Biometrical Journal最新文献

Longitudinal data are often subject to irregular visiting times, with outcomes and visit times influenced by a latent variable. Semi-parametric joint models that account for this dependence have been proposed; among these, the Sun model is the most suitable for count data as it employs a multiplicative link function. Semi-parametric joint models define an intercept function as the mean outcome when all covariates are set to zero; this is differenced out in the course of estimation and is consequently not estimated. The Sun estimator thus provides estimates of relative covariate effects, but is unable to provide estimates of absolute effects or of longitudinal prognosis in the absence of covariates. We extend the Sun model by additionally estimating the intercept term, showing that our extended estimator is consistent and asymptotically Normal. In simulations, our estimator outperforms the original Sun estimator in terms of bias and standard error and is also more computationally efficient. We apply our estimator to a longitudinal study of tumor recurrence among bladder cancer patients. Provided the intercept term can be adequately captured using splines, we recommend that our extended Sun estimator be used in place of the original estimator, since it leads to smaller bias, smaller standard errors, and allows estimation of the mean outcome trajectories.

In longitudinal observational studies, marginal structural models (MSMs) are used to analyze the causal effect of an exposure on the (time-to-event) outcome of interest, while accounting for exposure-affected time-dependent confounding. In the applied literature, inverse probability of treatment weighting (IPTW) has been widely adopted to estimate MSMs. An essential assumption for IPTW-based MSMs is positivity, which requires that, for any combination of measured confounders among individuals, there is a nonzero probability of receiving each treatment strategy. Positivity is crucial for valid causal inference through IPTW-based MSMs, but is often overlooked compared to confounding bias. Near-positivity violations, where certain treatments are theoretically possible but rarely observed due to randomness, are common in practical applications, particularly when the sample size is small, and they pose significant challenges for causal inference. This study investigates the impact of near-positivity violations on estimates from IPTW-based MSMs in survival analysis. Two algorithms are proposed for simulating longitudinal data from hazard-MSMs, accommodating near-positivity violations, a time-varying binary exposure, and a time-to-event outcome. Cases of near-positivity violations, where remaining unexposed is rare within certain confounder levels, are analyzed across various scenarios and weight truncation (WT) strategies. Through comprehensive simulations, this study shows that even minor near-positivity violations in longitudinal survival analyses can substantially destabilize IPTW-based estimators, inflating variance and bias, especially under aggressive WT. This work aims to serve as a critical warning against overlooking the positivity assumption or naively applying WT in causal studies using longitudinal observational data and IPTW.

With the spread and rapid advancement of black box machine learning (ML) models, the field of interpretable machine learning (IML) or explainable artificial intelligence (XAI) has become increasingly important over the last decade. This is particularly relevant for survival analysis, where the adoption of IML techniques promotes transparency, accountability, and fairness in sensitive areas, such as clinical decision-making processes, the development of targeted therapies, interventions, or in other medical or healthcare-related contexts. More specifically, explainability can uncover a survival model's potential biases and limitations and provide more mathematically sound ways to understand how and which features are influential for prediction or constitute risk factors. However, the lack of readily available IML methods may have deterred practitioners from leveraging the full potential of ML for predicting time-to-event data. We present a comprehensive review of the existing work on IML methods for survival analysis within the context of the general IML taxonomy. In addition, we formally detail how commonly used IML methods, such as individual conditional expectation (ICE), partial dependence plots (PDP), accumulated local effects (ALE), different feature importance measures, or Friedman's H-interaction statistics can be adapted to survival outcomes. An application of several IML methods to data on breast cancer recurrence in the German Breast Cancer Study Group (GBSG2) serves as a tutorial or guide for researchers, on how to utilize the techniques in practice to facilitate understanding of model decisions or predictions.

