We read with great interest the recent article by Welsh et al. titled ‘Change in physical activity and its association with decline in kidney function: A UK Biobank-based cohort study’ in Journal of Cachexia, Sarcopenia and Muscle [1]. The study finds that increased physical activity may protect kidney function, as suggested by the modest yet significant associations observed in large-scale analyses using eGFRCysC measurements. However, we note several biases in the use of the Cox proportional hazards (CoxPH) model that the authors did not address.

The established criteria may result in mixed censoring outcomes, that is, right-censoring and interval-censoring events [2, 3]. Events of kidney function diagnosed through medical records could result in interval-censoring if they occurred between follow-up visits, and right-censoring for diagnosed between the end of follow-up and the time of data analysis. The CoxPH model primarily handles right-censored data. In contrast, the accelerated failure time (AFT) model is often preferred for scenarios involving various types of censored data [4]. The AFT model can effectively handle left-censored, right-censored and interval-censored data by appropriately adjusting the likelihood function [5]. By using the ‘survival’ and ‘icenReg’ packages, mixed censored data can be fitted and analysed, and event times can be estimated [6].

Moreover, the CoxPH model requires the proportional hazards assumption, meaning that covariate effects are constant over time [7]. If this assumption is violated, the model may not provide unbiased estimates of the coefficients, and the predictions may not be reliable. The authors should utilize Schoenfeld residuals or alternative methods to evaluate the proportional hazards assumption for the association between covariates and the risk of kidney function. Schoenfeld residuals are calculated as the differences between the observed and expected values of covariates at each failure time [8]. If the residuals exhibit a systematic change over time, it suggests that the effect of the covariate may be time-dependent. When the proportional hazards assumption does not hold, authors should use a stratified Cox model, a Cox model with time-varying effects, or an AFT model instead of the standard CoxPH model [4, 9].

In conclusion, we believe that a re-evaluation considering the potential impact of censoring events and the proportional hazards assumption is necessary. Further research is anticipated to provide more empirical data and clearer insights into this field.

我们饶有兴趣地阅读了 Welsh 等人最近在《恶病质、肌肉减少症和肌肉杂志》上发表的题为“身体活动的变化及其与肾功能下降的关系：一项基于英国生物样本库的队列研究”的文章 [1]。研究发现，增加身体活动可能会保护肾功能，正如在使用 eGFRCysC 测量的大规模分析中观察到的适度但显着的关联所表明的那样。然而，我们注意到作者在使用 Cox 比例风险 （CoxPH） 模型时存在一些偏见。

既定标准可能会导致混合删失结果，即右删失和区间删失事件 [2， 3]。如果通过病历诊断的肾功能事件发生在两次随访之间，则可能导致区间删失，而在随访结束和数据分析时间之间诊断的事件则可能导致右删失。CoxPH 模型主要处理右删失数据。相比之下，加速失效时间 （AFT） 模型通常适用于涉及各种类型删失数据的场景 [4]。AFT 模型可以通过适当调整似然函数来有效处理左删失、右删失和区间删失数据 [5]。通过使用 “survival” 和 “icenReg” 包，可以拟合和分析混合删失数据，并可以估计事件时间 [6]。

此外，CoxPH 模型需要比例风险假设，这意味着协变量效应随时间变化是恒定的 [7]。如果违反此假设，则模型可能无法提供系数的无偏估计，并且预测可能不可靠。作者应利用 Schoenfeld 残差或其他方法来评估协变量与肾功能风险之间关联的比例风险假设。Schoenfeld 残差计算为每个失效时间协变量的观测值和预期值之间的差值 [8]。如果残差随时间表现出系统性变化，则表明协变量的影响可能与时间有关。当比例风险假设不成立时，作者应使用分层 Cox 模型、具有时变效应的 Cox 模型或 AFT 模型，而不是标准的 CoxPH 模型 [4， 9]。

总之，我们认为有必要重新评估审查事件的潜在影响和比例风险假设。预计进一步的研究将为该领域提供更多的实证数据和更清晰的见解。