Cardiovascular Research Center, Shiraz University of Medical Sciences, Shiraz, Iran.
Department of Biostatistics, School of Medicine, Shiraz University of Medical Sciences, Shiraz, Iran.
Biomed Res Int. 2020 Apr 22;2020:2905167. doi: 10.1155/2020/2905167. eCollection 2020.
Landmark model (LM) is a dynamic prediction model that uses a longitudinal biomarker in time-to-event data to make prognosis prediction. This study was designed to improve this model and to apply it to assess the cardiovascular risk in on-treatment blood pressure patients. A frailty parameter was used in LM, landmark frailty model (LFM), to account the frailty of the patients and measure the correlation between different landmarks. The proposed model was compared with LM in different scenarios respecting data missing status, sample size (100, 200, and 400), landmarks (6, 12, 24, and 48), and failure percentage (30, 50, and 100%). Bias of parameter estimation and mean square error as well as deviance statistic between models were compared. Additionally, discrimination and calibration capability as the goodness of fit of the model were evaluated using dynamic concordance index (DCI), dynamic prediction error (DPE), and dynamic relative prediction error (DRPE). The proposed model was performed on blood pressure data, obtained from systolic blood pressure intervention trial (SPRINT), in order to calculate the cardiovascular risk. Dynpred, coxme, and coxphw packages in the R.3.4.3 software were used. It was proved that our proposed model, LFM, had a better performance than LM. Parameter estimation in LFM was closer to true values in comparison to that in LM. Deviance statistic showed that there was a statistically significant difference between the two models. In the landmark numbers 6, 12, and 24, the LFM had a higher DCI over time and the three landmarks showed better performance in discrimination. Both DPE and DRPE in LFM were lower in comparison to those in LM over time. It was indicated that LFM had better calibration in comparison to its peer. Moreover, real data showed that the structure of prognostic process was predicted better in LFM than in LM. Accordingly, it is recommended to use the LFM model for assessing cardiovascular risk due to its better performance.
landmark 模型（LM）是一种动态预测模型，它使用时间事件数据中的纵向生物标志物来进行预后预测。本研究旨在改进该模型，并将其应用于评估治疗中血压患者的心血管风险。在 LM 中使用了脆弱性参数，即 landmark 脆弱性模型（LFM），以考虑患者的脆弱性并测量不同 landmark 之间的相关性。在不同的数据缺失情况、样本量（100、200 和 400）、landmark（6、12、24 和 48）和失败百分比（30、50 和 100%）的场景下，将提出的模型与 LM 进行了比较。比较了模型之间的参数估计偏差、均方误差和偏差统计量。此外，还使用动态一致性指数（DCI）、动态预测误差（DPE）和动态相对预测误差（DRPE）评估了模型的拟合优度，即区分和校准能力。使用 R.3.4.3 软件中的 Dynpred、coxme 和 coxphw 包对血压数据进行了分析，这些数据来自收缩压干预试验（SPRINT），以计算心血管风险。结果表明，与 LM 相比，我们提出的 LFM 模型具有更好的性能。与 LM 相比，LFM 中的参数估计更接近真实值。偏差统计量表明，两个模型之间存在统计学上的显著差异。在 landmark 数量为 6、12 和 24 时，LFM 随着时间的推移具有更高的 DCI，并且这三个 landmark 在区分方面表现更好。随着时间的推移，LFM 的 DPE 和 DRPE 均低于 LM。这表明 LFM 的校准效果优于其同类产品。此外，实际数据表明，LFM 比 LM 更能准确预测预后过程的结构。因此，建议使用 LFM 模型来评估心血管风险，因为它具有更好的性能。
