Lifetime Data Analysis最新文献

The added value of candidate predictors for risk modeling is routinely evaluated by comparing the performance of models with or without including candidate predictors. Such comparison is most meaningful when the estimated risk by the two models are both unbiased in the target population. Very often data for candidate predictors are sourced from nonrepresentative convenience samples. Updating the base model using the study data without acknowledging the discrepancy between the underlying distribution of the study data and that in the target population can lead to biased risk estimates and therefore an unfair evaluation of candidate predictors. To address this issue assuming access to a well-calibrated base model, we propose a semiparametric method for model fitting that enforces good calibration. The central idea is to calibrate the fitted model against the base model by enforcing suitable constraints in maximizing the likelihood function. This approach enables unbiased assessment of model improvement offered by candidate predictors without requiring a representative sample from the target population, thus overcoming a significant practical challenge. We study theoretical properties for model parameter estimates, and demonstrate improvement in model calibration via extensive simulation studies. Finally, we apply the proposed method to data extracted from Penn Medicine Biobank to inform the added value of breast density for breast cancer risk assessment in the Caucasian woman population.

Data analysis methods for the study of treatments or exposures in relation to a clinical outcome in the presence of competing risks have a long history, often with inference targets that are hypothetical, thereby requiring strong assumptions for identifiability with available data. Here data analysis methods are considered that are based on single and higher dimensional marginal hazard rates, quantities that are identifiable under standard independent censoring assumptions. These lead naturally to joint survival function estimators for outcomes of interest, including competing risk outcomes, and provide the basis for addressing a variety of data analysis questions. These methods will be illustrated using simulations and Women's Health Initiative cohort and clinical trial data sets, and additional research needs will be described.

Linear mixed models are traditionally used for jointly modeling (multivariate) longitudinal outcomes and event-time(s). However, when the outcomes are non-Gaussian a quantile regression model is more appropriate. In addition, in the presence of some time-varying covariates, it might be of interest to see how the effects of different covariates vary from one quantile level (of outcomes) to the other, and consequently how the event-time changes across different quantiles. For such analyses linear quantile mixed models can be used, and an efficient computational algorithm can be developed. We analyze a dataset from the Acute Lymphocytic Leukemia (ALL) maintenance study conducted by Tata Medical Center, Kolkata. In this study, the patients suffering from ALL were treated with two standard drugs (6MP and MTx) for the first two years, and three biomarkers (e.g. lymphocyte count, neutrophil count and platelet count) were longitudinally measured. After treatment the patients were followed nearly for the next three years, and the relapse-time (if any) for each patient was recorded. For this dataset we develop a Bayesian quantile joint model for the three longitudinal biomarkers and time-to-relapse. We consider an Asymmetric Laplace Distribution (ALD) for each outcome, and exploit the mixture representation of the ALD for developing a Gibbs sampler algorithm to estimate the regression coefficients. Our proposed model allows different quantile levels for different biomarkers, but still simultaneously estimates the regression coefficients corresponding to a particular quantile combination. We infer that a higher lymphocyte count accelerates the chance of a relapse while a higher neutrophil count and a higher platelet count (jointly) reduce it. Also, we infer that across (almost) all quantiles 6MP reduces the lymphocyte count, while MTx increases the neutrophil count. Simulation studies are performed to assess the effectiveness of the proposed approach.

This paper reconsiders several results of historical and current importance to nonparametric estimation of the survival distribution for failure in the presence of right-censored observation times, demonstrating in particular how Volterra integral equations help inter-connect the resulting estimators. The paper begins by considering Efron's self-consistency equation, introduced in a seminal 1967 Berkeley symposium paper. Novel insights provided in the current work include the observations that (i) the self-consistency equation leads directly to an anticipating Volterra integral equation whose solution is given by a product-limit estimator for the censoring survival function; (ii) a definition used in this argument immediately establishes the familiar product-limit estimator for the failure survival function; (iii) the usual Volterra integral equation for the product-limit estimator of the failure survival function leads to an immediate and simple proof that it can be represented as an inverse probability of censoring weighted estimator; (iv) a simple identity characterizes the relationship between natural inverse probability of censoring weighted estimators for the survival and distribution functions of failure; (v) the resulting inverse probability of censoring weighted estimators, attributed to a highly influential 1992 paper of Robins and Rotnitzky, were implicitly introduced in Efron's 1967 paper in its development of the redistribution-to-the-right algorithm. All results developed herein allow for ties between failure and/or censored observations.