Canonical correlation analysis (CCA) is a widely used multivariate method in omics research for integrating high-dimensional datasets. CCA identifies hidden links by deriving linear projections of observed features that maximally correlate datasets. An important requirement of standard CCA is that observations are independent of each other. As a result, it cannot properly deal with repeated measurements. Current CCA extensions dealing with these challenges either perform CCA on summarized data or estimate correlations for each measurement. While these techniques factor in the correlation between measurements, they are suboptimal for high-dimensional analysis and exploiting this data's longitudinal qualities. We propose a novel extension of sparse CCA that incorporates time dynamics at the latent variable level through longitudinal models. This approach addresses the correlation of repeated measurements while drawing latent paths, focusing on dynamics in the correlation structures. To aid interpretability and computational efficiency, we implement an $�{\ell }_0$ penalty to enforce fixed sparsity levels. We estimate these trajectories fitting longitudinal models to the low-dimensional latent variables, leveraging the clustered structure of high-dimensional datasets, thus exploring shared longitudinal latent mechanisms. Furthermore, modeling time in the latent space significantly reduces computational burden. We validate our model's performance using simulated data and show its real-world applicability with data from the Human Microbiome Project. This application highlights the model's ability to handle high-dimensional, sparsely, and irregularly observed data. Our CCA method for repeated measurements enables efficient estimation of canonical correlations across measurements for clustered data. Compared to existing methods, ours substantially reduces computational time in high-dimensional analyses as well as provides longitudinal trajectories that yield interpretable and insightful results.

Pseudo-observations are used to estimate the expectation of a function of interest in a population when survival data are incomplete due to censoring or truncation. Length-biased sampling is a special case of a left-truncation model, in which the truncation variable follows a uniform distribution. This phenomenon is commonly encountered in various fields such as survival analysis and epidemiology, where the event of interest is related to the length or duration of an underlying process. In such settings, the probability of observing a data point is higher for longer lengths, leading to biased sampling. The goal of this paper is to apply pseudo-observations to estimate the regression coefficients in the Cox proportional hazards model under length-biased right-censored (LBRC) data. We assess the accuracy and efficiency of two approaches that differ in their generation of pseudo-observations, comparing them with two prominent standard methods in the presence of LBRC data. The results demonstrate that the two proposed pseudo-observation methods are comparable to the standard methods in terms of standard error, with advantages in providing confidence intervals that are closer to the nominal level in large sample sizes and specific scenarios. Additionally, although length-biased data are a special case of left-truncated data, they must be addressed separately by utilizing the information that the left-truncation variable follows a uniform distribution, as the simulation results show. We also establish the consistency and asymptotic normality of one of the proposed estimators. Finally, we applied the method to analyze a real dataset from LBRC.

Often probabilities of nonstandard time-to-event endpoints are of interest, which are more complex than overall survival. One such probability is chronic graft-versus-host disease (GvHD-) and relapse-free survival, the probability of being alive, in remission, and not suffering from chronic GvHD after stem cell transplantation, with chronic GvHD being a recurrent event. Because the probabilities for endpoints with recurrent events may not fall monotonically, one should not use the Kaplan–Meier estimator for estimation, but the Aalen–Johansen estimator. The Aalen–Johansen is a consistent estimator even in non-Markov scenarios if state occupation probabilities are being estimated and censoring is random. In some multistate models, it is also possible to use linear combinations of Kaplan–Meier estimators, which do not depend on the Markov assumption but can estimate probabilities to be out of bounds. For these linear combinations, we propose a wild bootstrap procedure for inference and compare it with the wild bootstrap for the Aalen–Johansen estimator in non-Markov scenarios. In the proposed procedure, the limiting distribution of the Nelson–Aalen estimator is approximated using the wild bootstrap and transformed via the functional delta method. This approach is adaptable to different multistate models. Using real data, confidence bands are generated using the wild bootstrap for chronic GvHD- and relapse-free survival. Additionally, coverage probabilities of confidence intervals and confidence bands generated by Efron's bootstrap and the wild bootstrap are examined with simulations.

In multi-state models based on high-dimensional data, effective modeling strategies are required to determine an optimal, ideally parsimonious model. In particular, linking covariate effects across transitions is needed to conduct joint variable selection. A useful technique to reduce model complexity is to address homogeneous covariate effects for distinct transitions. We integrate this approach to data-driven variable selection by extended regularization methods within multi-state model building. We propose the fused sparse-group lasso (FSGL) penalized Cox-type regression in the framework of multi-state models combining the penalization concepts of pairwise differences of covariate effects along with transition-wise grouping. For optimization, we adapt the alternating direction method of multipliers (ADMM) algorithm to transition-specific hazards regression in the multi-state setting. In a simulation study and application to acute myeloid leukemia (AML) data, we evaluate the algorithm's ability to select a sparse model incorporating relevant transition-specific effects and similar cross-transition effects. We investigate settings in which the combined penalty is beneficial compared to global lasso regularization.

Clinical Trial Registration: The AMLSG 09-09 trial is registered with ClinicalTrials.gov (NCT00893399) and has been completed.