We estimate that the incidence of acute lower respiratory infections (ALRI) in the placebo group will be 0.065/child /year 39 and 12% of the ALRI will be pneumonia 1. We assume that 25% of pneumonias will be repeat episodes during the 18 month follow up period. Thus the incidence of the first or the only episode of pneumonia in the placebo group will be 0.0585/child/year (0.65*0.12*0.75). We expect a 35% reduction in the incidence of pneumonia in the vitamin D group given that 73% of children have vitamin D deficiency in the study area and that the incidence of pneumonia is 10 times higher in vitamin D deficient children than in normal children 18, 26. A study with 80% power and 95% significance to detect a 35% reduction in the incidence of pneumonia compared to the placebo group will require 22079 child months per group37. Since each child will be followed for 18 months the study will require 1227 child per group. Assuming a 20% loss to follow up the study requires 1472 child per group. In order to facilitate randomization and allocation of staff we have rounded this figure to 1500 child per group.