Carefully analysing data for a large number of locations, Bourgeois-Pichat
found that deaths during the last eleven months of infancy were uniformly
distributed on a log-cube transform of age, independent of the level of
mortality. He found that, When plotted on the log-cube time scale, the
cumulative number of deaths after the first month ...
(Show more)Carefully analysing data for a large number of locations, Bourgeois-Pichat
found that deaths during the last eleven months of infancy were uniformly
distributed on a log-cube transform of age, independent of the level of
mortality. He found that, When plotted on the log-cube time scale, the
cumulative number of deaths after the first month tend to follow a straight line, similar to the development of body weight (Bourgeois-Pichat 1951a, b). The relationship is surprising, since one would expect the cumulative deaths risks, and not cumulative deaths, to follow the increase in body weight. Therefore, we instead suggest that the cumulative hazards function on the same time transformation is linear during the last eleven months of infancy, implying an exponential distribution on the time transformed data. We compare the Bourgeois-Pichat model with our own for several locations in Sweden going back to the eighteenth century, as well as for the entire country. Doing so, we find that the two models produce similar results for populations with low or moderately high infant mortality but diverge when infant mortality is high. In addition to being more intuitive and directly related to progress in body weight, the advantages using our model are threefold: First, the proposed model fits better, especially in populations with high infant mortality, and second, the estimation of exogeneous and endogenous infant mortality is easily performed with standard survival analysis programs. Third, the proposed model allows easy estimation in the case of right censored and/or left truncated data.
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