In the article by Rahman et al., a cohort study was conducted. There are other study designs as well, such as case control studies, randomized controlled clinical trials, cross-sectional studies, etc. In the case control studies, people with a specific condition are compared with people without that condition and medical records and memory recall is used to make associations. Such a methodology can not be applied to the large sample set used here. Clinical trials introduce the condition in a particular sample set, which of course was not possible in this case. Imagine having to expose someone to arsenic! And cross-sectional studies relate a condition and some potential causal factors at some given point of time, so studies spread over time (such as the one by Rahman et al.) cannot be conducted with such a design. So, it seems like cohort study was the only possible design for this study. Having said that, doesn't mean this study could not be improved upon (if repeated). The researchers can certainly minimize the bias and improve upon the design by introducing more parameters, such as history of infant deaths in the samples, etc.
Hope this helps.