An alternative approach—which has sufficient accuracy to make a rough estimate of statistical power^{1}—is to calculate the expected number of deaths in the cohort over a given period of follow-up. For the purpose of this exercise, the committee chose a 10-year follow-up beginning in 2005 and ending in 2015. Calculations were made for each AFHS subject who was alive on January 1, 2005, by making use of the U.S. life table (NCHS, 2004c) for men. Specifically, for each subject we multiplied the age-specific probabilities of surviving in each age interval across the length of follow-up, subtracting this probability from unity to obtain the cumulative probability of dying, and then summing over all subjects. In equation form—for each AFHS subject alive on January 1, 2005—if one designates p_{a} as the probability of surviving through each 1-year age interval a, then the estimated probability of dying over a specified period of follow-up is:
and e, the estimated number of deaths in the cohort, is the sum of each subject’s contribution
where agealive was the age of the subject on January 1, 2005, and agefollowup is the age of each subject in 2015. Calculations were truncated at age 99.
AFHS staff provided the committee with a denominalized file containing the relevant information to carry out this calculation (AFHS, 2005). The data comprised a randomly assigned ID number; an indicator for whether the subject was a Ranch Hand or comparison veteran; the year the subject was last known to be alive; age at that year; and an indicator of whether the subject participated in one or more cycle exams (compliant in the study’s terminology) or not (noncompliant).
The calculations, which were performed on data for compliant subjects only, yield estimates for deaths from all causes combined. To partition these estimated deaths according to specific causes, the percentages of deaths from selected causes for ages 60–89 years (in 5-year intervals) were extracted from National Center for Health Statistics data (NCHS, 2004a) and averaged across the intervals. This exercise yielded the following estimates for the proportion of deaths for some of the most common causes of death:
Malignant neoplasms: 33.9 percent of all deaths
Diseases of the heart: 23.6 percent of all deaths
Chronic lower respiratory diseases: 7.5 percent of all deaths