A marginalized two-part model for longitudinal semicontinuous data

Abstract

In health services research, it is common to encounter semicontinuous data, characterized by a point mass at zero followed by a right-skewed continuous distribution with positive support. Examples include health expenditures, in which the zeros represent a subpopulation of patients who do not use health services, while the continuous distribution describes the level of expenditures among health services users. Longitudinal semicontinuous data are typically analyzed using two-part random-effect mixtures with one component that models the probability of health services use, and a second component that models the distribution of log-scale positive expenditures among users. However, because the second part conditions on a non-zero response, obtaining interpretable effects of covariates on the combined population of health services users and non-users is not straightforward, even though this is often of greatest interest to investigators. Here, we propose a marginalized two-part model for longitudinal data that allows investigators to obtain the effect of covariates on the overall population mean. The model additionally provides estimates of the overall population mean on the original, untransformed scale, and many covariates take a dual population average and subject-specific interpretation. Using a Bayesian estimation approach, this model maintains the flexibility to include complex random-effect structures and easily estimate functions of the overall mean. We illustrate this approach by evaluating the effect of a copayment increase on health care expenditures in the Veterans Affairs health care system over a four-year period.

Enrollment in early head start and oral health-related quality of life

“…We used a marginalized semicontinuous two-part model with random effects to estimate the effect of EHS on ECOHIS prevalence and mean ECOHIS severity scores at follow-up [43–45]. We used a semicontinuous model because our outcome, ECOHIS, has a large proportion of zeros (58%).…”

“…The first part of the marginalized semicontinuous model [43] was a logistic regression with random effects to examine the effect of the binary independent variable, EHS, on ECOHIS prevalence at follow-up (ECOHIS ≥ 1). $$\text{log }true[\frac{{\Pi }_{\text{italicij}}}{1-{\Pi }_{\mathit{\text{ij}}}}true]={\beta }_0+{\beta }_1{x}_{1i}+{\beta }_2{x}_{2\text{italicij}}+{\beta }_3{x}_{3\text{italicij}}+{\beta }_4{x}_{4\text{italicij}}+b_i,$$where π ij was the probability of having any negative impact to OHRQoL (ECOHIS ≥ 1) at follow-up for the j th child in the i th EHS program cluster conditional on the cluster-specific effect, b i .…”

Estimating marginal and incremental effects in the analysis of medical expenditure panel data using marginalized two-part random-effects generalized Gamma models: Evidence from China healthcare cost data

“…In addition, the m2RGGMs proposed here are built upon marginalization of the random-effects generalized Gamma models in Part (II) of the two-part models. This is beyond and superior to the lognormal models in Su et al 28 and Smith et al 30 …”

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

“…For illustration, we have ignored this correlation in our analysis, to focus on developing and illustrating methods and results. Such extensions have been given for estimating effects on total cost using the marginalized TPM . Extending the Mult‐TPM to clustered data would require software to fit log‐binomial models with random effects and incorporating a joint model structure such as that in the work of Tooze et al, linking cluster random effects in parts I and II of the Std‐TPM.…”