# Risk Difference HELP

#### FallStudent2022

##### New Member
The following paragraph is from a recent JAMA publication: “Effect of Tocilizumab on Disease Activity in Patients with Active Polymyalgia Rheumatica Receiving Glucocorticoid Therapy: A Randomized Clinical Trial”
Sample Size Calculation:
To estimate the required sample size, based on the results of a previous open-label study of tocilizumab in patients with early polymyalgia rheumatica, (10) we selected a 35% between group difference for the primary end point (i.e., achievement of the primary outcome in 25% of the placebo group vs 60% of the tocilizumab group). An improvement of 20% to 40% between
groups is considered clinically important in other rheumatic diseases treated by biologics, such as rheumatoid arthritis (29) or a recent therapeutical trial in polymyalgia rheumatica. (6)
With the 2-sided α risk set at .05, a total of 90 patients (45 in each group) provided 90% power for detecting a 35% difference in the primary end point (ie, a relative risk of 1.4). Assuming that about 10% of patients would not complete the trial, a sample size of 100 participants (50 in each group) was planned.
Q. Find the error in the above Sample Size Calculation paragraph. Note that you do not need to know anything about “power” here.

#### Karabiner

##### TS Contributor
Do you mean, computational/statistical mistakes, or mistakes of substantial claims?
What would you suggest as the answer?

With kind regards

Karabiner

#### hlsmith

##### Less is more. Stay pure. Stay poor.
I see the error, but are you just wanting me to give you the answer? As a student, where would the teaching moment be if I did that.

#### FallStudent2022

##### New Member
I see the error, but are you just wanting me to give you the answer? As a student, where would the teaching moment be if I did that.

• The RR of 1.4 is the error. Relative to one another 60%/25% (placebo vs. intervention), when you divide you get 2.4.

#### hlsmith

##### Less is more. Stay pure. Stay poor.
Yup. So if it was powered for a smaller risk diff, which is on the absolute scale, a larger relative difference would likely be adequately powered be default but represent an inconsistency in the prior text.

Of note, the calculation of risk differences (absolute scale) are typically preferred over relative differences given they are more easily understood by clinicians. They also allow for easy calculations of number needed to treat.