How to obtain the confidence interval from a P value

2011; 343 doi: (Published 8 August 2011)
Cite this as: 2011;343:d2090

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It is with great interest I read the most recent instalment in this series. I wish to thank the Authors for these contributions.

Unfortunately I believe that there may be a typo in the formulae presented. Instead of taking a logarithm to the base 10 of the p-value (Log(P)) I believe the formulae should have taken the Natural logarithm to base e (Ln(P)).


Gordon S. Doig

Competing interests: None declared

Gordon S. Doig, Biostatistician

University of Sydney, Sydney, Australia, NSW

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We commend Professors Altman and Bland for their papers on how to obtain confidence intervals from p-values (1) and how to obtain p-values from confidence intervals (2). Incomplete reporting of data and analysis results are still common, and simple methods that allow computation of missing items are needed to facilitate interpretation of study results and their incorporation into meta-analysis.

The methods and formulae presented by Altman and Bland are appropriate for studies of independent groups, such as randomized trials and unmatched cohort studies. For studies with a paired design, such as matched case-control studies, paired cohort studies, and cross-over clinical trials, different formulae are required (3).

In addition to the calculation of unreported confidence intervals and p-values, it may be useful to reconstruct missing data tables, particularly for studies with binary outcomes. For independent data studies reporting risk difference, risk ratio, or odds ratio, Pietrantonj (4) gives methods based on estimates, confidence intervals, and sample sizes. Reconstruction of a paired 2x2 table is given in Hirji and Fagerland (3).

One important consideration for the methods in references (1-4) is the accuracy of the measures that are used in the calculations. Preliminary results suggest that two significant digits are sufficient to obtain fairly accurate results (3,4).

Morten W. Fagerland, Unit of Biostatistics and Epidemiology, Oslo University Hospital, Norway

Karim F. Hirji, Department of Epidemiology and Biostatistics, Muhimbili University of Health and Allied Sciences, Dar es Salaam, Tanzania

1. Altman DG, Bland JM. How to obtain the confidence interval from a P value. BMJ 2011; 343:d2090

2. Altman DG, Bland JM. How to obtain the P value from a confidence interval. BMJ 2011; 343:d2304

3. Hirji KF, Fagerland MW. Calculating unreported confidence intervals for paired data. BMC Med Res Methodol 2011; 11:66

4. Pietrantonj CD. Four-fold table cell frequencies imputation in meta analysis. Stat Med 2006; 25:2299-2322.

Competing interests: None declared

Morten W. Fagerland, Researcher

Karim F. Hirji

Unit of Biostatistics and Epidemiology, Oslo University Hospital

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