The Aalen-Johansen estimator generalizes the Kaplan-Meier estimator for independently left-truncated and right-censored survival data to estimating the transition probability matrix of a time-inhomogeneous Markov model with finite state space. Such multi-state models have a wide range of applications for modelling complex courses of a disease over the course of time, but the Markov assumption may often be in doubt. If censoring is entirely unrelated to the multi-state data, it has been noted that the Aalen-Johansen estimator, standardized by the initial empirical distribution of the multi-state model, still consistently estimates the state occupation probabilities. Recently, this result has been extended to transition probabilities using landmarking, which is, inter alia, useful for dynamic prediction. We complement these results in three ways. Firstly, delayed study entry is a common phenomenon in observational studies, and we extend the earlier results to multi-state data also subject to left-truncation. Secondly, we present a rigorous proof of consistency of the Aalen-Johansen estimator for state occupation probabilities, on which also correctness of the landmarking approach hinges, correcting, simplifying and extending the earlier result. Thirdly, our rigorous proof motivates wild bootstrap resampling. Our developments for left-truncation are motivated by a prospective observational study on the occurrence and the impact of a multi-resistant infectious organism in patients undergoing surgery. Both the real data example and simulation studies are presented. Studying wild bootstrap is motivated by the fact that, unlike drawing with replacement from the data, it is desirable to have a technique that works both with non-Markov models subject to random left-truncation and right-censoring and with Markov models where left-truncation and right-censoring need not be entirely random.
High-dimensional sparse modeling with censored survival data is of great practical importance, and several methods have been proposed for variable selection based on different models. However, the impact of biased sample caused by left-truncation and covariates measurement error to variable selection is not fully explored. In this paper, we mainly focus on the additive hazards model and analyze the high-dimensional survival data subject to left-truncation and measurement error in covariates. We develop the three-stage procedure to correct the error effect, select variables, and estimate the pa…
Partially observed cured data occur in the analysis of spontaneous abortion (SAB) in observational studies in pregnancy. In contrast to the traditional cured data, such data has an observable `cured' portion as women who do not abort spontaneously. The data is also subject to left truncate in addition to right-censoring because women may enter or withdraw from a study any time during their pregnancy. Left truncation in particular causes unique bias in the presence of a cured portion. In this paper, we study a cure rate model and develop a conditional nonparametric maximum likelihood approach. …
Nonparametric estimation of a state entry time distribution conditional on a "past" state occupation in a progressive multistate model with current status data
Division of Cancer Epidemiology and Genetics, National Cancer Institute（癌症流行病学与遗传学系，国家癌症研究所）；Department of Biostatistics, University of Florida（生物统计学系，佛罗里达大学）
The analysis of causal effects when the outcome of interest is possibly truncated by death has a long history in statistics and causal inference. The survivor average causal effect is commonly identified with more assumptions than those guaranteed by the design of a randomized clinical trial or using sensitivity analysis. This paper demonstrates that individual level causal effects in the `always survivor' principal stratum can be identified with no stronger identification assumptions than randomization. We illustrate the practical utility of our methods using data from a clinical trial on pat…
The analysis left truncated and right censored data is very common in survival and reliability analysis. In lifetime studies patients often subject to left truncation in addition to right censoring. For example, in bone marrow transplant studies based on International Bone Marrow Transplant Registry (IBMTR), the patients who die while waiting for the transplants will not be reported to the IBMTR. In this paper, we develop novel U-statistics under left truncation and right censoring. We prove the $\sqrt{n}$-consistency of the proposed U-statistics. We derive the asymptotic distribution of the U…
Recent advances in causal mediation analysis have formalized conditions for estimating direct and indirect effects in various contexts. These approaches have been extended to a number of models for survival outcomes including accelerated failure time (AFT) models which are widely used in a broad range of health applications given their intuitive interpretation. In this setting, it has been suggested that under standard assumptions, the "difference" and "product" methods produce equivalent estimates of the indirect effect of exposure on the survival outcome. We formally show that these two meth…
Truncation is a statistical phenomenon that occurs in many time to event studies. For example, autopsy-confirmed studies of neurodegenerative diseases are subject to an inherent left and right truncation, also known as double truncation. When the goal is to study the effect of risk factors on survival, the standard Cox regression model cannot be used when the data is subject to truncation. Existing methods which adjust for both left and right truncation in the Cox regression model require independence between the survival times and truncation times, which may not be a reasonable assumption in …
We rigorously extend the widely used wild bootstrap resampling technique to the multivariate Nelson-Aalen estimator under Aalen's multiplicative intensity model. Aalen's model covers general Markovian multistate models including competing risks subject to independent left-truncation and right-censoring. This leads to various statistical applications such as asymptotically valid confidence bands or tests for equivalence and proportional hazards. This is exemplified in a data analysis examining the impact of ventilation on the duration of intensive care unit stay. The finite sample properties of…
University of Maryland, Baltimore County（马里兰大学巴尔的摩县分校）
Multi-state survival analysis (MSA) uses multi-state models for the analysis of time-to-event data. In medical applications, MSA can provide insights about the complex disease progression in patients. A key challenge in MSA is the accurate subject-specific prediction of multi-state model quantities such as transition probability and state occupation probability in the presence of censoring. Traditional multi-state methods such as Aalen-Johansen (AJ) estimators and Cox-based methods are respectively limited by Markov and proportional hazards assumptions and are infeasible for making subject-spe…
In survival studies, classical inferences for left-truncated data require quasi-independence, a property that the joint density of truncation time and failure time is factorizable into their marginal densities in the observable region. The quasi-independence hypothesis is testable; many authors have developed tests for left-truncated data with or without right-censoring. In this paper, we propose a class of test statistics for testing the quasi-independence which unifies the existing methods and generates new useful statistics such as conditional Spearman's rank correlation coefficient. Asympt…
Multi-state Models For Disease Histories Based On Longitudinal Data
Statistical Consulting Unit StaBLab, Department of Statistics, LMU Munich（慕尼黑大学统计咨询单元StaBLab，统计学系）；Department of Genetic Epidemiology, University of Regensburg（雷根斯堡大学生物遗传流行病学系）；Munich Center for Machine Learning, LMU Munich（慕尼黑机器学习中心，慕尼黑大学）；Faculty of Informatics and Data Science, University of Regensburg（雷根斯堡大学信息科学与数据科学学院）
