Population-based surveys are possible sources from which to draw representative control data for case-control studies. However, these surveys involve complex sampling that could lead to biased estimates of measures of association if not properly accounted for in analyses. Approaches to incorporating complex-sampled controls in density-sampled case-control designs have not been examined.
We used a simulation study to evaluate the performance of different approaches to estimating incidence density ratios (IDR) from case-control studies with controls drawn from complex survey data using risk-set sampling. In simulated population data, we applied four survey sampling approaches, with varying survey sizes, and assessed the performance of four analysis methods for incorporating survey-based controls.
Estimates of the IDR were unbiased for methods that conducted risk-set sampling with probability of selection proportional to survey weights. Estimates of the IDR were biased when sampling weights were not incorporated, or only included in regression modeling. The unbiased analysis methods performed comparably and produced estimates with variance comparable to biased methods. Variance increased and confidence interval coverage decreased as survey size decreased.
Unbiased estimates are obtainable in risk-set sampled case-control studies using controls drawn from complex survey data when weights are properly incorporated.

The nested case-control (NCC) design is widely used in epidemiologic studies as a cost-effective subcohort sampling method to study the association between a disease and its potential risk factors. NCC data are commonly analyzed using Thomas\' partial likelihood approach under the Cox proportional hazards model assumption. However, the linear modeling form in the Cox model may be insufficient for practical applications, especially when there are a large number of risk factors under investigation. In this paper, we consider a partially linear single index proportional hazard model, which includes a linear component for covariates of interest to yield easily interpretable results and a nonparametric single index component to adjust for multiple confounders effectively. We propose to approximate the nonparametric single index function by polynomial splines and estimate the parameters of interest using an iterative algorithm based on the partial likelihood. Asymptotic properties of the resulting estimators are established. The proposed methods are evaluated using simulations and applied to an NCC study of ovarian cancer.