Estimating survival probabilities by exposure levels: utilizing vital statistics and complex survey data with mortality follow‐up

We present a two-step approach for estimating hazard rates and, consequently, survival probabilities, by levels of general categorical exposure. The resulting estimator utilizes three sources of data: vital statistics data and census data are used at the first step to estimate the overall hazard rate for a given combination of gender and age group, and cohort data constructed from a nationally representative complex survey with linked mortality records, are used at the second step to divide the overall hazard rate by exposure levels. We present an explicit expression for the resulting estimator and consider two methods for variance estimation that account for complex multistage sample design: (1) the leaving-one-out jackknife method, and (2) the Taylor linearization method, which provides an analytic formula for the variance estimator. The methods are illustrated with smoking and all-cause mortality data from the US National Health Interview Survey Linked Mortality Files, and the proposed estimator is compared with a previously studied crude hazard rate estimator that uses survey data only. The advantages of a two-step approach and possible extensions of the proposed estimator are discussed. Copyright © 2015 John Wiley & Sons, Ltd.