Risk stratification based on prediction models has become increasingly important in preventing and managing chronic diseases. However, due to cost- and time-limitations, not every population can have resources for collecting enough detailed individual-level information on a large number of people to develop risk prediction models. A more practical approach is to use prediction models developed from existing studies and calibrate them with relevant summary-level information of the target population. Many existing studies were conducted under the population-based case-control design. Gail et al. (J Natl Cancer Inst 81:1879-1886, 1989) proposed to combine the odds ratio estimates obtained from case-control data and the disease incidence rates from the target population to obtain the baseline hazard function, and thereby the pure risk for developing diseases. However, the approach requires the risk factor distribution of cases from the case-control studies be same as the target population, which, if violated, may yield biased risk estimation. In this article, we propose two novel weighted estimating equation approaches to calibrate the baseline risk by leveraging the summary information of (some) risk factors in addition to disease-free probabilities from the targeted population. We establish the consistency and asymptotic normality of the proposed estimators. Extensive simulation studies and an application to colorectal cancer studies demonstrate the proposed estimators perform well for bias reduction in finite samples.

We consider measurement error models for two variables observed repeatedly and subject to measurement error. One variable is continuous, while the other variable is a mixture of continuous and zero measurements. This second variable has two sources of zeros. The first source is episodic zeros, wherein some of the measurements for an individual may be zero and others positive. The second source is hard zeros, i.e., some individuals will always report zero. An example is the consumption of alcohol from alcoholic beverages: some individuals consume alcoholic beverages episodically, while others never consume alcoholic beverages. However, with a small number of repeat measurements from individuals, it is not possible to determine those who are episodic zeros and those who are hard zeros. We develop a new measurement error model for this problem, and use Bayesian methods to fit it. Simulations and data analyses are used to illustrate our methods. Extensions to parametric models and survival analysis are discussed briefly.

Doubly censored failure time data occur in many areas and for the situation, the failure time of interest usually represents the elapsed time between two related events such as an infection and the resulting disease onset. Although many methods have been proposed for regression analysis of such data, most of them are conditional on the occurrence time of the initial event and ignore the relationship between the two events or the ancillary information contained in the initial event. Corresponding to this, a new sieve maximum likelihood approach is proposed that makes use of the ancillary information, and in the method, the logistic model and Cox proportional hazards model are employed to model the initial event and the failure time of interest, respectively. A simulation study is conducted and suggests that the proposed method works well in practice and is more efficient than the existing methods as expected. The approach is applied to an AIDS study that motivated this investigation.

In studies with time-to-event outcomes, multiple, inter-correlated, and time-varying covariates are commonly observed. It is of great interest to model their joint effects by allowing a flexible functional form and to delineate their relative contributions to survival risk. A class of semiparametric transformation (ST) models offers flexible specifications of the intensity function and can be a general framework to accommodate nonlinear covariate effects. In this paper, we propose a partial-linear single-index (PLSI) transformation model that reduces the dimensionality of multiple covariates into a single index and provides interpretable estimates of the covariate effects. We develop an iterative algorithm using the regression spline technique to model the nonparametric single-index function for possibly nonlinear joint effects, followed by nonparametric maximum likelihood estimation. We also propose a nonparametric testing procedure to formally examine the linearity of covariate effects. We conduct Monte Carlo simulation studies to compare the PLSI transformation model with the standard ST model and apply it to NYU Langone Health de-identified electronic health record data on COVID-19 hospitalized patients’ mortality and a Veteran’s Administration lung cancer trial.

Abstract

The case-cohort design obtains complete covariate data only on cases and on a random sample (the subcohort) of the entire cohort. Subsequent publications described the use of stratification and weight calibration to increase efficiency of estimates of Cox model log-relative hazards, and there has been some work estimating pure risk. Yet there are few examples of these options in the medical literature, and we could not find programs currently online to analyze these various options. We therefore present a unified approach and R software to facilitate such analyses. We used influence functions adapted to the various design and analysis options together with variance calculations that take the two-phase sampling into account. This work clarifies when the widely used “robust” variance estimate of Barlow (Biometrics 50:1064–1072, 1994) is appropriate. The corresponding R software, CaseCohortCoxSurvival, facilitates analysis with and without stratification and/or weight calibration, for subcohort sampling with or without replacement. We also allow for phase-two data to be missing at random for stratified designs. We provide inference not only for log-relative hazards in the Cox model, but also for cumulative baseline hazards and covariate-specific pure risks. We hope these calculations and software will promote wider use of more efficient and principled design and analysis options for case-cohort studies.