# Imbalance p values for baseline covariates in randomized controlled trials: a last resort for the use of p values? A pro and contra debate

Authors Stang A, Baethge C

Received 4 January 2018

Accepted for publication 2 March 2018

Published 8 May 2018 Volume 2018:10 Pages 531—535

Checked for plagiarism Yes

Review by Single anonymous peer review

Peer reviewer comments 3

Editor who approved publication: Professor Irene Petersen

Andreas Stang,1,2 Christopher Baethge3,4

1Center of Clinical Epidemiology, Institute of Medical Informatics, Biometry and Epidemiology, Medical Faculty, University Hospital of Essen, Hufelandstr, Essen, Germany; 2Department of Epidemiology, School of Public Health, Boston University, Boston, MA, USA; 3Department of Psychiatry and Psychotherapy, University of Cologne Medical School, Cologne, Germany; 4Editorial Offices, Deutsches Ärzteblatt and Deutsches Ärzteblatt International, Deutscher Ärzte-Verlag, Cologne, Germany

Background: Results of randomized controlled trials (RCTs) are usually accompanied by a table that compares covariates between the study groups at baseline. Sometimes, the investigators report p values for imbalanced covariates. The aim of this debate is to illustrate the pro and contra of the use of these p values in RCTs.
Pro: Low p values can be a sign of biased or fraudulent randomization and can be used as a warning sign. They can be considered as a screening tool with low positive-predictive value. Low p values should prompt us to ask for the reasons and for potential consequences, especially in combination with hints of methodological problems.
Contra: A fair randomization produces the expectation that the distribution of p values follows a flat distribution. It does not produce an expectation related to a single p value. The distribution of p values in RCTs can be influenced by the correlation among covariates, differential misclassification or differential mismeasurement of baseline covariates. Given only a small number of reported p values in the reports of RCTs, judging whether the realized p value distribution is, indeed, a flat distribution becomes difficult. If p values ≤0.005 or ≥0.995 were used as a sign of alarm, the false-positive rate would be 5.0% if randomization was done correctly, and five p values per RCT were reported.
Conclusion: Use of a low p value as a warning sign that randomization is potentially biased can be considered a vague heuristic. The authors of this debate are obviously more or less enthusiastic with this heuristic and differ in the consequences they propose.

Keywords: randomized controlled trial, distribution, statistical, random allocation

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