Power and statistical analysis

Consistent with the overall study goal outlined earlier, the study was powered to detect the overall public health impact of the intervention based on an assumption that the intervention would improve access and increase the number of facility births. We therefore estimated the power to detect the impact of implementation of HBB training in facilities to improve the mortality rates at the population (registry) level. Assuming a PMR of 25/1000 among newborns ≥1500 g, a standard deviation of 10 between clusters, and a correlation across the periods of 0.3 (based on historic registry data), the study had an estimated power of 82 % to detect a 20 % reduction in PMR among newborns ≥1500 g.

While the study was not powered to detect an interaction effect between intervention and site or to detect differences in secondary mortality outcomes, the study had sufficient sample size to provide valuable information about these secondary outcomes, e.g., the effect of the intervention based on the subset of deliveries that occurred at the HBB trained health facilities. Under the original design assumptions about heterogeneity of risk across clusters and the correlation within clusters over time, the sample sizes within the HBB-facility deliveries provided 80 % power to detect a 30 % risk reduction and a 90 % power to detect a 35 % reduction in mortality risk in these facilities. Absent significant differences in the primary outcome or this important secondary outcome, the analyses were constructed to provide point and interval estimates of the magnitude of both public health and in-facility benefit obtained from the intervention.

The primary outcome was tested using a linear mixed model that incorporated a random cluster-effect term to account for correlation within clusters across time and a fixed binary-time effect (pre-post HBB) that represented the treatment effect. The dependent variable was the cluster PMR aggregated separately across the pre and post periods. Secondary mortality outcomes were analyzed using linear mixed models, incorporating both random-cluster effects and fixed effects for pre and post periods. The interaction between site and treatment was tested for the primary and secondary outcomes. Secondary parameter estimates of combinations of time and period evaluated whether the treatment effect changed over the course of the study.