Maruyama Nami, Takahashi Fumiaki, Takeuchi Masahiro
Clinical Statistics, Pfizer Japan, Inc., Tokyo, Japan.
J Biopharm Stat. 2009 Sep;19(5):779-90. doi: 10.1080/10543400903105174.
In longitudinal data, interest is usually focused on the repeatedly measured variable itself. In some situations, however, the pattern of variation of the variable over time may contain information about a separate outcome variable. In such situations, longitudinal data provide an opportunity to develop predictive models for future observations of the separate outcome variable given the current data for an individual. In particular, longitudinally changing patterns of repeated measurements of a variable measured up to time t, or trajectories, can be used to predict an outcome measure or event that occurs after time t. In this article, we propose a method for predicting an outcome variable based on a generalized linear model, specifically, a logistic regression model, the covariates of which are variables that characterize the trajectory of an individual. Since the trajectory of an individual contains estimation error, the proposed logistic regression model constitutes a measurement error model. The model is fitted in two steps. First, a linear mixed model is fitted to the longitudinal data to estimate the random effect that characterizes the trajectory for each individual while adjusting for other covariates. In the second step, a conditional likelihood approach is applied to account for the estimation error in the trajectory. Prediction of an outcome variable is based on the logistic regression model in the second step. The receiver operating characteristic curve is used to compare the discrimination ability of a model with trajectories to one without trajectories as covariates. A simulation study is used to assess the performance of the proposed method, and the method is applied to clinical trial data.
在纵向数据中，关注点通常集中在重复测量的变量本身。然而，在某些情况下，该变量随时间的变化模式可能包含有关另一个独立结局变量的信息。在这种情况下，纵向数据提供了一个机会，可根据个体的当前数据为独立结局变量的未来观测值建立预测模型。特别是，在时间(t)之前测量的变量的纵向变化模式，即轨迹，可用于预测在时间(t)之后发生的结局指标或事件。在本文中，我们提出了一种基于广义线性模型，具体来说是逻辑回归模型，来预测结局变量的方法，该模型的协变量是表征个体轨迹的变量。由于个体的轨迹包含估计误差，因此所提出的逻辑回归模型构成了一个测量误差模型。该模型分两步拟合。首先，对纵向数据拟合一个线性混合模型，以估计在调整其他协变量的同时表征每个个体轨迹的随机效应。在第二步中，应用条件似然方法来考虑轨迹中的估计误差。结局变量的预测基于第二步中的逻辑回归模型。使用受试者工作特征曲线来比较具有轨迹的模型与没有轨迹作为协变量的模型的判别能力。通过模拟研究来评估所提出方法的性能，并将该方法应用于临床试验数据。
