The effect size

Clinical trials in orthodontics assess the potential benefits (or harms) of the applied treatments. The final assessment is conducted by using a measure that represents the size of the benefit (or harm), if a benefit exists, of 1 treatment over the comparator. This measure is called effect size and shows the degree by which 1 therapy differs from the other ( Table I ). A clinical (and statistical) judgment is made on whether this effect size is great enough to set the 2 treatments apart and helps us to decide whether 1 therapy is preferable over the other in a clinical setting. In this article, we will present common effect measures.

Table I
Measures of effect
Measure of effect Description No effect
Mean difference Absolute difference between means Mean 1 – mean 0 0
Risk difference Absolute difference between risks Risk 1 – risk 0 0
Relative risk reduction Absolute risk reduction divided by the baseline risk in the control group (Risk 1 – risk 0 )/risk 0 0%
Risk ratio Risk of an event in 1 treatment group vs risk of the event in the control or other group Risk 1 /risk 0
risk 0 / risk 1
Odds ratio Odds of an event in 1 treatment group vs odds of the event in the control or other group Odds 1 /odds 0
odds 0 /odds 1
Rate ratio The rate of the event in 1 treatment group vs the rate of the event in the control or other group Rate 1 /rate 0
rate 0 /rate 1
1 (hazard ratio)
Numbers needed to treat Number of patients to be treated to prevent 1 event 1/absolute risk difference expressed as a decimal fraction Infinity

The mean difference is an effect measure that is easily understood because it represents the difference between the means of 2 continuous outcomes and takes the units of the outcome. For example, what is the mean difference in months for achieving Class II correction with a Herbst appliance vs headgear? If the mean durations to achieve Class II correction in our sample are 6 months with the Herbst and 8 months with the headgear, then the mean difference is 2 months. This is interpreted as follows: the Herbst appliance needs on average 2 months less time to achieve the Class II correction compared with the headgear. A mean difference of 0 indicates no difference on average between the 2 treatments.

For the risk difference, risk is the probability that an event such as a bond failure will occur. The risk difference gives the absolute difference in risk between the 2 treatment groups and is used with binary outcomes (yes or no). For example, what is the risk difference of bracket failures between conventional and self-ligating brackets? If the risks or proportions of bracket failures in our sample are 5% for conventional brackets and 7% for self-ligating brackets, then the risk difference is 2%. It is interpreted as follows: conventional brackets on average have a 2% lower risk or probability of failing compared with self-ligating brackets. A risk difference of 0 indicates no difference between the 2 treatments.

With the same example of risk difference, the relative risk reduction is (7% – 5%)/5% = 40%. This is interpreted as follows: the use of conventional brackets on average decreases the risk or probability of failure by 40% compared with self-ligating brackets. If we compare the relative risk reduction value with the risk difference, we can see how different effect measures can give different impressions of the effect of interventions. A relative risk reduction of 0 indicates no difference between the 2 treatments.

The risk ratio or relative risk is a relative measure of effect rather than an absolute, and it is also used for binary outcomes. Risk is the proportion of failures in each treatment group. So, if in the self-ligating bracket group the risk is 0.07 or 7% and in the conventional bracket group the risk is 0.05 or 5%, the risk ratio is 0.07/0.05 = 1.4. It is interpreted as follows: the risk of failure (proportion of failure) for self-ligating brackets is 40% higher compared with conventional brackets, or the risk of failure for self-ligating brackets is 1.4 times that of conventional brackets. A risk ratio of 1 indicates no difference in effect between treatment groups, a risk ratio greater than 1 indicates that the risk is higher for self-ligating brackets, and a risk ratio less than 1 indicates that the risk of failure is higher for conventional brackets. The interpretation also obviously depends on which treatment group is selected for the numerator and which for the denominator. It is common practice to use the control or standard therapy as the denominator and the new intervention as the numerator.

The risk ratio is used more often than the risk difference because it is considered a more consistent estimate across different situations ( Table II ). Ideally, both the relative effect (risk ratio or odds ratio) and the absolute effect (risk difference) should be reported, since neither the relative measure nor the absolute measure alone gives a complete picture of the effect and its implications. For example, if the risk of bond failure with adhesive A is 0.02, doubling the risk, when using adhesive B, to 0.04 would indicate doubling the risk ratio; this, however, would only mean 2 more events out of 100 observations (risk difference, 0.04 – 0.02 = 0.02). In this scenario, presenting only the risk ratio is likely to make the reader overestimate the effect of the type of adhesive on bond failure.

Apr 8, 2017 | Posted by in Orthodontics | Comments Off on The effect size

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