Duration of the common cold and similar continuous outcomes should be analyzed on the relative scale: a case study of two zinc lozenge trials

Harri Hemilä

doi:10.1186/s12874-017-0356-y

Abstract

BackgroundThe relative scale has been used for decades in analysing binary data in epidemiology. In contrast, there has been a long tradition of carrying out meta-analyses of continuous outcomes on the absolute, original measurement, scale. The biological rationale for using the relative scale in the analysis of binary outcomes is that it adjusts for baseline variations; however, similar baseline variations can occur in continuous outcomes and relative effect scale may therefore be often useful also for continuous outcomes. The aim of this study was to determine whether the relative scale is more consistent with empirical data on treating the common cold than the absolute scale.MethodsIndividual patient data was available for 2 randomized trials on zinc lozenges for the treatment of the common cold. Mossad (Ann Intern Med 125:81–8, 1996) found 4.0 days and 43% reduction, and Petrus (Curr Ther Res 59:595–607, 1998) found 1.77 days and 25% reduction, in the duration of colds. In both trials, variance in the placebo group was significantly greater than in the zinc lozenge group. The effect estimates were applied to the common cold distributions of the placebo groups, and the resulting distributions were compared with the actual zinc lozenge group distributions.ResultsWhen the absolute effect estimates, 4.0 and 1.77 days, were applied to the placebo group common cold distributions, negative and zero (i.e., impossible) cold durations were predicted, and the high level variance remained. In contrast, when the relative effect estimates, 43 and 25%, were applied, impossible common cold durations were not predicted in the placebo groups, and the cold distributions became similar to those of the zinc lozenge groups.ConclusionsFor some continuous outcomes, such as the duration of illness and the duration of hospital stay, the relative scale leads to a more informative statistical analysis and more effective communication of the study findings. The transformation of continuous data to the relative scale is simple with a spreadsheet program, after which the relative scale data can be analysed using standard meta-analysis software. The option for the analysis of relative effects of continuous outcomes directly from the original data should be implemented in standard meta-analysis programs.

Highlights

The relative scale has been used for decades in analysing binary data in epidemiology
The Mossad et al [9] and the Petrus et al [10] trials were selected because individual patient data (IPD) were available and because both of them found that zinc lozenges had a significant effect on common cold duration (Additional file 1)
The calculations are described in Additional file 4. This comparison of the absolute scale against the relative scale in the analysis of the treatment effects on common cold duration focused on 2 randomized trials; the zinc gluconate lozenge trial by Mossad et al [9] and the zinc acetate lozenge trial by Petrus et al [10]

Summary

Introduction

The relative scale has been used for decades in analysing binary data in epidemiology. There has been a long tradition of carrying out meta-analyses of continuous outcomes on the absolute, original measurement, scale. The aim of this study was to determine whether the relative scale is more consistent with empirical data on treating the common cold than the absolute scale. The “absolute scale” indicates comparison on the scale of the original measurements such as days in the case of common cold duration. Meta-analyses of binary outcomes on the relative scale have led to less heterogeneity than analyses on the absolute scale (risk difference) [3]. The relative scale cannot yield negative predicted values, whereas the absolute scale can

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