[ulfw]

Can someone explain the numbers to me?

"After five years, 88% of patients who took the daily pill after the removal of their tumour were still alive, compared with 78% of patients treated with a placebo. Overall, there was a 51% lower risk of death for those who received osimertinib compared with those who received placebo."

So 88% instead of 78% without the pill were still alive five years on. I assume that is the maximum range they could test. How was the 51% then calculated?

Edit: thank you all for the explanation. That makes a lot of sense!

[teraflop]

If 22% of patients in the placebo group died, and 12% in the test group, then that's a reduction of 1 - (12/22) = 45% in the risk of death over that time interval.

The true value could easily be 51% if the percentages reported in the Guardian were rounded.

[cjbgkagh]

You could subtract both percentages by the baseline average risk of death for 5 years at the age group that people are most likely to get this type of cancer.

[fithisux]

The article makes the assumption that those that took the placebo represent the typical post removal patient (an assumption).

So, for 100 untreeated patients 22 would die. Now for these 100 placebo patients, if they took the pill, they would die 12 (another assumption that the two populations are the same).

The reduction is (22-12) / 22 = 10/22 is the risk of death if untreated.

The complementary percentage is

12/22 approx 51%.

However this does not come with confidence intervals.

[adriand]

If you think about the numbers as 12% died vs 22% died, then the 51% intuitively makes more sense, although I don’t know if this is the correct explanation. My guess is that 12 and 22 are rounded numbers.

[evandijk70]

Based on the abstract of the article https://www.nejm.org/doi/full/10.1056/NEJMoa2304594?query=fe...,

I actually think the other explanations are wrong. They are probably reporting the Hazard Ratio, which is more often used as primary outcome for efficacy of drug than 5 year survival. (See for example: https://en.wikipedia.org/wiki/Hazard_ratio)

The hazard ratio, under some assumptions, tries to estimate the relative risk of dying per unit of time. The benefit of this measure is that there is not some artificial cutoff (the difference between a death at 4 years and 364 days and 5 years and 1 day is neglible).

[dullcrisp]

22% of those who took the placebo died versus 12% with the medication. Seems it’d be a 45% improvement with those numbers.