Ngwa Julius S, Cabral Howard J, Cheng Debbie M, Pencina Michael J, Gagnon David R, LaValley Michael P, Cupples L Adrienne
Department of Biostatistics, Boston University, School of Public Health, 801 Massachusetts Ave, CT 3rd Floor, Boston, MA, 02118, USA.
Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health, 615 North Wolfe St, Baltimore, MD, 21205, USA.
BMC Med Res Methodol. 2016 Nov 3;16(1):148. doi: 10.1186/s12874-016-0248-6.
Typical survival studies follow individuals to an event and measure explanatory variables for that event, sometimes repeatedly over the course of follow up. The Cox regression model has been used widely in the analyses of time to diagnosis or death from disease. The associations between the survival outcome and time dependent measures may be biased unless they are modeled appropriately.
In this paper we explore the Time Dependent Cox Regression Model (TDCM), which quantifies the effect of repeated measures of covariates in the analysis of time to event data. This model is commonly used in biomedical research but sometimes does not explicitly adjust for the times at which time dependent explanatory variables are measured. This approach can yield different estimates of association compared to a model that adjusts for these times. In order to address the question of how different these estimates are from a statistical perspective, we compare the TDCM to Pooled Logistic Regression (PLR) and Cross Sectional Pooling (CSP), considering models that adjust and do not adjust for time in PLR and CSP.
In a series of simulations we found that time adjusted CSP provided identical results to the TDCM while the PLR showed larger parameter estimates compared to the time adjusted CSP and the TDCM in scenarios with high event rates. We also observed upwardly biased estimates in the unadjusted CSP and unadjusted PLR methods. The time adjusted PLR had a positive bias in the time dependent Age effect with reduced bias when the event rate is low. The PLR methods showed a negative bias in the Sex effect, a subject level covariate, when compared to the other methods. The Cox models yielded reliable estimates for the Sex effect in all scenarios considered.
We conclude that survival analyses that explicitly account in the statistical model for the times at which time dependent covariates are measured provide more reliable estimates compared to unadjusted analyses. We present results from the Framingham Heart Study in which lipid measurements and myocardial infarction data events were collected over a period of 26 years.
典型的生存研究跟踪个体直至发生某一事件,并测量该事件的解释变量,有时在随访过程中会重复测量。Cox回归模型已广泛应用于疾病诊断时间或死亡时间的分析。除非对生存结果与时间依赖性测量之间的关联进行适当建模,否则可能会产生偏差。
在本文中,我们探讨了时间依赖性Cox回归模型(TDCM),该模型在事件发生时间数据分析中量化了协变量重复测量的效应。该模型在生物医学研究中常用,但有时未明确调整时间依赖性解释变量的测量时间。与调整这些时间的模型相比,这种方法可能会产生不同的关联估计。为了从统计学角度解决这些估计差异有多大的问题,我们将TDCM与合并逻辑回归(PLR)和横截面合并(CSP)进行比较,同时考虑在PLR和CSP中调整和不调整时间的模型。
在一系列模拟中,我们发现时间调整后的CSP与TDCM结果相同,而在高事件率情况下,PLR与时间调整后的CSP和TDCM相比显示出更大的参数估计。我们还观察到未调整的CSP和未调整的PLR方法存在向上偏差。时间调整后的PLR在时间依赖性年龄效应上存在正偏差,事件率较低时偏差减小。与其他方法相比,PLR方法在性别效应(个体水平协变量)上存在负偏差。在所有考虑的情况下,Cox模型对性别效应产生了可靠的估计。
我们得出结论,与未调整的分析相比,在统计模型中明确考虑时间依赖性协变量测量时间的生存分析提供了更可靠的估计。我们展示了弗雷明汉心脏研究的结果,该研究在26年期间收集了血脂测量和心肌梗死数据事件。