A flexible two-part random effects model for correlated medical costs

Abstract

In this paper, we propose a flexible "two-part" random Effects model (Olsen and Schafer 2001;Tooze, Grunwald, and Jones 2002) for correlated medical cost data. Typically, medical cost data are right-skewed, involve a substantial proportion of zero values, and may exhibit heteroscedasticity. In many cases, such data is also obtained in hierarchical form, e.g., on patients served by the same physician. The proposed model specification therefore consists of two generalized linear mixed models (GLMM), linked together by correlated random Effects. Respectively, and conditionally on the random Effects and covariates, we model the odds of cost being positive (Part I) using a GLMM with a logistic link and the mean cost (Part II) given that costs were actually incurred using a generalized gamma regression model with random Effects and a scale parameter that is allowed to depend on covariates (c.f. Manning, Basu, and Mullahy 2005). The class of generalized gamma distributions is very flexible and includes the lognormal, gamma, inverse gamma and Weibull distributions as special cases. We demonstrate how to carry out estimation using the Gaussian quadrature techniques conveniently implemented in SAS Proc NLMIXED. The proposed model is used to analyze pharmacy cost data on 56,245 adult patients clustered within 239 physicians in a mid-western U.S. managed care organization.

The relationship between baseline health and longitudinal costs of hospital use

“…The resulting estimates provide population averaged effects, in the sense that they show the average difference in hospital costs between individuals in different health states. This is often the relevant viewpoint from a policy or societal perspective (Liu et al, 2010). It can be expected, for example based on the well-known relationship between time to death and healthcare expenditures, that the different parts of the three-part model are correlated.…”

“…We have opted for the use of a marginal model framework instead of a random effects model, in which correlation between the different parts of the models is explicitly modeled (Liu, 2009;Liu et al, 2010). The marginal model was chosen because of the interest in the population averaged effects.…”

“…The marginal model was chosen because of the interest in the population averaged effects. As noted by Liu et al (2010), random effects models can also be used to estimate population average effects by averaging over the distribution of the random effects. In case the individual effects indeed follow the distribution specified by the correlated random effects model, this model might yield more efficient population averaged estimates.…”

Estimating Healthcare Demand for an Aging Population: A Flexible and Robust Bayesian Joint Model

“…In addition, the potential nonlinear effects of age could vary with other demographic characteristics, such as gender, resulting in an interaction effect that influences healthcare demand in a nonlinear fashion. Fourth, both the count of hospital visits and medical expenditure are known to be skewed (Liu et al 2010). Although, some authors have argued in favour of log 2 transformations to deal with skewness, this can be problematic.…”

“…We model the count of hospital visits made by an individual using a Poisson hurdle model (Mullahy 1986) and we model out-of-pocket medical expenditure using a semicontinuous model (Liu et al 2010). The Poisson hurdle model (semicontinuous model) consists of two components: a Bernoulli component that models the probability of hospitalisation (any positive expense) and a truncated Poisson component (log-normally distributed component) that models the number of hospital visits (amount of money spent) among users.…”