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Peter Cummings, MD, MPH

Arch Pediatr Adolesc Med. 2007;161(5):518-519.

The ARCHIVES has published 2 randomized trials of duct tape therapy for warts.^1-2 A commentary³ regarding the most recent of these trials² pointed out that confidence intervals for the size of the treatment effect were not given in the results. The commentary³ provided confidence intervals in a table, but these were intervals for the observed outcome proportions in each trial arm, not intervals for the estimated effect of treatment.

Any study that compares 2 or more groups should calculate statistics that compare the group outcomes, along with estimates of precision for those comparisons, such as confidence intervals. This advice is given by the International Committee of Medical Journal Editors⁴ and by the Consolidated Standards of Reporting Trials guidelines for the reporting of randomized controlled trials.⁵ The ARCHIVES recommends the use of point estimates and confidence intervals in its instructions to authors⁶ and has endorsed this practice in editorials.^7-9 Despite these recommendations, neither trial of duct tape therapy reported estimates or confidence intervals for the effect of treatment on wart resolution.^1-2

The main outcomes for the duct tape trials were binary (Table 1), so appropriate statistics for treatment effects include risk ratios, risk differences, and odds ratios (Table 2).¹⁰ Odds ratios have a desirable symmetry; if we compare the treatment arm with the control arm, the odds ratio for the undesirable outcome (wart remaining) will be the inverse of the odds ratio for the desirable outcome (wart resolution). But when more than 10% of participants have the outcome, odds ratios are difficult to interpret because they will not approximate risk ratios well.^10-14 The risk difference has a clear meaning, but a difference (additive) model assumes that treatment changes the outcome by adding a fixed proportion to the outcome proportion in the control group. Often a ratio (multiplicative) model is more plausible or fits the data more closely; this model assumes that treatment changes the outcome by multiplying the control group outcome proportion by a fixed ratio.^15-17 Risk ratios are often a useful summary statistic for treatment effects.¹⁷ However, they lack the symmetry of odds ratios; the risk ratio for the harmful outcome is usually not the inverse of the risk ratio for the beneficial outcome. This asymmetry is apparent for the duct tape trials; the trial by de Haen et al² found a greater treatment effect using the risk ratio for wart resolution, whereas the trial by Focht et al¹ found a greater treatment effect using the risk ratio for the wart remaining at the end of follow-up. A reasonable approach would be to report both risk ratios with their confidence intervals.

View this table: [in this window] [in a new window] [as a PowerPoint slide]   Table 1. Outcomes From 2 Randomized Controlled Trials of Duct Tape Treatment for Warts*

View this table: [in this window] [in a new window] [as a PowerPoint slide]   Table 2. Treatment Effect Estimates Comparing Duct Tape Therapy With a Control Arm From 2 Randomized Controlled Trials of Treatment for Warts

In their commentary, Van Cleve et al³ used power calculations to estimate that the study by de Haen et al² had only 26% power to find a statistically significant difference between the observed treatment risk difference of 10% and a hypothetical risk difference of 0%. When the observed trial difference is not statistically significant, such a post hoc calculation will always estimate that power was less than 50%.¹⁸ Power calculations are an inefficient method for interpreting results, as they provide an estimate for only one assumed effect size compared with the null hypothesis. After a study is completed, the size of the effect can be estimated from the data, and confidence intervals allow us to see how compatible all possible effects are with the observed results.^18-20

Editor's Note: Matthew M. Davis, MD, MAPP, has read this letter but declined to reply.

AUTHOR INFORMATION

REFERENCES
1. Focht DR III, Spicer C, Fairchok MP. The efficacy of duct tape vs cryotherapy in the treatment of verruca vulgaris (the common wart). Arch Pediatr Adolesc Med. 2002;156:971-974. FREE FULL TEXT 2. de Haen M, Spigt MG, van Uden CJ, van Neer P, Feron FJ, Knottnerus A. Efficacy of duct tape vs placebo in the treatment of verruca vulgaris (warts) in primary school children. Arch Pediatr Adolesc Med. 2006;160:1121-1125. FREE FULL TEXT 3. Van Cleave J, Kemper AR, Davis MM. Interpreting negative results from an underpowered clinical trial: warts and all. Arch Pediatr Adolesc Med. 2006;160:1126-1129. FREE FULL TEXT 4. International Committee of Medical Journal Editors. Uniform requirements for manuscripts submitted to biomedical journals. JAMA. 1997;277:927-934. FREE FULL TEXT 5. Moher D, Schulz KF, Altman D. The CONSORT statement: revised recommendations for improving the quality of reports of parallel-group randomized trials. JAMA. 2001;285:1987-1991. FREE FULL TEXT 6. Archives of Pediatrics and Adolescent Medicine. Instructions for Authors. http://archpedi.ama-assn.org/misc/ifora.dtl#Statistics. Accessed Nov 20, 2006.7. Rivara FP, Cummings P. Writing for publication in Archives of Pediatrics & Adolescent Medicine. Arch Pediatr Adolesc Med. 2001;155:1090-1092. FREE FULL TEXT 8. Cummings P, Rivara FP. Reporting statistical information in medical journal articles. Arch Pediatr Adolesc Med. 2003;157:321-324. FREE FULL TEXT 9. Cummings P, Rivara FP, Koepsell TD. Writing informative abstracts for journal articles. Arch Pediatr Adolesc Med. 2004;158:1086-1088. FREE FULL TEXT 10. Cummings P, Weiss NS. Summarizing evidence: systematic reviews and meta-analysis. In: Clinical Epidemiology: The Study of the Outcome of Illness. New York City, NY: Oxford University Press; 2006:157-174.11. Welch HG, Koepsell TD. Insurance and the risk of ruptured appendix. N Engl J Med. 1995;332:396-397. WEB OF SCIENCE | PUBMED 12. Sackett DL, Deeks JJ, Altman DG. Down with odds ratios! Evid Based Med. 1996;1:164-166. FREE FULL TEXT 13. Altman DG, Deeks JJ, Sackett DL. Odds ratios should be avoided when events are common. BMJ. 1998;317:1318. FREE FULL TEXT 14. Schwartz LM, Woloshin S, Welch HG. Misunderstanding about the effects of race and sex on physicians' referrals for cardiac catheterization. N Engl J Med. 1999;341:279-283. FULL TEXT | WEB OF SCIENCE | PUBMED 15. Breslow NE, Day NE. The Design and Analysis of Cohort Studies. Vol II. Lyon, France: International Agency for Research on Cancer; 1987:142-146. Statistical Methods in Cancer Research.16. Deeks JJ, Altman DG. Effect measures for meta-analysis of trials with binary outcomes. In: Egger M, Smith GD, Altman DG, eds. Systematic Reviews in Health Care: Meta-analysis in Context. London, England: BMJ Publishing Group; 2001:313-335.17. Deeks JJ. Issues in the selection of a summary statistic for meta-analysis of clinical trials with binary outcomes. Stat Med. 2002;21:1575-1600. FULL TEXT | WEB OF SCIENCE | PUBMED 18. Goodman SN, Berlin JA. The use of predicted confidence intervals when planning experiments and the misuse of power when interpreting results. Ann Intern Med. 1994;121:200-206. FREE FULL TEXT 19. Smith AH, Bates MN. Confidence limit analyses should replace power calculations in the interpretation of epidemiologic studies. Epidemiology. 1992;3:449-452. WEB OF SCIENCE | PUBMED 20. Rothman KJ, ed, Greenland S, ed. Approaches to statistical analysis. In: Modern Epidemiology. Philadelphia, Pa: Lippincott-Raven; 1998:183-199.

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