Medical Statistics: Understanding medication statistics

Question

I'm reading some of the educational material for a new therapy that can help treat PPMS (Primary Progressive Multiple Sclerosis).

I'm having difficulty understanding their use of statistics.

Let's first talk in general terms:

If person A has 100 oranges, and person B has 75 oranges, then person B has 25% fewer oranges than person A.

We compute this as:

(100-75)/100 = 0.25 = 25%

Now let's get to the educational material. It states:

Overall, the percent of people with 12-week CDP was 32.9% of Ocrevus-treated people vs. 39.3% of placebo-treated people. Another way of looking at this data is to say that people treated with Ocrevus were 24% less likely to have disability progression than those treated with placebo.

I don't get it. Using the same formula as above, (39.3-32.9)/39.3 = .163 = 16%

Yet the educational material uses a figure of 24%, not 16%.

How do they obtain that figure, and is it a common (fair, straightforward) or uncommon (misleading) way to represent that data?

(Please note that I am in no way suggesting anything is fair or misleading. I am only stating that I don't understand and am confused by what I have read.)

Answer 1

24 % is the decrease in odds ratio, where, for each treatment option, $$ odds = \frac{n\ cases}{n\ controls} = \frac{n\ cases}{n\ total-n\ cases} $$

Thus, odds of having CDP in the treated group are $32.9/(100-32.9) = 0.490$; odds in the placebo group: $39.3/(100-39.3) = 0.647$. Ratio of these odds is $0.490/0.647=0.757$, which is 24.3 % smaller than 1 (odds ratio under no effect).

Odds ratio probably is the most common way of presenting effects in epidemiology studies with case-control outcome, but I agree with you that the writers' presentation is unclear - "less likely" could refer to any other related measures, like odds difference, risk ratio, risk difference etc. As to which measure is more appropriate - entire chapters are written about that, just look up any textbook of epidemiology.