Unified approach (Chen and Chen in J R Stat Soc B 62(3):449–460, 2000) uses a working regression model to extract information from auxiliary variables in two-stage study for computing an efficient estimator of regression parameter. As far as we know, the method is limited to deal with missing complete at random data in a simple monotone missing data pattern. In this research, we extend the unified approach to estimate regression models with nonmonotone missing at random data. We describe an inverse probability weighting estimator condition on estimators from a set of working regression models which contains information from incomplete data and auxiliary variables. The proposed method is flexible and can easily accommodate incomplete data and auxiliary variables. We investigate the finite-sample performance of the proposed estimators using simulation studies and further illustrate the estimation method on a case–control study investigating the risk factors of hip fractures.

统一方法（Chen和Chen在JR Stat Soc B 62（3）：449–460，2000年发表）使用工作回归模型从两阶段研究的辅助变量中提取信息，以计算回归参数的有效估计量。据我们所知，该方法仅限于以简单的单调缺失数据模式处理随机数据的缺失完全。在这项研究中，我们扩展了统一的方法来估计具有随机数据的非单调缺失的回归模型。我们从一组工作回归模型的估计量上描述了一个逆概率加权估计量条件，该模型包含来自不完整数据和辅助变量的信息。所提出的方法是灵活的，并且可以容易地容纳不完整的数据和辅助变量。