Subgroup analyses in randomised controlled trials: quantifying the risks of false-positives and false-negatives

Authors: Brookes ST, Whitley E, Peters TJ, Mulheran PA, Egger M, Davey Smith G

Journal: Health Technology Assessment Volume: 5 Issue: 33

Publication date: October 2001



Brookes ST, Whitley E, Peters TJ, Mulheran PA, Egger M, Davey Smith G.Subgroup analyses in randomised controlled trials: quantifying the risks of false-positives and false-negatives. Health Technol Assess 2001;5(33)

Download: Citation (for this publication as a .ris file) (7.0 KB)

Journal issues* can be purchased by completing the form.

The cost of reports varies according to number of pages and postage address. The minimum cost for a copy sent to a UK address is £30.00. We will contact you on receipt of your completed form to advise you of actual cost. If you have any queries, please contact

*We regret that unfortunately we are unable to supply bound print copies of Health Technology Assessment published before issue 12:31. However, PDFs are available to print from the "Downloads" tab of the issue page.


No responses have been published. If you would like to submit a response to this publication, please do so using the form below.

Comments submitted to the NIHR Journals Library are electronic letters to the editor. They enable our readers to debate issues raised in research reports published in the Journals Library. We aim to post within 2 working days all responses that contribute substantially to the topic investigated, as determined by the Editors.

Your name and affiliations will be published with your comment.

Once published, you will not have the right to remove or edit your response. The Editors may add, remove, or edit comments at their absolute discretion.

Post your response



Middle Initial

Occupation / Job title

Affiliation / Employer



Other authors

For example, if you are responding as a team or group. Please ensure you include full names and separate these using commas

Statement of competing interests

We believe that readers should be aware of any competing interests (conflicts of interest).

The International Committee of Medical Journal Editors (ICMJE) define competing interests as including: financial relationships with industry (for example through employment, consultancies, stock, ownership, honoraria, and expert testimony), either directly or through immediate family; personal relationships; academic competition; and intellectual passion.

If yes, provide details below:

Enter response title

Enter response message


Security key

Regenerate security key

By submitting your response, you are stating that you agree to the terms & conditions

The full text of this issue is available as a PDF document from the Downloads section on this page.



Subgroup analyses are common in randomised controlled trials (RCTs). There are many easily accessible guidelines on the selection and analysis of subgroups but the key messages do not seem to be universally accepted and inappropriate analyses continue to appear in the literature. This has potentially serious implications because erroneous identification of differential subgroup effects may lead to inappropriate provision or withholding of treatment.


(1) To quantify the extent to which subgroup analyses may be misleading. (2) To compare the relative merits and weaknesses of the two most common approaches to subgroup analysis: separate (subgroup-specific) analyses of treatment effect and formal statistical tests of interaction. (3) To establish what factors affect the performance of the two approaches. (4) To provide estimates of the increase in sample size required to detect differential subgroup effects. (5) To provide recommendations on the analysis and interpretation of subgroup analyses.


The performances of subgroup-specific and formal interaction tests were assessed by simulating data with no differential subgroup effects and determining the extent to which the two approaches (incorrectly) identified such an effect, and simulating data with a differential subgroup effect and determining the extent to which the two approaches were able to (correctly) identify it. Initially, data were simulated to represent the 'simplest case' of two equal-sized treatment groups and two equal-sized subgroups. Data were first simulated with no differential subgroup effect and then with a range of types and magnitudes of subgroup effect with the sample size determined by the nominal power (50-95%) for the overall treatment effect. Additional simulations were conducted to explore the individual impact of the sample size, the magnitude of the overall treatment effect, the size and number of treatment groups and subgroups and, in the case of continuous data, the variability of the data. The simulated data covered the types of outcomes most commonly used in RCTs, namely continuous (Gaussian) variables, binary outcomes and survival times. All analyses were carried out using appropriate regression models, and subgroup effects were identified on the basis of statistical significance at the 5% level.


While there was some variation for smaller sample sizes, the results for the three types of outcome were very similar for simulations with a total sample size of greater than or equal to 200. With simulated simplest case data with no differential subgroup effects, the formal tests of interaction were significant in 5% of cases as expected, while subgroup-specific tests were less reliable and identified effects in 7-66% of cases depending on whether there was an overall treatment effect. The most common type of subgroup effect identified in this way was where the treatment effect was seen to be significant in one subgroup only. When a simulated differential subgroup effect was included, the results were dependent on the nominal power of the simulated data and the type and magnitude of the subgroup effect. However, the performance of the formal interaction test was generally superior to that of the subgroup-specific analyses, with more differential effects correctly identified. In addition, the subgroup-specific analyses often suggested the wrong type of differential effect. The ability of formal interaction tests to (correctly) identify subgroup effects improved as the size of the interaction increased relative to the overall treatment effect. When the size of the interaction was twice the overall effect or greater, the interaction tests had at least the same power as the overall treatment effect. However, power was considerably reduced for smaller interactions, which are much more likely in practice. The inflation factor required to increase the sample size to enable detection of the interaction with the same power as the overall effect varied with the size of the interaction. For an interaction of the same magnitude as the overall effect, the inflation factor was 4, and this increased dramatically to of greater than or equal to 100 for more subtle interactions of < 20% of the overall effect. Formal interaction tests were generally robust to alterations in the number and size of the treatment and subgroups and, for continuous data, the variance in the treatment groups, with the only exception being a change in the variance in one of the subgroups. In contrast, the performance of the subgroup-specific tests was affected by almost all of these factors with only a change in the number of treatment groups having no impact at all.


While it is generally recognised that subgroup analyses can produce spurious results, the extent of the problem is almost certainly under-estimated. This is particularly true when subgroup-specific analyses are used. In addition, the increase in sample size required to identify differential subgroup effects may be substantial and the commonly used 'rule of four' may not always be sufficient, especially when interactions are relatively subtle, as is often the case. CONCLUSIONS--RECOMMENDATIONS FOR SUBGROUP ANALYSES AND THEIR INTERPRETATION: (1) Subgroup analyses should, as far as possible, be restricted to those proposed before data collection. Any subgroups chosen after this time should be clearly identified. (2) Trials should ideally be powered with subgroup analyses in mind. However, for modest interactions, this may not be feasible. (3) Subgroup-specific analyses are particularly unreliable and are affected by many factors. Subgroup analyses should always be based on formal tests of interaction although even these should be interpreted with caution. (4) The results from any subgroup analyses should not be over-interpreted. Unless there is strong supporting evidence, they are best viewed as a hypothesis-generation exercise. In particular, one should be wary of evidence suggesting that treatment is effective in one subgroup only. (5) Any apparent lack of differential effect should be regarded with caution unless the study was specifically powered with interactions in mind. CONCLUSIONS--RECOMMENDATIONS FOR RESEARCH: (1) The implications of considering confidence intervals rather than p-values could be considered. (2) The same approach as in this study could be applied to contexts other than RCTs, such as observational studies and meta-analyses. (3) The scenarios used in this study could be examined more comprehensively using other statistical methods, incorporating clustering effects, considering other types of outcome variable and using other approaches, such as Bootstrapping or Bayesian methods.

Share this page

Email this page
Publication updates

If you would like to receive information on publications and the latest news, click below to sign up.