I don't know how the Gates Foundation functions, so the level of which Bill should be implicated in the failings of this study are unclear to me. It sounds like the study would have been fairly inexpensive, and thus relegated to maybe just a footnote on one afternoon for Bill.
The eugenics-style arguments seen up in the parent comment seem to be a result of over-extrapolation of his "Innovating to zero" TED talk[1]. He alludes to, but does not cite, statistics correlating quality of life, health, and number of children. I also cannot find a concrete source, but playing around with wolfram alpha, it seems like there is at least a correlation according to their datasets[2].
[1] https://www.ted.com/talks/bill_gates/transcript?language=en#... [2] https://www.wolframalpha.com/input/?i=life+expectancy+%7C+ch...