Endgames Statistical Question

Multiple hypothesis testing and Bonferroni’s correction

BMJ 2014; 349 doi: https://doi.org/10.1136/bmj.g6284 (Published 20 October 2014) Cite this as: BMJ 2014;349:g6284
  1. Philip Sedgwick, reader in medical statistics and medical education1
  1. 1Institute for Medical and Biomedical Education, St George’s, University of London, London, UK
  1. p.sedgwick{at}sgul.ac.uk

Researchers assessed the effectiveness of a multifaceted intervention directed at general practitioners on six year mortality and morbidity in patients with newly diagnosed type 2 diabetes. A cluster randomised controlled study design was used. Clustering was at the GP level. The intervention consisted of regular follow-up and individualised goal setting for patients, which was supported by prompting of doctors, clinical guidelines, feedback, and continuing medical education. The control treatment consisted of routine care, and doctors were free to choose any treatment and change it over time. Participants were aged 40 years or more, had been diagnosed as having diabetes during 1989 to 1991, and had survived until six year follow-up. In total, 874 patients were recruited, with 459 allocated to the intervention and 415 allocated to the control.1

The primary outcomes were overall mortality, incidence of diabetic retinopathy, urinary albumin concentration ≥15 mg/L, myocardial infarction, and stroke in patients without these outcomes at baseline. The critical level of significance was 0.05 (5%). At the end of follow-up, the treatment groups differed significantly only in one of the five primary outcomes. A lower proportion of the intervention group had a urinary albumin concentration ≥15 mg/L (22.5% v 30.8%; P=0.04). When multiple testing was taken into account using Bonferroni’s adjustment, no significant differences in the primary outcomes were observed. It was concluded that, in primary care, individualised goals with educational and surveillance support did not affect six year mortality and morbidity in patients with newly diagnosed type 2 diabetes.

Which of the following statements, if any, are true?

  • a) The maximum probability of a type I error occurring for a single hypothesis test was 0.05 (5%)

  • b) The overall type I error rate for the five hypothesis tests of the primary outcomes was no greater than 0.05 (5%)

  • c) Bonferroni’s correction …

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