Meta analysis are used to gain power but sometimes fail to show significant results.

When this is the case, researchers use to conclude to the absence of difference or a lack of power.

When the occurence of an endpoint is infrequent, number of patients needed to show a difference can be extremely high. Is it robust to use a sample size calculator to conclude if the absence of results of a meta analysis is likely due to a lack of power or to the absence of a difference?

In other terms, in a meta analysis comparing acetaminophen to ibuprofen, authors concluded to similar side effects. However, kidney impairements were scarce (1 per 1000 participants). Therefore, to show an increase of 50% (from 1‰ to 1,5‰) with alpha 0.05 and beta 0.10, 50 000 participants would be needed, and the meta analysis gathers only 27000.

If we pool severe side effects together, frequency comes to 1,4% so with te same calcul (to show an increase of 50% (from 1,4% to 2,1%) with alpha 0.05 and beta 0.10) 3 000 participants are needed and the meta analysis gathered 30 000 patients for this endpoint.

Is it robust to base oneself on that kind of sample size calcul to say that this meta analysis has sufficient power to show that severe side effects occurs similarly but we lack power to conclude concerning kidney failures ?

Help from the community would be appreciate :-)