Empirical Likelihood for the Two Part Cost Models

Co-Principal Investigators: Eugene Laska, Ph.D., Morris Meisner, Ph.D., Carole Siegel, Ph.D., Joseph Wanderling, MA

PROJECT GOALS

Analysis of the cost of competing interventions is a common theme in many health services research projects. A two part cost model corresponds to a population in which a fraction, p, of the population have one distribution of costs, say S and the remaining 1-p have a second distribution. The simplest situation occurs when every member of one of the parts of the population has a single cost that is zero. The generic goal of this project is the development of methodologies that enable valid statistical comparisons of interventions with respect to such cost distributions. During this period our specific aim was to obtain a distribution free statistical approach for comparing the costs of two treatments.

RESEARCH ACTIVITIES AND RESULTS

In the two part model, the comparison of two treatments involves two distinct statistical procedures a test of 1) equality of the proportion p and 2) equality of the distributions of cost, S. We have previously developed a nonparametric test of the equality of the proportions in the two groups [REF}. Our approach to testing equality of the distributions of costs is based on Empirical Likelihood (EL.) EL is a relatively recently developed theory with excellent statistical properties that obtain in a nonparametric setting. The best known use of the method is for estimating a density function, which is part of virtually all statistical analysis packages. We were able to write an expression for the EL test and developed a computer program to implement the procedure. The general EL theory does not apply in this rather complicated case, but we hypothesized that asymptotically the test would follow a chi square distribution. We wrote several simulation programs in Mathematica and tested our speculation for several assumed distributions of S and values of p. Unfortunately, these simulations have not provided evidence that the classical asymptotic chi square theory applies in this setting. Further work will be required to determine the asymptotic distributions of this test.

POLICY IMPLICATIONS

Statistical approaches to the analysis of cost has largely been based on normal distribution assumptions, whereas costs are known to be nonnormal. Procedures that recognize the two part nature of the cost distribution and that also eliminate erroneous distributional assumptions will enable more appropriate statistical methods that will more validly inform decision makers.

PLANS

Limited progress in our aim to develop nonparametric statistical methods was made. We intend to make a few more attempts at determining the asymptotic distribtion of the test statistic. If we are unsuccessful we will abandon this approach in two part models. Developing nonparametric methods for CEA still remains a goal.

Entered: July 17, 2003