Center for Biostatistics in AIDS Research, Department of Biostatistics, Harvard School of Public Health, FXB 514, 651 Huntington Avenue, Boston, MA 02115, USA.
Biostatistics. 2012 Jul;13(3):440-54. doi: 10.1093/biostatistics/kxr028. Epub 2011 Sep 15.
We propose to analyze panel count data using a spline-based semiparametric projected generalized estimating equation (GEE) method with the proportional mean model E(N(t)|Z) = Λ(0)(t) e(β(0)(T)Z). The natural logarithm of the baseline mean function, logΛ(0)(t), is approximated by a monotone cubic B-spline function. The estimates of regression parameters and spline coefficients are obtained by projecting the GEE estimates into the feasible domain using a weighted isotonic regression (IR). The proposed method avoids assuming any parametric structure of the baseline mean function or any stochastic model for the underlying counting process. Selection of the working covariance matrix that accounts for overdispersion improves the estimation efficiency and leads to less biased variance estimations. Simulation studies are conducted using different working covariance matrices in the GEE to investigate finite sample performance of the proposed method, to compare the estimation efficiency, and to explore the performance of different variance estimates in presence of overdispersion. Finally, the proposed method is applied to a real data set from a bladder tumor clinical trial.
我们建议使用基于样条的半参数投影广义估计方程(GEE)方法分析面板计数数据,该方法采用比例均值模型 E(N(t)|Z) = Λ(0)(t) e(β(0)(T)Z)。基线均值函数的自然对数 logΛ(0)(t) 通过单调三次 B 样条函数进行近似。通过使用加权单调回归(IR)将 GEE 估计值投影到可行域中,来获得回归参数和样条系数的估计值。该方法避免了对基线均值函数的任何参数结构或潜在计数过程的任何随机模型的假设。选择考虑过离散度的工作协方差矩阵可以提高估计效率,并导致偏差较小的方差估计。通过在 GEE 中使用不同的工作协方差矩阵进行模拟研究,以研究所提出方法的有限样本性能,比较估计效率,并在存在过离散度的情况下探索不同方差估计的性能。最后,将该方法应用于膀胱癌临床试验的真实数据集。