Improving main analysis by borrowing information from auxiliary data

Abstract

In many clinical and observational studies, auxiliary data from the same subjects, such as repeated measurements or surrogate variables, will be collected in addition to the data of main interest. Not directly related to the main study, these auxiliary data in practice are rarely incorporated into the main analysis, though they may carry extra information that can help improve the estimation in the main analysis. Under the setting where part of or all subjects have auxiliary data available, we propose an effective weighting approach to borrow the auxiliary information by building a working model for the auxiliary data, where improvement of estimation precision over the main analysis is guaranteed regardless of the specification of the working model. An information index is also constructed to assess how well the selected working model works to improve the main analysis. Both theoretical and numerical studies show the excellent and robust performance of the proposed method in comparison to estimation without using the auxiliary data. Finally, we utilize the Atherosclerosis Risk in Communities study for illustration.

An Efficient Data Integration Scheme for Synthesizing Information from Multiple Secondary Datasets for the Parameter Inference of the Main Analysis

“…To take into account the strong associations among the primary endpoint and secondary outcomes, Chen et al. (2022) proposed a computationally efficient estimation approach that incorporates information from one secondary outcome into the main model. Specifically, the enhanced estimator can be obtained by the following reweighted estimating equation: $$$$\begin{equation} \sum _{i=1}^{n}\hat{p}_{ki}{\bm { g}}({\bm { D}}_{0i};{\bm{\beta }})={\bf 0}, \end{equation}$$$$where the nonnegative weights $$\hat{p}_{ki}$$ are estimated by maximizing $$\prod _{i=1}^np_{ki}$$ with respect to $$p_{ki}$$ and $${\bm{\theta }}_k$$ under the following constraints: $$$$\begin{equation} \sum _{i=1}^n p_{ki}=1, \quad \sum _{i=1}^np_{ki}R_{ki}{\bm { h}}_k({\bm { D}}_{ki};{\bm{\theta }}_k)={\bf 0}.$$…”

“…The estimating function $${\bm { h}}_k({\bm { D}}_{ki};{\bm{\theta }}_k)$$ is derived from a working model parameterized by $${\bm{\theta }}_k$$ for the data $${\bm { D}}_{ki}$$, such as generalized estimating equations (Liang & Zeger, 1986). To improve the estimation efficiency for the main parameter β , the dimension of the function $${\bm { h}}_k({\bm { D}}_{ki};{\bm{\theta }}_k)$$ should be larger than the dimension of the corresponding nuisance parameter vector $${\bm{\theta }}_{k}$$, thus rendering an overidentified function (Chen et al., 2022). Specific examples of overidentified functions in the literature are provided in Section G of the Supporting Information, which considers longitudinal or cross‐sectional secondary outcomes.…”

“…To circumvent these issues, Chen et al. (2022, 2023) proposed a reweighting estimation scheme that efficiently and robustly delivered information from a secondary dataset without the need for joint modeling. However, this approach is applicable only if there is only one secondary dataset.…”

Synthesizing secondary data into survival analysis to improve estimation efficiency

“…The existing works about information borrowing under the survival framework can be summarized into three categories: one is meta‐analysis by integrating information between multiple independent studies (Parmar et al., 1998; Tierney et al., 2007; Y. Wei et al., 2015); one is to use known information from external large studies to enhance analysis of the internal study (Huang et al., 2016; J. He et al., 2019; Shang & Wang, 2017); the last one is to use secondary outcome (Chen et al., 2020a; Song et al., 2002; Tsiatis & Davidian, 2004). The first two categories extract information from external studies, which requires a different data structure compared to our paper.…”

“…Chen et al. (2020a) proposed a semiparametric reweighting scheme to deliver the information from a secondary model to the main generalized linear model. However, the proposed method cannot be directly applied to survival analysis.…”