We found effect modification even when we omitted the PEACE studies (see Supplemental Material, Tables 4 and 5), for the effect of NO2 on asthma symptoms, with higher associations for asthmatics and during the summer (the latter based on two studies in one stratum).
It may be that one treatment strategy is more effective in one stratum than the other, and perhaps even that one treatment strategy is more effective in one stratum, but the other is more effective in the other stratum.
Also, the probability that (X2, X3) is observed differs: in one stratum it is 0.2; in the other, 0.8.
Peto et al argued that "believing that a treatment effect exists in one stratum of patients, even though no overall significant treatment effect exists, is a common error".
If an unmatched design fails to include controls in one stratum of C, the entire table will be discarded, along with precious cases.
On the other hand, hybrid designs are intended to permit determinations of efficacy using different endpoints in different strata for example, direct superiority to placebo in one stratum and non-inferiority to an active control in a different stratum.
Analyses were stratified with patients discharged from Vejle Hospital in one stratum and patients from other hospitals in another because Vejle Hospital initiated urgent referrals several years prior to the national implementation.
It has even been argued that "believing that a treatment effect exists in one stratum of patients, even though no overall significant treatment effect exists, is a common error" (24, p. 15).
As pointed out by Wang et al. (3), such assessments should adjust for the number of subgroup factors since whenever a sample is split in two, by chance the treatment group difference in one stratum will be greater than that in another.
