Estimating medical costs from a transition model

📝 Abstract

Nonparametric estimators of the mean total cost have been proposed in a variety of settings. In clinical trials it is generally impractical to follow up patients until all have responded, and therefore censoring of patient outcomes and total cost will occur in practice. We describe a general longitudinal framework in which costs emanate from two streams, during sojourn in health states and in transition from one health state to another. We consider estimation of net present value for expenditures incurred over a finite time horizon from medical cost data that might be incompletely ascertained in some patients. Because patient specific demographic and clinical characteristics would influence total cost, we use a regression model to incorporate covariates. We discuss similarities and differences between our net present value estimator and other widely used estimators of total medical costs. Our model can accommodate heteroscedasticity, skewness and censoring in cost data and provides a flexible approach to analyses of health care cost.

💡 Analysis

Nonparametric estimators of the mean total cost have been proposed in a variety of settings. In clinical trials it is generally impractical to follow up patients until all have responded, and therefore censoring of patient outcomes and total cost will occur in practice. We describe a general longitudinal framework in which costs emanate from two streams, during sojourn in health states and in transition from one health state to another. We consider estimation of net present value for expenditures incurred over a finite time horizon from medical cost data that might be incompletely ascertained in some patients. Because patient specific demographic and clinical characteristics would influence total cost, we use a regression model to incorporate covariates. We discuss similarities and differences between our net present value estimator and other widely used estimators of total medical costs. Our model can accommodate heteroscedasticity, skewness and censoring in cost data and provides a flexible approach to analyses of health care cost.

📄 Content

arXiv:0805.2496v1 [stat.AP] 16 May 2008 IMS Collections Beyond Parametrics in Interdisciplinary Research: Festschrift in Honor of Professor Pranab K. Sen Vol. 1 (2008) 350–363 c⃝Institute of Mathematical Statistics, 2008 DOI: 10.1214/193940307000000266 Estimating medical costs from a transition model Joseph C. Gardiner1, Lin Liu2 and Zhehui Luo3 Michigan State University Abstract: Nonparametric estimators of the mean total cost have been pro- posed in a variety of settings. In clinical trials it is generally impractical to follow up patients until all have responded, and therefore censoring of patient outcomes and total cost will occur in practice. We describe a general longi- tudinal framework in which costs emanate from two streams, during sojourn in health states and in transition from one health state to another. We con- sider estimation of net present value for expenditures incurred over a finite time horizon from medical cost data that might be incompletely ascertained in some patients. Because patient specific demographic and clinical charac- teristics would influence total cost, we use a regression model to incorporate covariates. We discuss similarities and differences between our net present value estimator and other widely used estimators of total medical costs. Our model can accommodate heteroscedasticity, skewness and censoring in cost data and provides a flexible approach to analyses of health care cost.

1. Introduction Estimating cost from medical follow-up studies has been the focus of extensive methodological research. Cost data in observational studies exhibit several features such as heteroscedasticity, skewness and censoring that must be addressed in sta- tistical modeling so that ensuing inference would be valid. In clinical trials it is generally impractical to prolong a study until all patients have responded, and therefore inevitably censoring of patient outcomes and total cost will occur in prac- tice. Since costs are incurred over time, the cumulative cost C(t) at time t is a nonnegative monotone function. Cost accumulation ends at an event time T , for example at death for lifetime cost, or at a specified finite time horizon τ. Interest lies in estimating the mean cost µ = E(C(T ∗)) where T ∗= min(T, τ). Because T could be precluded from observation by censoring at time U, that is, when T > U, the corresponding cost would be complete only if U ≥T ∗. Several nonparametric estimators of µ have been proposed in a variety of settings with regression mod- els being the mainstay for assessing the influence of patient-specific characteristics (eg, treatments, demographics, comorbidity) on cost (for example, Bang and Tsi- ∗Supported by the Agency for Healthcare Research & Quality under grant 1R01 HS14206. 1Division of Biostatistics, Department of Epidemiology, B629 West Fee Hall, Michigan State University, East Lansing, MI 48824, USA, e-mail: jgardiner@epi.msu.edu 2Now at Eli Lilly and Company, US Medical Division, Indianapolis, Indiana 46285, USA, e-mail: liu lin ll@lilly.com 3Now at RTI International, Behavioral Health Economics Program, 3040 Cornwallis Rd., Re- search Triangle Park, NC 27709, USA, e-mail: zluo@rti.org AMS 2000 subject classifications: Primary 62N01, 60J27; secondary 62G05. Keywords and phrases: censoring, Kaplan-Meier estimator, longitudinal data, Markov model, inverse-weighting, random-effects. 350 Estimating medical costs 351 atis [2, 3], Baser et al. [4, 5], Lin [13, 14], Lin et al. [15], O’Hagan and Stevens [17], Strawderman [18] and Gardiner et al. [8]). This article adopts a broader view of the cumulative cost {C(t) : 0 ≤t ≤τ} within the framework of a longitudinal model. Section 2 describes all the substan- tive aspects of our models starting with an underlying finite state stochastic process for the evolution of patient events as they occur over time. The states are different health conditions that the patient presents over the period [0, τ]. Costs emanate from two streams, during sojourn in health states and in transition from one health state to another. We consider estimation of net present value (NPV) for expendi- tures incurred over [0, τ]. Regression models for the event history process and for observed costs are used to incorporate covariates. Section 3 outlines the method of estimation of NPV from a patient sample of time-censored event history data. We then discuss similarities and differences between our net present value estima- tor and other widely used estimators of total medical costs. Section 4 is a brief summary and conclusion.
2. Stochastic model 2.1. Transition and sojourn cost A stochastic process X = {X(t) : t ∈T } on the interval T = [0, τ] where τ < ∞, describes the health states of a patient from the relevant population under study. The time τ is the maximum limit of observation for all cost and patient outcomes. The state space of X is finite and labeled E= {0, . . . , m} and consists of several transient states, such as “well”, “recovery”, “relapse”

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