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- Copula-based analysis of dependent current status data with semiparametric
linear transformation model-
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Abstract: Abstract This paper discusses regression analysis of current status data with dependent censoring, a problem that often occurs in many areas such as cross-sectional studies, epidemiological investigations and tumorigenicity experiments. Copula model-based methods are commonly employed to tackle this issue. However, these methods often face challenges in terms of model and parameter identification. The primary aim of this paper is to propose a copula-based analysis for dependent current status data, where the association parameter is left unspecified. Our method is based on a general class of semiparametric linear transformation models and parametric copulas. We demonstrate that the proposed semiparametric model is identifiable under certain regularity conditions from the distribution of the observed data. For inference, we develop a sieve maximum likelihood estimation method, using Bernstein polynomials to approximate the nonparametric functions involved. The asymptotic consistency and normality of the proposed estimators are established. Finally, to demonstrate the effectiveness and practical applicability of our method, we conduct an extensive simulation study and apply the proposed method to a real data example.
PubDate: 2024-08-24
- Special issue dedicated to Mitchell H. Gail, M.D. Ph.D.
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PubDate: 2024-06-24
- A flexible time-varying coefficient rate model for panel count data
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Abstract: Abstract Panel count regression is often required in recurrent event studies, where the interest is to model the event rate. Existing rate models are unable to handle time-varying covariate effects due to theoretical and computational difficulties. Mean models provide a viable alternative but are subject to the constraints of the monotonicity assumption, which tends to be violated when covariates fluctuate over time. In this paper, we present a new semiparametric rate model for panel count data along with related theoretical results. For model fitting, we present an efficient EM algorithm with three different methods for variance estimation. The algorithm allows us to sidestep the challenges of numerical integration and difficulties with the iterative convex minorant algorithm. We showed that the estimators are consistent and asymptotically normally distributed. Simulation studies confirmed an excellent finite sample performance. To illustrate, we analyzed data from a real clinical study of behavioral risk factors for sexually transmitted infections.
PubDate: 2024-05-28
DOI: 10.1007/s10985-024-09630-1
- Risk projection for time-to-event outcome from population-based
case–control studies leveraging summary statistics from the target
population-
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Abstract: Abstract 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.
PubDate: 2024-05-28
DOI: 10.1007/s10985-024-09626-x
- Measurement error models with zero inflation and multiple sources of
zeros, with applications to hard zeros-
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Abstract: Abstract 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.
PubDate: 2024-05-28
DOI: 10.1007/s10985-024-09627-w
- A constrained maximum likelihood approach to developing well-calibrated
models for predicting binary outcomes-
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Abstract: Abstract 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.
PubDate: 2024-05-08
DOI: 10.1007/s10985-024-09628-9
- Competing risks and multivariate outcomes in epidemiological and clinical
trial research-
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Abstract: Abstract 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.
PubDate: 2024-05-06
DOI: 10.1007/s10985-024-09629-8
- Regression analysis of doubly censored failure time data with ancillary
information-
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Abstract: Abstract 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.
PubDate: 2024-04-20
DOI: 10.1007/s10985-024-09625-y
- Partial-linear single-index transformation models with censored data
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Abstract: Abstract 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.
PubDate: 2024-04-16
DOI: 10.1007/s10985-024-09624-z
- Cox model inference for relative hazard and pure risk from stratified
weight-calibrated case-cohort data-
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Abstract: 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.
PubDate: 2024-04-02
DOI: 10.1007/s10985-024-09621-2
- On the role of Volterra integral equations in self-consistent,
product-limit, inverse probability of censoring weighted, and
redistribution-to-the-right estimators for the survival function-
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Abstract: Abstract 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.
PubDate: 2024-03-21
DOI: 10.1007/s10985-024-09623-0
- Bias of the additive hazard model in the presence of causal effect
heterogeneity-
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Abstract: Abstract Hazard ratios are prone to selection bias, compromising their use as causal estimands. On the other hand, if Aalen’s additive hazard model applies, the hazard difference has been shown to remain unaffected by the selection of frailty factors over time. Then, in the absence of confounding, observed hazard differences are equal in expectation to the causal hazard differences. However, in the presence of effect (on the hazard) heterogeneity, the observed hazard difference is also affected by selection of survivors. In this work, we formalize how the observed hazard difference (from a randomized controlled trial) evolves by selecting favourable levels of effect modifiers in the exposed group and thus deviates from the causal effect of interest. Such selection may result in a non-linear integrated hazard difference curve even when the individual causal effects are time-invariant. Therefore, a homogeneous time-varying causal additive effect on the hazard cannot be distinguished from a time-invariant but heterogeneous causal effect. We illustrate this causal issue by studying the effect of chemotherapy on the survival time of patients suffering from carcinoma of the oropharynx using data from a clinical trial. The hazard difference can thus not be used as an appropriate measure of the causal effect without making untestable assumptions.
