Simpson's Paradox in a Clinical Trial

A clinical trial tests a drug on two subgroups. In subgroup A (mild cases): 81/87 (93%) of treated patients recover vs 234/270 (87%) of untreated. In subgroup B (severe cases): 192/263 (73%) of treated patients recover vs 55/80 (69%) of untreated. The drug improves recovery rates in both subgroups. Now compute the overall recovery rates (combining subgroups) for treated vs untreated. Explain the apparent contradiction and identify the lurking variable that causes it.