Transition probability estimation plays a critical role in multi-state modeling, especially in clinical research. This paper investigates the application of semi-Markov and Markov renewal frameworks to the EBMT dataset, focusing on six clinical states encountered during hematopoietic stem cell transplantation. By comparing Aalen-Johansen (AJ) and Dabrowska-Sun-Horowitz (DSH) estimators, we demonstrate that semi-Markov models, which incorporate sojourn times, provide a more nuanced and temporally sensitive depiction of patient trajectories compared to memoryless Markov models. The DSH estimator consistently yields smoother probability curves, particularly for transitions involving prolonged states. We use empirical process theory and Burkholder-Davis-Gundy inequality to show weak convergence of the estimator. Future work includes extending the framework to accommodate advanced covariate structures and non-Markovian dynamics.
Estimating customer lifetime value (CLV or LTV) is extremely important for making better business decisions. The proposed flexible proportional hazards model allows an estimation of lifetime value in contractual settings. This approach takes advantage of a churn model, which is assumed to be available.
Proportional hazards are a common assumption when designing confirmatory clinical trials in oncology. With the emergence of immunotherapy and novel targeted therapies, departure from the proportional hazard assumption is not rare in nowadays clinical research. Under non-proportional hazards, the hazard ratio does not have a straightforward clinical interpretation, and the log-rank test is no longer the most powerful statistical test even though it is still valid. Nevertheless, the log-rank test and the hazard ratio are still the primary analysis tools, and traditional approaches such as sample…
Loss of power and clear description of treatment differences are key issues in designing and analyzing a clinical trial where non-proportional hazard is a possibility. A log-rank test may be very inefficient and interpretation of the hazard ratio estimated using Cox regression is potentially problematic. In this case, the current ICH E9 (R1) addendum would suggest designing a trial with a clinically relevant estimand, e.g., expected life gain. This approach considers appropriate analysis methods for supporting the chosen estimand. However, such an approach is case specific and may suffer lack …
The classical approach to analyze time-to-event data, e.g. in clinical trials, is to fit Kaplan-Meier curves yielding the treatment effect as the hazard ratio between treatment groups. Afterwards commonly a log-rank test is performed in order to investigate whether there is a difference in survival, or, depending on additional covariates, a Cox proportional hazard model is used. However, in numerous trials these approaches fail due to the presence of non-proportional hazards, resulting in difficulties of interpreting the hazard ratio and a loss of power. When considering equivalence or non-inf…
The semi-parametric Cox proportional hazards regression model has been widely used for many years in several applied sciences. However, a fully parametric proportional hazards model, if appropriately assumed, can often lead to more efficient inference. To tackle the extreme non-robustness of the traditional maximum likelihood estimator in the presence of outliers in the data under such fully parametric proportional hazard models, a robust estimation procedure has recently been proposed extending the concept of the minimum density power divergence estimator (MDPDE) under this set-up. In this pa…
A fundamental concept in two-arm non-parametric survival analysis is the comparison of observed versus expected numbers of events on one of the treatment arms (the choice of which arm is arbitrary), where the expectation is taken assuming that the true survival curves in the two arms are identical. This concept is at the heart of the counting-process theory that provides a rigorous basis for methods such as the log-rank test. It is natural, therefore, to maintain this perspective when extending the log-rank test to deal with non-proportional hazards, for example by considering a weighted sum o…
In this paper, our proposal consists of incorporating frailty into a statistical methodology for modeling time-to-event data, based on non-proportional hazards regression model. Specifically, we use the generalized time-dependent logistic (GTDL) model with a frailty term introduced in the hazard function to control for unobservable heterogeneity among the sampling units. We also add a regression in the parameter that measures the effect of time, since it can directly reflect the influence of covariates on the effect of time-to-failure. The practical relevance of the proposed model is illustrat…
One of the most common ways researchers compare survival outcomes across treatments when confounding is present is using Cox regression. This model is limited by its underlying assumption of proportional hazards; in some cases, substantial violations may occur. Here we present and compare approaches which attempt to address this issue, including Cox models with time-varying hazard ratios; parametric accelerated failure time models; Kaplan-Meier curves; and pseudo-observations. To adjust for differences between treatment groups, we use Inverse Probability of Treatment Weighting based on the pro…
Survival analysis of DNA mutation motifs with penalized proportional hazards
抗体是我们免疫系统的重要组成部分，通过一个复杂的过程来结合各种病原体。这个过程涉及随机突变编码这些抗体的DNA序列，以找到具有改进结合的变体，尽管突变在序列位点上并不均匀分布。免疫学家观察到这种不均匀性与“突变基序”一致，突变基序是影响给定位点发生突变的可能性的短DNA序列。量化基序对突变率的影响是具有挑战性的：大量可能的基序使这个统计问题高维，而未观察到的历史的突变过程导致一个非平凡的数据缺失问题。我们引入了一个$\ell_1$ -惩罚比例风险模型来推断突变基序及其影响。为了估计模型参数，我们的方法使用Monte Carlo EM算法边缘化未知的突变顺序。我们表明，我们的方法比目前的方法更好地模拟数据，并导致更简约的模型。比例风险突变过程的应用，据我们所知，新的和形式化的统计框架，可以很容易地扩展到分析其他生物特征对突变率的影响，目前的方法。
Age- and time-varying proportional hazards models for employment discrimination
我们使用离散时间比例风险模型的时间非自愿就业终止。该模型使我们能够检查雇员年龄的持续影响以及该影响是否随时间而变化，从而概括早期的工作[Kadane和Woodworth J. Bus。经济中央集权主义者22（2004）182- 193]。我们将对数危险面（超过年龄和时间）建模为薄板样条，这是表面拟合的惩罚似然方法的贝叶斯平滑先验实现[Wahba（1990）Spline Models for Observational Data. SIAM]。表面的非线性分量只有两个参数，平滑度和各向异性。第一个是比例参数，控制曲面的整体平滑度;第二个是各向异性，控制随时间和年龄变化的相对平滑度。对于任何固定值的各向异性参数，前相当于一个高斯过程与线性漂移的时间-年龄平面容易计算的特征向量和特征值，只依赖于配置的数据在时间-年龄平面和各向异性参数。这一模式适用于公司在决定解雇谁时被指控不成比例地解雇老年工人的法律案件。我们说明了应用程序的建模方法，使用数据从一个实际的歧视案件。
One-sample survival tests in the presence of non-proportional hazards in oncology clinical trials
Oncostat, CESP, INSERM U1018（INSERM U1018）；University Paris-Saclay（巴黎萨克雷大学）；Department of Statistics and Acturial Science（统计与精算学系）；University of Hong Kong（香港大学）
Studies to compare the survival of two or more groups using time-to-event data are of high importance in medical research. The gold standard is the log-rank test, which is optimal under proportional hazards. As the latter is no simple regularity assumption, we are interested in evaluating the power of various statistical tests under different settings including proportional and non-proportional hazards with a special emphasize on crossing hazards. This challenge has been going on for many years now and multiple methods have already been investigated in extensive simulation studies. However, in…
We develop a functional proportional hazards mixture cure (FPHMC) model with scalar and functional covariates measured at the baseline. The mixture cure model, useful in studying populations with a cure fraction of a particular event of interest is extended to functional data. We employ the EM algorithm and develop a semiparametric penalized spline-based approach to estimate the dynamic functional coefficients of the incidence and the latency part. The proposed method is computationally efficient and simultaneously incorporates smoothness in the estimated functional coefficients via roughness …
