Marginalized Two-Part Joint Modeling of Longitudinal Semi-Continuous Responses and Survival Data: With Application to Medical Costs

Sayed Jamal Mirkamali,(Din) Ding-Geng Chen,Farid Zayeri,Anoshirvan Kazemnejad,Mohadeseh Shojaei Shahrokhabadi

doi:10.3390/math9202603

Abstract

Non-negative continuous outcomes with a substantial number of zero values and incomplete longitudinal follow-up are quite common in medical costs data. It is thus critical to incorporate the potential dependence of survival status and longitudinal medical costs in joint modeling, where censorship is death-related. Despite the wide use of conventional two-part joint models (CTJMs) to capture zero-inflation, they are limited to conditional interpretations of the regression coefficients in the model’s continuous part. In this paper, we propose a marginalized two-part joint model (MTJM) to jointly analyze semi-continuous longitudinal costs data and survival data. We compare it to the conventional two-part joint model (CTJM) for handling marginal inferences about covariate effects on average costs. We conducted a series of simulation studies to evaluate the superior performance of the proposed MTJM over the CTJM. To illustrate the applicability of the MTJM, we applied the model to a set of real electronic health record (EHR) data recently collected in Iran. We found that the MTJM yielded a smaller standard error, root-mean-square error of estimates, and AIC value, with unbiased parameter estimates. With this MTJM, we identified a significant positive correlation between costs and survival, which was consistent with the simulation results.

Highlights

In many medical studies, the measurement of the primary outcome may be via a semi-continuous random variable that combines a continuous distribution with point masses at one or more locations [1]
We propose a new extension of a marginalized two-part model for a joint analysis of longitudinal and survival data that accounts for the semi-continuous nature of longitudinal medical costs data
Extending the conventional two-part joint model (CTJM) proposed by Liu et al [14] and Rustand et al [1], which has been widely used to jointly model semi-continuous data and survival outcomes, we propose a more flexible marginalized two-part joint model (MTJM) by using marginalized two-part (MTP) models instead of conventional two-part (CTP) models for the longitudinal part

Summary

Introduction

The measurement of the primary outcome may be via a semi-continuous random variable that combines a continuous distribution with point masses at one or more locations [1]. A particular type of semi-continuous outcome is characterized by a point mass at zero and positive values that usually follow a skewed distribution [2]. Two-part models are often used to analyze such semi-continuous data. These models consist of two separate model parts, with part I to model the zero values and part II to model the continuous values. Some researchers have shown an increased interest in analyzing the semi-continuous outcomes by modeling the discrete zero component separately from the nonzero continuous component [4]. It has been suggested that ignoring the potential dependency between the components can lead to biased results [2,5,8]

Objectives

Methods

Results

Discussion

Conclusion