flexible mixture distributions are often needed to accommodate both the excess zeros and the typically skewed distribution of nonzero values. Various models have been introduced over the past three decades to accommodate such data, including hurdle models, zero-inflated models, and two-part semicontinuous models. This tutorial describes recent modeling strategies for zero-modified count and semicontinuous data and highlights their role in health services research studies. Part 1 of the tutorial, presented here, provides a general overview of the topic. Part 2, appearing as a companion piece in this issue of Statistics in Medicine, discusses three case studies illustrating applications of the methods to health services research. Copyright © 2016 John Wiley & Sons, Ltd.

Two‐part models for cost with zeros to decompose effects of covariates on probability of cost, mean nonzero cost, and mean total cost

“…However, the adjusted and population average methods also provide estimates of covariate effects on total cost, ie, marginal effects. The two methods have been compared for this latter purpose in the context of zero‐inflated count models, but further comparison of both methods for semicontinuous cost data and with marginalized two‐part models would be of interest. Second, it is sometimes of interest to evaluate cost results on an absolute dollar basis, rather than the relative (factor) changes of the models described in this paper.…”

“…Covariate effects on total cost can also be estimated from a single model for cost including zero values, although this approach ignores the mixture nature of the cost outcome. Recent work has proposed marginalized two‐part models to give estimates of the effect of a particular variable on total (marginal) cost adjusting for other variables in the model, ie, comparing patients with the same but unspecified values of other variables . Finite‐mixture models have also been used to obtain marginal covariate effects in some special cases .…”

“…Finite‐mixture models have also been used to obtain marginal covariate effects in some special cases . There has also been a substantial amount of recent work on estimating covariate effects on total mean counts in zero‐inflated count models, a similar issue, including marginalized two‐part models, estimates based on average predicted values (APVs), and other related approaches . Some of these methods are described in more detail below.…”

Level of Agreement Between Problem Gamblers’ and Collaterals’ Reports: A Bayesian Random-Effects Two-Part Model

“…A flexible model that allows for both the inclusion of zeros and the skewed continuous responses is a two-part model2 (Neelon et al Smith 2016; Olsen and Schafer 2001). A two-part model splits the model into two distinct parts, and it models the presence of zeros using a binary model, while it models the actual non-zero losses using a skewed continuous distribution, such as the gamma or lognormal distribution.…”

Comparative Assessment of Utilization and Hospital Outcomes of Veterans Receiving VA and Non‐VA Outpatient Dialysis

“…Our outcome of hospital days over the 2‐year period after each patient's first ESRD dialysis date of service is a count variable with overdispersion and excess zeros, so we fit Poisson, negative binomial, zero‐inflated Poisson, and negative binomial (ZINB) regression models that are appropriate for this type of outcome (McCullaugh and Nelder ; Neelon, O'Malley, and Smith ). The ZINB was the best fit model based on Akaike information criteria (AIC, Akaike ).…”