Estimation of attributable number of deaths and standard errors from simple and complex sampled cohorts

Estimates of the attributable number of deaths (AD) from all causes can be obtained by first estimating population attributable risk (AR) adjusted for confounding covariates, and then multiplying the AR by the number of deaths determined from vital mortality statistics that occurred in the population for a specific time period. Proportional hazard regression estimates of adjusted relative hazards obtained from mortality follow-up data from a cohort is combined with a joint distribution of risk factor and confounders to compute an adjusted AR. Two estimators of adjusted AR are examined. These estimators differ according to which reference population is used to obtain the joint distribution of risk factor and confounders. Two types of reference populations were considered: (i) the population represented by the baseline cohort and (ii) a population that is external to the cohort. Methods used in survey sampling are applied to obtain estimates of the variance of the AD estimator. These variances can be applied to data that range from simple random samples to multistage stratified cluster samples, which are used in national household surveys. The variance estimation of AD is illustrated in an analysis of excess deaths due to having a non-ideal body mass index using the second National Health and Examination Survey (NHANES) Mortality Study and the 1999-2002 NHANES. These methods can also be used to estimate the attributable number of cause-specific deaths and their standard errors when the time period for the accrual of deaths is short.