Cost-effectiveness analysis under multiple effectiveness outcomes: A probabilistic approach.

Probability based criteria are proposed for the assessment of cost-effectiveness of a new treatment compared to a standard treatment when there are multiple effectiveness measures. Depending on the preferences of a policy maker, there are several options to define such criteria. Two such metrics are investigated in detail. One metric is defined as the conditional probability that a new treatment is more effective with respect to the multiple effectiveness measures for patients having lower costs under the new treatment. A second metric is defined as the conditional probability that a new treatment is less costly for patients having greater health benefits under the new treatment. The metrics offer considerable flexibility to a policy maker as thresholds for cost and effectiveness can be incorporated into the metrics. Parametric confidence limits are developed using a percentile bootstrap approach assuming multivariate normality for the joint distribution of the log(cost) and effectiveness measures. A non-parametric estimation procedure is also developed using the theory of U-statistics. Numerical results indicate that the proposed confidence limits accurately maintain coverage probabilities. The methodologies are illustrated using a study on the treatment of type two diabetes. Code implementing the proposed methods are provided in the supporting information.

Cost-Efficient Multiply Matched Case-Control Study Designs.

In multiply matched case-control studies, a number of cases and controls may be included in each matched set. However, when per-participant costs between cases and controls differ, investigators should be aware of how the numbers of cases and controls per matched set affect the overall total study cost. Traditional statistical approaches to designing case-control studies do not account for study costs. Given an effect size, the power to detect differences is typically a function of the numbers of cases and controls within each matched set. Therefore, the same level of statistical power will be achieved based on various combinations of the numbers of cases and controls. Typical matched case-control studies match a case to a number of controls by levels of 1 or more known factors. Several authors have shown that for study designs with 1 case per matched set, the optimal number of controls within each matched set that minimizes the total study cost is the square root of the ratio of the cost of a case to the cost of a control. Herein, we extend this result to the setting of a multiply matched case-control study design, when 1 or more cases are matched to controls within each matched set. A Shiny web application implementation of the proposed methods is presented.

Cost-efficient clinical studies with continuous time survival outcomes.

Time-to-event outcomes are common in clinical studies. For example, the time to a first major adverse cardiovascular event (MACE, defined as CVD death, nonfatal myocardial infarction, or stroke) is a commonly used outcome in cardiovascular outcome trials. Owing to the lengthy time frame and other factors, the high costs of conducting such studies has been identified as one of the major obstacles in conducting clinical trials in the United States. However, typical approaches for designing clinical trials with time-to-event outcomes do not consider study costs. For a given effect size (eg, hazard ratio), the power to detect differences between two groups is typically a function of the total number of events observed in the study. Therefore, the same level of power will be achieved based on various combinations of the total number of participants, length of enrollment and total follow-up times, and group allocation probability. Herein, we provide a general framework for designing cost-efficient studies comparing treatments with respect to continuous time-to-event outcomes. Among the various designs that achieve the desired level of power to detect a given effect size for a fixed type-I error level, the optimal cost-efficient design is the design that minimizes the expected total study cost. The method is general and can be used for Cox proportional hazards models or Aalen additive models, and under various recruitment and censoring assumptions. The proposed approach for designing cost-efficient studies is illustrated for a Weibull time-to-event outcome with uniform recruitment and exponentially distributed censoring time. The case of an additive hazards model is also described. A Shiny web application implementation of the proposed methods is presented.

A simple framework to identify optimal cost-effective risk thresholds for a single screen: Comparison to Decision Curve Analysis.

Decision Curve Analysis (DCA) is a popular approach for assessing biomarkers and risk models, but does not require costs and thus cannot identify optimal risk thresholds for actions. Full decision analyses can identify optimal thresholds, but typically used methods are complex and often difficult to understand. We develop a simple framework to calculate the Incremental Net Benefit for a single-time screen as a function of costs (for tests and treatments) and effectiveness (life-years gained). We provide simple expressions for the optimal cost-effective risk-threshold and, equally importantly, for the monetary value of life-years gained associated with the risk-threshold. We consider the controversy over the risk-threshold to screen women for mutations in BRCA1/2. Importantly, most, and sometimes even all, of the thresholds identified by DCA are infeasible based on their associated dollars per life-year gained. Our simple framework facilitates sensitivity analyses to cost and effectiveness parameters. The proposed approach estimates optimal risk thresholds in a simple and transparent manner, provides intuition about which quantities are critical, and may serve as a bridge between DCA and a full decision analysis.

Frequency of Evidence-Based Screening for Retinopathy in Type 1 Diabetes.

BACKGROUND: In patients who have had type 1 diabetes for 5 years, current recommendations regarding screening for diabetic retinopathy include annual dilated retinal examinations to detect proliferative retinopathy or clinically significant macular edema, both of which require timely intervention to preserve vision. During 30 years of the Diabetes Control and Complications Trial (DCCT) and its longitudinal follow-up Epidemiology of Diabetes Interventions and Complications (EDIC) study, retinal photography was performed at intervals of 6 months to 4 years. METHODS: We used retinal photographs from the DCCT/EDIC study to develop a rational screening frequency for retinopathy. Markov modeling was used to determine the likelihood of progression to proliferative diabetic retinopathy or clinically significant macular edema in patients with various initial retinopathy levels (no retinopathy or mild, moderate, or severe nonproliferative diabetic retinopathy). The models included recognized risk factors for progression of retinopathy. RESULTS: Overall, the probability of progression to proliferative diabetic retinopathy or clinically significant macular edema was limited to approximately 5% between retinal screening examinations at 4 years among patients who had no retinopathy, 3 years among those with mild retinopathy, 6 months among those with moderate retinopathy, and 3 months among those with severe nonproliferative diabetic retinopathy. The risk of progression was also closely related to mean glycated hemoglobin levels. The risk of progression from no retinopathy to proliferative diabetic retinopathy or clinically significant macular edema was 1.0% over 5 years among patients with a glycated hemoglobin level of 6%, as compared with 4.3% over 3 years among patients with a glycated hemoglobin level of 10%. Over a 20-year period, the frequency of eye examinations was 58% lower with our practical, evidence-based schedule than with routine annual examinations, which resulted in substantial cost savings. CONCLUSIONS: Our model for establishing an individualized schedule for retinopathy screening on the basis of the patient's current state of retinopathy and glycated hemoglobin level reduced the frequency of eye examinations without delaying the diagnosis of clinically significant disease. (Funded by the National Institute of Diabetes and Digestive and Kidney Diseases and others; DCCT/EDIC ClinicalTrials.gov numbers, NCT00360893 and NCT00360815 .).

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.

Likelihood inference for a two-stage design with treatment selection.

A conditional likelihood-based approach is proposed to construct confidence intervals for the parameters of interest in a two-stage design with treatment selection after the first stage. Both a Wald confidence interval and a confidence interval based on inverting the likelihood ratio test are proposed. The operating characteristics of these confidence intervals: the coverage probabilities and average confidence interval lengths, as well as the average bias and mean-square error of the corresponding point estimates, compare favorably with other available techniques. Possible extensions and an alternative unconditional approach based on the likelihood with missing at random mechanism are also briefly described.