notes competing risks - Eco 572 Research methods in...

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Eco 572: Research methods in Demography Competing Risks Let us work through the example in the textbook on multiple decrement and associated single decrement life tables, see Boxes 4.1 and 4.2 on pages 77 and 85. Rather than just repeat all the calculations, however, I will illustrate a simpler approach to cause- deleted tables based on the assumption that cause-specific hazards are constant within each age interval. This approach gives almost the same results as the textbook, yet allows us to concentrate on the underlying concepts. We start by reading the data, which have deaths for all causes and from neoplasms for U.S. females in 1991. I also include the l x and n a x columns. . set type double . infile age D Di lx a using /// > (19 observations read) Multiple Decrements The first task is to estimate mortality due to neoplasms in the presence of other causes. We start by estimating overall survival using conventional life table techniques. Then we compute conditional probabilities of death. (These usually would have been computed on the way to l x .) . gen q = 1-lx[_n+1]/lx (1 missing value generated) . replace q = 1 in -1 (1 real change made) The conditional probability of dying of a given cause given survival to the age group is obtained multiplying by the ratio of deaths of a given cause to all deaths: . gen qi = q * Di/D The unconditional probabilities of dying of any cause and of a given cause are obtained multiplying by the probability of the condition, which is l x . gen d = lx * q . gen di = lx * qi Let us print our results (1 of 6) [2/12/2008 10:38:03 AM]
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Eco 572: Research methods in Demography . format %8.5f q qi . format %8.0fc l d di . list age l q qi d di +----------------------------------------------------+ | age lx q qi d di | |----------------------------------------------------| 1. | 0 100,000 0.00783
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