基于函数型主成分分析的稀疏纵向数据建模研究

Modeling Research to Sparse Longitudinal Data based on Functional Principal Component Analysis

目的探索基于条件期望的函数型主成分分析方法(principal analysis by conditional expectation,PACE)在稀疏且不规则的纵向数据中的预测效果,评价其揭示总体变化趋势、个体特异的变异方式以及预测个体纵向变化轨迹的能力。方法采用R软件模拟生成样本量为200的三种不同稀疏情形的纵向数据集,通过数值模拟定量地评价PACE方法的降维及预测效果。结果根据累计方差贡献率达到85%,三种不同稀疏情形的纵向数据集最终选取的主成分个数分别为4、4、3,PACE方法在不同稀疏情形下预测结果均具有较小的均方误差(MSE),分别为0.1410、0.0670、0.0161,而且观测点个数越多预测效果越好。结论PACE方法可以实现在随访间隔不规则且数据稀疏的情况下,捕获纵向数据随时间变化的总体趋势,揭示个体特异的变异方式,预测个体的纵向轨迹。

Objective To explore the prediction effect of principal analysis by conditional expectation(PACE)in sparse and irregular longitudinal data,and evaluate its ability to reveal the overall change trend,individual specific variation pattern and predict individual longitudinal change trajectory.Methods The R software was used to simulate and generate longitudinal data sets of three different sparse cases with a sample size of 200,and the dimensionality reduction and prediction effects of the PACE method were quantitatively evaluated through numerical simulation.Results According to the cumulative variance contribution rate of 85%,the final number of principal components selected for the three longitudinal data sets with different sparse conditions were 4,4 and 3 respectively.The mean square error(MSE)of PACE method in different sparse conditions was 0.1410,0.0670 and 0.0161 respectively.And the more observation points,the better the prediction effect.Conclusion The PACE method can capture the overall trend of longitudinal data over time,reveal individual specific variation patterns,and predict individual longitudinal trajectories under the condition of irregular follow-up intervals and sparse data.