Table 3.

Minimum detectable effects, with 80% power and $\mathrm{\alpha }=0.0125$.

	Key parameter for estimating powera	Sample size per arm	Minimal detectable effect	Previous studies’ estimate (95% CI)
Change in mean birth weight (g)	${\mathrm{\sigma }}^2$	1,600	54	89 ($-27$, 204)b
Change in mean blood pressure (mm Hg)	${\mathrm{\sigma }}^2$	200	2.58	3.7 ($-0.6$, 8.1)c
Relative risk for stunting	$p_1$	1,600	0.81	0.79 (0.70, 0.89)d
Relative risk for HAPIN severe pneumonia	$p_1$	1,600	0.64	0.67 (0.45, 0.98)e

Note: For a fuller description of the literature and the choice of three of these effect estimates (birth weight, blood pressure, infant pneumonia), see Steenland et al. (2018). CI, confidence interval; HAPIN, Household Air Pollution Intervention Network.

^aOur key population parameters were the variance of continuous measures (${\mathrm{\sigma }}^2$) or the incidence rates among controls ($p_1$) for relative risks. We took our key parameter estimates from the previous studies listed in the last column, with the exception of the control rate for pneumonia, which was estimated from our early data from the trial (Smith et al. 2011).

^bThompson et al. (2011) is a substudy of a randomized trial of improved cookstoves in Guatemala (RESPIRE) in which those using stoves were compared to those not using stoves after adjusting for confounders.

^cMcCracken et al. (2007) is a study of 120 older women ($>38$ years of age) from the same randomized trial (RESPIRE), which adjusted for confounders.

^dThis comprehensive review article of the health effects of HAP exposure by Bruce et al. (2013) is based on two observational studies for moderate stunting [$z\text{-score}<2\text{standard}\text{deviations}\left(\text{SD}\right)$].

^eSmith et al. (2011), from the RESPIRE randomized trial, provides the estimated relative risk (RR) of 0.67, the RR for clinician-diagnosed severe pneumonia for children under 18 months of age. Our estimated background rate of 0.09 for controls is based on our observed severe pneumonia rate in both arms (treatment and control) in the HAPIN study (using the HAPIN severe pneumonia definition), with 20% of the child person time observed, and assuming the RESPIRE RR of 0.67 for intervention vs. controls.