A comparison of model parameter estimation methods for complex survey survival data

Abstract

When estimation of model parameters is the target in survey data, the inference on the model can be based on a pure model-based approach or a model-assisted approach which is a hybrid approach combining design-based and model-based methods. This study aims to compare these methods for survival data that are gathered from a stratified random sampling design. The Accelerated Failure Time (AFT) model was fitted to describe the relationship between the censored response variable and the explanatory variables. Resampling methods with different sample sizes and different sampling designs from a real dataset were considered in the study to generate samples. The AFT models were fitted to each of the samples using, firstly a pure model-based method ignoring the survey design and weights, secondly a model-based method with survey weights, and finally a model-assisted method considering both survey design and weights. Squared bias, variance, and mean squared error (MSE) were used to compare the three approaches. The AFT model, with all covariates and the best AFT model with the best set of covariates and distribution, were analyzed. Even though it was challenging to select the best method for all cases, the second and third approaches worked better for small samples than the first approach.