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Reporting of treatment effects from randomized trials: A plea for multivariable risk ratios

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Abstract

Clinicians are typically interested in the effects of medical interventions that apply to individual patients. Such individual effects are conditional effects rather than marginal (or population averaged) effects. When considering odds ratios, conditional (adjusted) and marginal (crude) effects may differ, even in a randomized trial with perfectly balanced baseline covariates, due to non-collapsibility of the odds ratio. Using a numerical example, we explained this phenomenon of non-collapsibility of the odds ratio and showed that the difference between conditional and marginal odds ratios depends on the strength of the association between a third (stratifying) variable and the outcome, as well as on the distribution of this stratifying variable in the trial population. Risk ratios are not affected by non-collapsibility and therefore, conditional and marginal risk ratios are the same when adjusting for well balanced baseline covariates in randomized trials. Reports on randomized trials should more often include treatment effects that are expressed as risk ratios rather than odds ratios. When odds ratios are used, adjustment for baseline covariates should be considered, also when these are well-balanced between the treatment groups.

Section snippets

Background

Randomized trials are considered the gold standard to study effects of medical interventions, primarily because randomization (theoretically) results in balanced distributions of confounders between the study groups. In reality, however, some of these confounders may not be well-balanced, resulting from flaws in the randomisation procedure or, more often, because of ‘bad luck’ [1], [2]. Then, the observed effect may not be (completely) attributable to the treatment under study, and adjustment

Clinical examples

In a randomized trial on the effect of tissue plasminogen activator vs. streptokinase thrombolytic therapy on mortality in patients with myocardial infarction, the crude odds ratio (OR) was 0.85 (95% CI 0.78–0.94; p-value = 0.0012) [6]. Adjustment for 17 well balanced baseline characteristics resulted in an OR of 0.82 (95% CI 0.74–0.91; p-value = 0.0002). In another randomized trial on insulin therapy in very-low-birth-weight infants the difference between crude and adjusted OR was more pronounced

Non-collapsibility of the odds ratio

Crude effect estimates are also called marginal, or collapsed, effects, and adjusted effect estimates are called conditional effects. If potential confounders are balanced between treatment groups in a randomized trial, adjustment for these characteristics is expected not to result in a change in the effect estimate, i.e. the marginal effect equals the conditional effect.

Indeed, when adjusting for balanced covariates, the marginal and conditional effect estimates are the same, when applying for

Precision

In linear models, adjustment for balanced covariates will not affect the estimate of the treatment effect, but will increase precision (smaller standard errors, confidence intervals and p-values). In logistic models, however, the effect estimate increases when adjusting for balanced covariates (moves away from the null effect), while the standard errors increase [6], [7]. Altogether, the change in the effect estimate is larger than the increase in the standard error of the estimate and as a

Personalized treatment effects

If the treatment effect is the same among men and women (i.e., no effect modification), the conditional effect is a more individualised effect, whereas the marginal effect is rather a population averaged effect. Obviously, a patient is either a man or a woman and not an average of the two sexes. Hence, the effect a patient will experience from a treatment is the effect as observed in either men or women. Thus, the effect an individual patient will experience is the conditional effect, not the

Odds ratio or risk ratio?

One of the advantages of odds ratios over risk ratios, is that odds ratios are symmetric with respect to ‘successes’ and ‘failures’, meaning for example that the odds ratio for mortality is exactly the reciprocal of the odds ratio for survival [14]. A disadvantage of odds ratios, as illustrated above, is the phenomenon of non-collapsibility, which may cause the marginal and the conditional treatment effects to differ considerably. Another feature of the odds ratio is that it is often

Conclusions

Clinicians are typically interested in the effects of medical interventions that apply to individual patients, which are conditional effects rather than marginal effects. However, when considering odds ratios, even in a perfectly balanced trial, conditional and marginal effects may differ due to non-collapsibility of the odds ratio. If covariate adjustment is indicated (for example to adjust for confounding) the situation becomes even more complicated, since it will be hard to distinguish

Competing Interests

All authors declare that they have no competing interests.

References (20)

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