One-Step Generalized Estimating Equations With Large Cluster Sizes
针对医学研究中簇规模大导致计算量过大的问题，提出一种一步广义估计方程估计量，避免全对求和与矩阵运算，在保持渐近效率的同时大幅降低计算负担。
Medical studies increasingly involve a large sample of independent clusters, where the cluster sizes are also large. Our motivating example from the 2010 Nationwide Inpatient Sample (NIS) has 8,001,068 patients and 1049 clusters, with average cluster size of 7627. Consistent parameter estimates can be obtained naively assuming independence, which are inefficient when the intra-cluster correlation (ICC) is high. Efficient generalized estimating equations (GEE) incorporate the ICC and sum all pairs of observations within a cluster when estimating the ICC. For the 2010 NIS, there are 92.6 billion pairs of observations, making summation of pairs computationally prohibitive. We propose a one-step GEE estimator that 1) matches the asymptotic efficiency of the fully-iterated GEE; 2) uses a simpler formula to estimate the ICC that avoids summing over all pairs; and 3) completely avoids matrix multiplications and inversions. These three features make the proposed estimator much less computationally intensive, especially with large cluster sizes. A unique contribution of this paper is that it expresses the GEE estimating equations incorporating the ICC as a simple sum of vectors and scalars.