Calculating Adjusted Survival Functions for complex sample survey data and application to vaccination coverage studies with National Immunization Survey (NIS)

Background: In vaccination studies with complex sample survey data, non-parametric survival functions may be useful. Recent publications have proposed several methods for evaluating the adjusted survival functions in non-population-based studies. However, alternative methods for calculating adjusted survival functions for complex sample survey data have not been described. Objectives: 1) Propose and describe two methods for calculating adjusted survival functions in the complex sample survey setting; 2) implement these two methods with SUDAAN software package; and 3) apply these two methods to 2011 National Immunization Survey (NIS) data. Methods: (1) The inverse probabilities of being in a certain group are defined as the new weights and applied to obtain the inverse probability weighting (IPW) adjusted Kaplan-Meier survival function. (2) Survival functions are evaluated for each of the unique combination of all levels of covariates in a complex sample survey obtained from a single Cox proportional hazards (PH) model, and the weighted average of these individual functions is calculated, with weights equal to the weighted sample size of the individual function, to obtain the Cox corrected group (CCG) adjusted survival function. Illustrative example: For illustration of the basic techniques rather than a thorough epidemiologic investigation of a specific research question, the two proposed methods were applied to 2011 National Immunization Survey (NIS) data. We estimated the adjusted survival function by age in days of children receiving the first dose of varicella vaccination by children’s family mobility status and by IPW, CCG, and crude Kaplan-Meier (KM) methods controlling for parents’ attitude toward vaccination, mother’s age group, and children first born status. Conclusions: If the Cox PH assumption is not met, then the IPW adjusted KM method is the only good choice among the two proposed methods, if adjusted survival estimates are desired. If the Cox PH assumption is valid, either the IPW or CCG methods can be used.