Setting sample size using cost efficiency in fMRI studies

Qing Guo,^1,3 Geoffrey Hall,² Margaret McKinnon,^2,4,7 Lehana Thabane,^1,3,5 Ron Goeree,^1,5,6 Eleanor Pullenayegum<sup>1,3,5

1</sup>Department of Epidemiology and Biostatistics, ²Department of Psychiatry and Behavioral Neurosciences, McMaster University, Hamilton, ON, Canada; ³Biostatistics Unit, ⁴Mood Disorders Program, ⁵Center for Evaluation of Medicine, ⁶Programs for Assesment of Technology in Health (PATH) Research Institute, St, Joseph’s Healthcare, Hamilton, ON, Canada; ⁷Kunin-Lunenfeld Applied Research Unit, Baycrest, Toronto, ON, Canada

Background: Sample size calculations are rarely performed for functional magnetic resonance imaging studies involving clinical populations. This may be due to uncertainty as to the size of expected effect and the variance of the blood oxygenation level dependent response. Moreover, existing sample size methods ignore the costs associated with performing the proposed study. The current paper describes how cost efficiency, a recently proposed method, can be used in conjunction with existing methods to address these issues.
Methods: Cost efficiency is the ratio of a study’s value to its cost, and sample size is chosen to maximize cost efficiency (ie, to maximize return on investment). It is suggested that sample size calculations begin by calculating the sample sizes required to achieve a given power, through varying the input parameters to the calculation over their plausible ranges. Cost efficiency can then help narrow the resulting range of sample sizes and help choose one sample size. The approach is illustrated through a recent functional magnetic resonance imaging study of autobiographical memory retrieval in patients with major depressive disorder.
An example: Setting power to 80% and type 1 error rate to 5%, the method of Mumford and Nichols was used to calculate sample size. There were no reported effect sizes for similar studies in the literature; consequently, this parameter was varied over its plausible range (Cohen’s d varying from 0.2 to 0.8). This yielded sample sizes ranging from 50 to 800. Within these, cost efficiency gave a sample size of 88.
Conclusion: Poor reporting of the input parameters to power-based methods of sample size determination results in a wide range of candidate sample sizes. The cost efficiency approach supplies a way of narrowing this range and choosing a sample size from that.

Keywords: cost efficiency, sample size, power, fMRI studies