arXiv subjects

Halina Frydman

Publications and source records attributed to Halina Frydman.

4 recordsLinked to original sources

arXiv2021

Dynamic estimation with random forests for discrete-time survival data

Time-varying covariates are often available in survival studies and estimation of the hazard function needs to be updated as new information becomes available. In this paper, we investigate several different easy-to-implement ways that random forests can be used for dynamic estimation of the survival or hazard function from discrete-time survival data. The results from a simulation study indicate that all methods can perform well, and that none dominates the others. In general, situations that are more difficult from an estimation point of view (such as weaker signals and less data) favour a global fit, pooling over all time points, while situations that are easier from an estimation point of view (such as stronger signals and more data) favor local fits.

stat.ME↗

arXiv2021

Statistical inference for a mixture of Markov jump processes

We estimate a general mixture of Markov jump processes. The key novel feature of the proposed mixture is that the transition intensity matrices of the Markov processes comprising the mixture are entirely unconstrained. The Markov processes are mixed with distributions that depend on the initial state of the mixture process. The new mixture is estimated from its continuously observed realizations using the EM algorithm, which provides the maximum likelihood (ML) estimates of the mixture's parameters. We derive the asymptotic properties of the ML estimators. To obtain estimated standard errors of the ML estimates of the mixture's parameters, an explicit form of the observed Fisher information matrix is derived. In its new form, the information matrix simplifies the conditional expectation of outer product of the complete-data score function in the Louis (1982) general matrix formula for the observed Fisher information matrix. Simulation study verifies the estimates' accuracy and confirms the consistency and asymptotic normality of the estimators. The developed methods are applied to a medical dataset, for which the likelihood ratio test rejects the constrained mixture in favor of the proposed unconstrained one. This application exemplifies the usefulness of a new unconstrained mixture for identification and characterization of homogeneous subpopulations in a heterogeneous population.

stat.ME↗

arXiv2020

Ensemble methods for survival function estimation with time-varying covariates

Survival data with time-varying covariates are common in practice. If relevant, they can improve on the estimation of survival function. However, the traditional survival forests - conditional inference forest, relative risk forest and random survival forest - have accommodated only time-invariant covariates. We generalize the conditional inference and relative risk forests to allow time-varying covariates. We also propose a general framework for estimation of a survival function in the presence of time-varying covariates. We compare their performance with that of the Cox model and transformation forest, adapted here to accommodate time-varying covariates, through a comprehensive simulation study in which the Kaplan-Meier estimate serves as a benchmark, and performance is compared using the integrated L2 difference between the true and estimated survival functions. In general, the performance of the two proposed forests substantially improves over the Kaplan-Meier estimate. Taking into account all other factors, under the proportional hazard (PH) setting, the best method is always one of the two proposed forests, while under the non-PH setting, it is the adapted transformation forest. K-fold cross-validation is used as an effective tool to choose between the methods in practice.

stat.AP↗

arXiv2019

An Ensemble Method for Interval-Censored Time-to-Event Data

Interval-censored data analysis is important in biomedical statistics for any type of time-to-event response where the time of response is not known exactly, but rather only known to occur between two assessment times. Many clinical trials and longitudinal studies generate interval-censored data; one common example occurs in medical studies that entail periodic follow-up. In this paper we propose a survival forest method for interval-censored data based on the conditional inference framework. We describe how this framework can be adapted to the situation of interval-censored data. We show that the tuning parameters have a non-negligible effect on the survival forest performance and guidance is provided on how to tune the parameters in a data-dependent way to improve the overall performance of the method. Using Monte Carlo simulations we find that the proposed survival forest is at least as effective as a survival tree method when the underlying model has a tree structure, performs similarly to an interval-censored Cox proportional hazards model fit when the true relationship is linear, and outperforms the survival tree method and Cox model when the true relationship is nonlinear. We illustrate the application of the method on a tooth emergence data set.

stat.ME↗