Inferring probabilities from rates: Extension to multiple decrement

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Abstract
Life table probabilities are developed for the multiple decrement table, a model in which each cause of death acts in the presence of other causes or is ‘dependent’, and for the associated single decrement table, which shows the operation of each cause as though it acted alone or ‘independently’. The decrement for the ith cause, , in the multiple decrement table is the number of deaths due to the ith cause out of l 0 births; our method is provided by (12). The ‘independent’ decrement for the ith cause is calculated as though no other cause were operating, from the beginning of the table, with arbitrary radix ; Equation (21) shows its close relation to deaths in the single decrement table for all causes together (4). The modification needed is to increase the r in the program for an ordinary life table by an amount that allows for the loss of exposure to the ith cause because of operation of other causes.

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