Tolerance Limits and Confidence Limits for Cost-Effectiveness Analysis
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Date
2016-01-01
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Department
Mathematics and Statistics
Program
Statistics
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Distribution Rights granted to UMBC by the author.
Distribution Rights granted to UMBC by the author.
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Abstract
The topic of cost-effectiveness analysis (CEA) deals with the development of methodologies that can be used to address the question of whether a new treatment or other health care intervention offers good value for the money. The methodologies that have been developed for CEA suitably merge information about health outcomes and costs, and helps health policy makers to allocate their resources in the most gainful way. Reallocating resources to more cost-effective interventions could dramatically increase the number of life years saved. In order to quantify cost-effectiveness, several measures have been proposed in the literature. The most common criteria are the Incremental Cost-Effectiveness Ratio (ICER) and the Incremental Net Benefit (INB). The Average Cost-Effectiveness Ratio (ACER) and Incremental Average Cost-Effectiveness Ratio (ACER) have also been proposed. While evaluating treatments regarding their costs and health benefits, traditional criteria involve comparison of only the means. Although the ICER and the INB have intuitive appeal and the calculation of point estimates is straightforward, the investigation of their statistical properties can be challenging. Within this context, several approaches for constructing confidence intervals for ICER and INB have been proposed. These include parametric methods (e.g. Taylor series expansion and Fieller'stheorem), and non-parametric procedures (e.g. various bootstrap methods). Combinations of these different methods, such as the combination of Fieller'smethod with the bootstrap, have also been proposed in the literature. The aforementioned parametric approaches assume normality or asymptotic normality for (cost, effectiveness). However, the nature of health service resource use is such that cost data are often highly skewed and log-normality may be more appropriate. Furthermore, the data can exhibit a large proportion of zeros. Additionally,even when normality holds, Fieller'smethod may fail to provide a finite confidence interval, and bootstrapping is usually employed with skewed data. It should also be noted that when the data are skewed, following a parametric distribution such as the log-normal, the inference problems of interest involve rather complicated parametric functions. In any case, INB, ICER, ACER and ACER are single statistical summary parameters that cannot adequately describe interplay between costs and benefits in the entire population. Another point to note is that the ICER and the INB are population-level tools; the treatment that maximizes the population'shealth, or has the best overall ICER (or INB), need not be the best choice for a specific individual. The research reported in the thesis is on the development of criteria that can bring out features not captured by the usual summary measures. For this, we consider random variables motivated by the definitions of the summary measures such as ICER, INB, etc., and discuss the computation of tolerance limits for the distribution of these random variables. These are limits that include a specified proportion or more of the population with a given confidence level, and they can be valuable tools for CEA, supplementing the information provided by traditional criteria. In particular, the medians and percentiles of such random variables are of obvious interest, and inference concerning these are addressed herein. The development of the tolerance limits in the thesis assumes that the joint distribution of cost and effectiveness is bivariate normal or log-normal/normal. The methodology used in the thesis include procedures for computing non-parametric tolerance limits, coupled with a bootstrap calibration for improved accuracy. The case of zero-inflated costs is also discussed. Furthermore, binary and Poisson effective measures are also considered, and interval estimation of the traditional parametric measures are addressed. Throughout the thesis, the methodologies are illustrated using both real and simulated cost-effectiveness data.