Parametric cost-effectiveness inference with skewed data

Estimating cost-effectiveness from claims and registry data with measured and unmeasured confounders

The analysis of observational data to determine the cost-effectiveness of medical treatments is complicated by the need to account for skewness, censoring, and the effects of measured and unmeasured confounders. We quantify cost-effectiveness as the Net Monetary Benefit (NMB), a linear combination of the treatment effects on cost and effectiveness that denominates utility in monetary terms. We propose a parametric estimation approach that describes cost with a Gamma generalized linear model and survival time (the canonical effectiveness variable) with a Weibull accelerated failure time model. To account for correlation between cost and survival, we propose a bootstrap procedure to compute confidence intervals for NMB. To examine sensitivity to unmeasured confounders, we derive simple approximate relationships between naïve parameters, assuming only measured confounders, and the values those parameters would take if there was further adjustment for a single unmeasured confounder with a specified distribution. A simulation study shows that the method returns accurate estimates for treatment effects on cost, survival, and NMB under the assumed model. We apply our method to compare two treatments for Stage II/III bladder cancer, concluding that the NMB is sensitive to hypothesized unmeasured confounders that represent smoking status and personal income.

Cost-effectiveness of national health insurance programs in high-income countries: A systematic review

OBJECTIVES

National health insurance is now common in most developed countries. This study reviews the evidence and synthesizes the cost-effectiveness information for national health insurance or disability insurance programs across high-income countries.

DATA SOURCES

A literature search using health, economics and systematic review electronic databases (PubMed, Embase, Medline, Econlit, RepEc, Cochrane library and Campbell library), was conducted from April to October 2015.

STUDY SELECTION

Two reviewers independently selected relevant studies by applying screening criteria to the title and keywords fields, followed by a detailed examination of abstracts.

DATA EXTRACTION

Studies were selected for data extraction using a quality assessment form consisting of five questions. Only studies with positive answers to all five screening questions were selected for data extraction. Data were entered into a data extraction form by one reviewer and verified by another.

EVIDENCE SYNTHESIS

Data on costs and quality of life in control and treatment groups were used to draw distributions for synthesis. We chose the log-normal distribution for both cost and quality-of-life data to reflect non-negative value and high skew. The results were synthesized using a Monte Carlo simulation, with 10,000 repetitions, to estimate the overall cost-effectiveness of national health insurance programs.

RESULTS

Four studies from the United States that examined the cost-effectiveness of national health insurance were included in the review. One study examined the effects of medical expenditure, and the remaining studies examined the cost-effectiveness of health insurance reforms. The incremental cost-effectiveness ratio (ICER) ranged from US$23,000 to US$64,000 per QALY. The combined results showed that national health insurance is associated with an average incremental cost-effectiveness ratio of US$51,300 per quality-adjusted life year (QALY). Based on the standard threshold for cost-effectiveness, national insurance programs are cost-effective interventions.

CONCLUSIONS

Although national health insurance programs have been introduced in most developed countries, only a few studies have examined their cost-effectiveness. All the selected studies revealed strong evidence to support health insurance programs or health reforms in the United States. The average ICER in this study is below the standard threshold for cost-effectiveness used in the US. The small number of relevant studies is the main limitation of this study.

Tolerance limits and tolerance intervals for ratios of normal random variables using a bootstrap calibration

This paper addresses the problem of deriving one-sided tolerance limits and two-sided tolerance intervals for a ratio of two random variables that follow a bivariate normal distribution, or a lognormal/normal distribution. The methodology that is developed uses nonparametric tolerance limits based on a parametric bootstrap sample, coupled with a bootstrap calibration in order to improve accuracy. The methodology is also adopted for computing confidence limits for the median of the ratio random variable. Numerical results are reported to demonstrate the accuracy of the proposed approach. The methodology is illustrated using examples where ratio random variables are of interest: an example on the radioactivity count in reverse transcriptase assays and an example from the area of cost-effectiveness analysis in health economics.

Probabilistic measures of cost-effectiveness

Several probability-based measures are introduced in order to assess the cost-effectiveness of a treatment. The basic measure consists of the probability that one treatment is less costly and more effective compared with another. Several variants of this measure are suggested as flexible options for cost-effectiveness analysis. The proposed measures are invariant under monotone transformations of the cost and effectiveness measures. Interval estimation of the proposed measures are investigated under a parametric model, assuming bivariate normality, and also non-parametrically. The delta method and a generalized pivotal quantity approach are both investigated under the bivariate normal model. A non-parametric U-statistics-based approach is also investigated for computing confidence intervals. Numerical results show that under bivariate normality, the solution based on generalized pivotal quantities exhibits accurate performance in terms of maintaining the coverage probability of the confidence interval. The non-parametric U-statistics-based solution is accurate for sample sizes that are at least moderately large. The results are illustrated using data from a clinical trial for prostate cancer therapy. Copyright © 2016 John Wiley & Sons, Ltd.