Calculating Adjusted Survival Functions for Complex Sample Survey Data and Application to Vaccination Coverage Studies with National Immunization Survey

Background: In vaccination studies with complex sample survey, survival functions have been used since 2002. 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 have not been described.
Objectives: Propose two methods for calculating adjusted survival functions in the complex sample survey setting; apply the two methods to 2011 National Immunization Survey (NIS) child data with SUDAAN software package.
Methods: 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 (KM) survival function. Survival functions are evaluated for each of the unique combination of all levels of predictors in complex sample survey obtained from Cox proportional hazards (PH) model, and the weighted average of these individual functions is defined as the Cox corrected group (CCG) adjusted survival function.
Results: The IPW and CCG methods were applied to generate adjusted cumulative vaccination coverage curves across children’s age in days receiving the first dose of varicella by family mobility status. The IPW adjusted cumulative varicella vaccination coverage curves could be consistent estimates of the true coverage curves, the IPW adjustment made the curve for moved family closer to the curve for not-moved family, and the IPW method significantly reduced the standard errors of the cumulative vaccination coverage across children age in days receiving the first dose of varicella comparing to the unadjusted KM method. The Cox PH assumption is not valid for 2011 NIS data.
Conclusions: If the Cox PH assumption is not met, then the IPW adjusted KM method is the only good choice, if adjusted survival estimates are desired. If the Cox PH assumption is valid, either the IPW or CCG methods can be used.