Sample size calculation in trials of public health interventions: a discussion of implications for health economists

• Published in: The Lancet (British edition) 2013-11, Vol.382 (S3), p.S64-S64
• Main Authors: Lloyd-Williams, Huw, MSc, Edwards, Rhiannon Tudor, Prof
• Format: Article
• Language: English
• Subjects: Case studies; clinical trials; cost effectiveness; diabetes; Economics; economists; Health promotion; Internal Medicine; Public health; Statistical analysis; Systematic review; willingness to pay
• ISSN: 0140-6736; 1474-547X
• DOI: 10.1016/S0140-6736(13)62489-7

Abstract Background Statistical analysis enables ascertainment of whether or not there are interesting differences in effects between two or more groups and allows inferences to be made about the population from which a sample comes. For those of us interested in these differences, to be able to report on their statistical significance is useful to help us remark on the confidence we have in our results. However, careful consideration should be given to the choice of sample size. We investigated recent developments in the methodological considerations surrounding issues of identification of an appropriate sample size for a study, investigating first the issue in the context of clinical trials before going on to discuss the issue in terms of public health. Methods In this discussion piece, we highlight recent developments in the area of sample size calculation. We then offer two case studies that provide examples of sample size estimation under different scenarios: when no power or sample size calculations have been mentioned and when power or sample size calculations have been done properly. The first was done by the UK prospective diabetes study group (1998) in which the sample size was 1148, although there was no explicit mention of how this sample size was calculated. The second case study was an example by Briggs and Gray (1998) on the study of intracranial aneurysms. They plotted the sample size requirements as a function of the maximum cost-effectiveness ratio. One can then, for a given level of cost effectiveness, work out the sample size needed for different levels of power. Findings Although clinical trials calculate sample sizes on the basis of clinical outcomes, we show that these sample sizes might not provide enough power for any economic assessment we might want to undertake, because economic assessments deal with both costs and treatment effects. Usually, economic assessment relates to estimation rather than hypothesis testing. Therefore, calculations of power and sample size in economic assessment are done in relation to some value of maximum willingness to pay (WTP) for a unit of treatment effect. The upper confidence limit of the incremental cost-effectiveness ratio of a cost-effective treatment must fall below the value of the maximum WTP and the sample size must provide enough power for this to be possible. Further, in economic assessment of public health interventions, the effective sample size might be less than the actual sample size