Table 2.

Differences in sample size for a trial by severity of pneumonia

	Incidence	Relative risk to be detected	Sample size needed in treatment group and in control group (combined)
All pneumonia	17 episodes per 100 child-years	0·78	1440 children
Severe pneumonia	5 episodes per 100 child-years	0·67	2300 children

In five studies, the incidence of WHO-defined severe pneumonia or severe-pneumonia with radiographic confirmation was approximately five episodes per 100 child-years in children below two years of age.11, 33, 34, 35, 36 The RESPIRE trial documented a relative risk of 0·67 for children with severe pneumonia in households with improved cookstoves, compared with those using traditional stoves.¹⁰ Using this information, we can calculate the necessary sample size using a difference in two proportions (assuming pneumonia events are independent). If the intervention and control groups are of equal size, 2300 children must be followed in their first two years of age to achieve 80% power with a conventional significance level of 0·05. A smaller sample size is acceptable for pneumonia of any severity because the number of cases will be higher. Although existing data are scarce, three previous studies have found that overall pneumonia incidence is about 3·4 times higher than that of severe pneumonia in children under three years of age (ie, 17 pneumonia episodes per 100 child-years vs 5 severe pneumonia episodes per 100 child-years).37, 38, 39 Under this assumption, and assuming a relative risk of 0·78 from RESPIRE and a 1-year follow-up, 1440 children are needed in each group for all pneumonias.