A note on the estimation of confidence intervals for cost-effectiveness when costs and effects are censored

<i>Background</i>. The relation between methodological advances in estimation of confidence intervals (CIs) for incremental cost-effectiveness ratios (ICER) and estimation of cost effectiveness in the presence of censoring has not been explored. The authors address the joint problem of estimating ICER precision in the presence of censoring. <i>Methods</i>. Using patient-level data (n = 168) on cost and survival from a published placebo-controlled trial, the authors compared 2 methods of measuring uncertainty with censored data: 1)Bootstrap with censor adjustment (BCA); 2) Fieller’s method with censor adjustment (FCA). The authors estimate the FCA over all possible values for the correlation (p) between costs and effects (range= –1 to +1) and also examine the use of the correlation between cases without censoring adjustment (i.e., simple time-on-study) for costs and effects as an approximation for. <i>Results</i>. Using time-on-study, which considers all censored observations as responders (deaths), yields 0.64 life-years gained at an additional cost of 87.9 for a cost per life-year of 137 (95% CI by bootstrap –5.9 to 392). Censoring adjustment corrects for the bias in the time-on-study approach and reduces the cost per life-year estimate to 132 (=72/0.54). Confidence intervals with censor adjustment were approximately 40% wider than the base-case without adjustment. Using the Fieller method with an approximation of based on the uncensored cost and effect correlation provides a 95% CI of (–48 to 529), which is very close to the BCA interval of (–52 to 504). <i>Conclusions</i>. Adjustment for censoring is necessary in cost-effectiveness studies to obtain unbiased estimates of ICER with appropriate uncertainty limits. In this study, BCA and FCA methods, the latter with approximated covariance, are simple to compute and give similar confidence intervals

Thinking outside the box: recent advances in the analysis and presentation of uncertainty in cost-effectiveness studies

As many more clinical trials collect economic information within their study design, so health economics analysts are increasingly working with patient-level data on both costs and effects. In this paper, we review recent advances in the use of statistical methods for economic analysis of information collected alongside clinical trials. In particular, we focus on the handling and presentation of uncertainty, including the importance of estimation rather than hypothesis testing, the use of the net-benefit statistic, and the presentation of cost-effectiveness acceptability curves. We also discuss the appropriate sample size calculations for cost-effectiveness analysis at the design stage of a study. Finally, we outline some of the challenges for future research in this area—particularly in relation to the appropriate use of Bayesian methods and methods for analyzing costs that are typically skewed and often incomplete

Cost-effectiveness acceptability curves - facts, fallacies and frequently asked questions

Cost-effectiveness acceptability curves (CEACs) have been widely adopted as a method to quantify and graphically represent uncertainty in economic evaluation studies of health-care technologies. However, there remain some common fallacies regarding the nature and shape of CEACs that largely result from the textbook illustration of the CEAC. This textbook CEAC shows a smooth curve starting at probability 0, with an asymptote to 1 for higher money values of the health outcome (). But this familiar ogive shape which makes the textbook CEAC look like a cumulative distribution function is just one special case of the CEAC. The reality is that the CEAC can take many shapes and turns because it is a graphic transformation from the cost-effectiveness plane, where the joint density of incremental costs and effects may straddle quadrants with attendant discontinuities and asymptotes. In fact CEACs: (i) do not have to cut the y-axis at 0; (ii) do not have to asymptote to 1; (iii) are not always monotonically increasing in ; and (iv) do not represent cumulative distribution functions (cdfs). Within this paper we present a gallery of CEACs in order to identify the fallacies and illustrate the facts surrounding the CEAC. The aim of the paper is to serve as a reference tool to accompany the increased use of CEACs within major medical journals

Probabilistic analysis of cost-effectiveness models: choosing between treatment strategies for gastroesophageal reflux disease

