# Statistical analysis of cost-effectiveness data Willan AR, Briggs AH (2006) ISBN: 978-0-470-85626-0; 210 pages; £45.00, €60.80, \$90.00 Wiley; http://www.wiley.com/

## Authors

This book succeeds in its aim of giving a simple and understandable presentation of a wide range of topics in health economics and an overview of statistical methods used in the analysis of cost-effectiveness data. As well as providing an excellent overview of parameters of interest in the health economics, it also presents recent methodological developments in this area. The book is designed for students in the final year undergraduate mathematics and statistics courses or postgraduate social sciences courses. It is also intended to serve as a reference for statisticians and health economists in academia and the pharmaceutical industry.

Health economics is a relatively young discipline and there are plenty of recent methodological developments in this area. Parameters of interest in the cost-effectiveness analysis (CEA) are difference between treatment arms with respect to effectiveness Δe, difference between treatment arms of mean costs over the duration if interest Δc, and variances and covariances of those estimators.

The incremental cost-effectiveness ratio (ICER) is defined as Δce. If the measure of effectiveness is the probability of surviving then the ICE is cost of saving a life (or preventing a death). If the measure of effectiveness is mean survival or mean quality-adjusted survival, the ICER is the cost of achieving an extra year or quality adjusted year of life (QALY), respectively. In summary, the ICER is the cost of an additional unit of effectiveness if a new treatment is adopted over the standard treatment. This needs to be compared with what a policy maker is willing to pay (it is called willingness-to-pay) and is denoted by λ

The cost effectiveness (CE) plane is a graph with the mean effectiveness Δe and mean cost over duration of interest Δc, plotted on horizontal and vertical axis, respectively. It is used for the interpretation of cost-effectiveness analyses. The plane has four quadrants: north east (NE), south west (SW), north west (NW) and south east (SE). Where Δe is positive (NE or SE quadrants), the new treatment is cost-effective if, and only if, the ICER<λ However, where Δe is negative (NW or SW quadrants), the new treatment is cost-effective if, and only if, the ICER>λ.

Sometimes there are concerns when making statistical inference (e.g. interpretation of the confidence interval and problem with the ratio statistics) on the ICER, then the incremental net benefit (INB) approach can be applied where the INB is defined as Δeλ–Δc.

The standard approach that includes the direct estimation of the parameters: mean incremental cost, effects, their variance and covariance required to formulate either the ICER or the net benefit statistics and it is described in Chapters 2–8. Modelling is another approach and involves the separate components of the CE equation, in order to build indirect estimates of incremental cost and effectiveness and it is presented in more details in Chapter 9. The starting chapter, Chapter 1, introduces the cost-effectiveness data, the cost-effectiveness plane, the ICER and INB. Chapter 2 is devoted to methods for estimating Δe and Δc and their variance and covariance for non-censored data while Chapter 3 deals with methods of estimation for the same parameters but only for censored data. Chapter 4 considers methods for estimating ICER and INB with their confidence intervals such as cost-effectiveness acceptability curves, bootstrap methods and the Bayesian approach. In Chapter 5, the methods from the previous chapters are illustrated with examples. The comprehensive review of sample size determination for cost-effectiveness trials using frequentist and Bayesian approach is described in Chapter 6. Regression methods for the covariate adjustment of cost-effectiveness analyses are reviewed in Chapter 7. The data from multinational and multicentre clinical trials in cost-effectiveness analyses are described in Chapter 8. Statistical modelling is involved in the estimation of cost-effectiveness parameters and presented in Chapter 9.

This is an enormously useful book, concise and clearly written, which deserves to find readers among students of statistics and health economics, and researchers in academic and pharmaceutical environments. I enjoyed very much reading this book.