When choosing between mutually exclusive treatment options, it is common to construct a cost-effectiveness frontier on the cost-effectiveness plane that represents efficient points from among the treatment choices. Treatment options internal to the frontier are considered inefficient and are excluded either by strict dominance or by appealing to the principle of extended dominance. However, when uncertainty is considered, options excluded under the baseline analysis may form part of the cost-effectiveness frontier. By adopting a Bayesian approach, where distributions for model parameters are specified, uncertainty in the decision concerning which treatment option should be implemented is addressed directly. The approach is illustrated using an example from a recently published cost-effectiveness analysis of different possible treatment strategies for gastroesophageal reflux disease.It is argued that probabilistic analyses should be encouraged because they have potential to quantify the strength of evidence in favor of particular treatment choices

BeppoSAX observations of the Seyfert 1 Galaxy NGC 3516

We present the results of two observations of the bright Seyfert 1 galaxy NGC 3516, obtained with BeppoSAX in 1996 November and 1997 March. Useful signal is detected between 0.2 and 60 keV, allowing for the first time the simultaneous observation of all main spectral features. The source was brighter by a factor 2 at the second epoch of observation. Both spectra present a strong Fe Kalpha line, and a reflection hump at high energy. An absorption edge at 0.8 keV is visible in the later spectrum, but not in the earlier one, indicating that this feature is strongly variable.Comment: to appear in : The Active X-ray Sky: Results from BeppoSAX and Rossi-XTE, Nuclear Physics B Proceedings Supplements, L. Scarsi, H. Bradt, P. Giommi and F. Fiore (eds.), Elsevier Science B.V. 4 pages LateX and 6 ps figures, using espcrc2 and epsfi

Oscillations in radioactive exponential decay

Several older and recent reports provided evidence for the oscillatory character of the exponential decay law in radioactive decay and attempted to explain it with basic physics. We show here that the measured effects observed in some of the cases, namely in the decay of 226Ra, 32Si in equilibrium, and 36Cl, can be explained with the temperature variations

Validation of an ear tag–based accelerometer system for detecting grazing behavior of dairy cows

peer-reviewedThe objective of the study was to develop a grazing algorithm for an ear tag–based accelerometer system (Smartbow GmbH, Weibern, Austria) and to validate the grazing algorithm with data from a noseband sensor. The ear tag has an acceleration sensor, a radio chip, and temperature sensor for calibration and it can monitor rumination and detect estrus and localization. To validate the ear tag, a noseband sensor (RumiWatch, Itin and Hoch GmbH, Liestal, Switzerland) was used. The noseband sensor detects pressure and acceleration patterns, and, with a software program specific to the noseband, pressure and acceleration patterns are used to classify data into eating, ruminating, drinking, and other activities. The study was conducted at the University of Minnesota West Central Research and Outreach Center (Morris, MN) and at Teagasc Animal and Grassland Research and Innovation Centre (Moorepark, Fermoy, Co. Cork, Ireland). During May and June 2017, observational data from Minnesota and Ireland were used to develop the grazing algorithm. During September 2018, data were collected by the ear tag and noseband sensor from 12 crossbred cows in Minnesota for a total of 248 h and from 9 Holstein-Friesian cows in Ireland for a total of 248 h. A 2-sided t-test was used to compare the percentage of grazing and nongrazing time recorded by the ear tag and the noseband sensor. Pearson correlations and concordance correlation coefficients (CCC) were used to evaluate associations between the ear tag and noseband sensor. The percentage of total grazing time recorded by the ear tag and by the noseband sensor was 37.0% [95% confidence interval (CI): 32.1 to 42.0] and 40.5% (95% CI: 35.5 to 45.6), respectively, in Minnesota, and 35.4% (95% CI: 30.6 to 40.2) and 36.9% (95% CI: 32.1 to 41.8), respectively, in Ireland. The ear tag and noseband sensor agreed strongly for monitoring grazing in Minnesota (r = 0.96; 95% CI: 0.94 to 0.97, CCC = 0.95) and in Ireland (r = 0.92; 95% CI: 0.90 to 0.94, CCC = 0.92). The results suggest that there is potential for the ear tag to be used on pasture-based dairy farms to support management decision-making