PubDate: 2024-03-11
DOI: 10.1007/s10985-024-09616-z
- On variable selection in a semiparametric AFT mixture cure model
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Abstract: Abstract In clinical studies, one often encounters time-to-event data that are subject to right censoring and for which a fraction of the patients under study never experience the event of interest. Such data can be modeled using cure models in survival analysis. In the presence of cure fraction, the mixture cure model is popular, since it allows to model probability to be cured (called the incidence) and the survival function of the uncured individuals (called the latency). In this paper, we develop a variable selection procedure for the incidence and latency parts of a mixture cure model, consisting of a logistic model for the incidence and a semiparametric accelerated failure time model for the latency. We use a penalized likelihood approach, based on adaptive LASSO penalties for each part of the model, and we consider two algorithms for optimizing the criterion function. Extensive simulations are carried out to assess the accuracy of the proposed selection procedure. Finally, we employ the proposed method to a real dataset regarding heart failure patients with left ventricular systolic dysfunction.
PubDate: 2024-03-04
DOI: 10.1007/s10985-024-09619-w
- A Bayesian quantile joint modeling of multivariate longitudinal and
time-to-event data-
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Abstract: Abstract 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.
PubDate: 2024-03-01
DOI: 10.1007/s10985-024-09622-1
- Pseudo-value regression trees
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Abstract: Abstract This paper presents a semi-parametric modeling technique for estimating the survival function from a set of right-censored time-to-event data. Our method, named pseudo-value regression trees (PRT), is based on the pseudo-value regression framework, modeling individual-specific survival probabilities by computing pseudo-values and relating them to a set of covariates. The standard approach to pseudo-value regression is to fit a main-effects model using generalized estimating equations (GEE). PRT extend this approach by building a multivariate regression tree with pseudo-value outcome and by successively fitting a set of regularized additive models to the data in the nodes of the tree. Due to the combination of tree learning and additive modeling, PRT are able to perform variable selection and to identify relevant interactions between the covariates, thereby addressing several limitations of the standard GEE approach. In addition, PRT include time-dependent effects in the node-wise models. Interpretability of the PRT fits is ensured by controlling the tree depth. Based on the results of two simulation studies, we investigate the properties of the PRT method and compare it to several alternative modeling techniques. Furthermore, we illustrate PRT by analyzing survival in 3,652 patients enrolled for a randomized study on primary invasive breast cancer.
PubDate: 2024-02-25
DOI: 10.1007/s10985-024-09618-x
- The built-in selection bias of hazard ratios formalized using structural
causal models-
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Abstract: Abstract It is known that the hazard ratio lacks a useful causal interpretation. Even for data from a randomized controlled trial, the hazard ratio suffers from so-called built-in selection bias as, over time, the individuals at risk among the exposed and unexposed are no longer exchangeable. In this paper, we formalize how the expectation of the observed hazard ratio evolves and deviates from the causal effect of interest in the presence of heterogeneity of the hazard rate of unexposed individuals (frailty) and heterogeneity in effect (individual modification). For the case of effect heterogeneity, we define the causal hazard ratio. We show that the expected observed hazard ratio equals the ratio of expectations of the latent variables (frailty and modifier) conditionally on survival in the world with and without exposure, respectively. Examples with gamma, inverse Gaussian and compound Poisson distributed frailty and categorical (harming, beneficial or neutral) distributed effect modifiers are presented for illustration. This set of examples shows that an observed hazard ratio with a particular value can arise for all values of the causal hazard ratio. Therefore, the hazard ratio cannot be used as a measure of the causal effect without making untestable assumptions, stressing the importance of using more appropriate estimands, such as contrasts of the survival probabilities.
PubDate: 2024-02-15
DOI: 10.1007/s10985-024-09617-y
- Quantile difference estimation with censoring indicators missing at random
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Abstract: Abstract In this paper, we define estimators of distribution functions when the data are right-censored and the censoring indicators are missing at random, and establish their strong representations and asymptotic normality. Besides, based on empirical likelihood method, we define maximum empirical likelihood estimators and smoothed log-empirical likelihood ratios of two-sample quantile difference in the presence and absence of auxiliary information, respectively, and prove their asymptotic distributions. Simulation study and real data analysis are conducted to investigate the finite sample behavior of the proposed methods.
PubDate: 2024-01-18
DOI: 10.1007/s10985-023-09614-7
- A Bayesian proportional hazards mixture cure model for interval-censored
data-
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Abstract: Abstract The proportional hazards mixture cure model is a popular analysis method for survival data where a subgroup of patients are cured. When the data are interval-censored, the estimation of this model is challenging due to its complex data structure. In this article, we propose a computationally efficient semiparametric Bayesian approach, facilitated by spline approximation and Poisson data augmentation, for model estimation and inference with interval-censored data and a cure rate. The spline approximation and Poisson data augmentation greatly simplify the MCMC algorithm and enhance the convergence of the MCMC chains. The empirical properties of the proposed method are examined through extensive simulation studies and also compared with the R package “GORCure”. The use of the proposed method is illustrated through analyzing a data set from the Aerobics Center Longitudinal Study.
PubDate: 2023-11-28
DOI: 10.1007/s10985-023-09613-8
- Efficiency of the Breslow estimator in semiparametric transformation
models-
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Abstract: Abstract Semiparametric transformation models for failure time data consist of a parametric regression component and an unspecified cumulative baseline hazard. The nonparametric maximum likelihood estimator (NPMLE) of the cumulative baseline hazard can be summarized in terms of weights introduced into a Breslow-type estimator (Weighted Breslow). At any given time point, the weights invoke an integral over the future of the cumulative baseline hazard, which presents theoretical and computational challenges. A simpler non-MLE Breslow-type estimator (Breslow) was derived earlier from a martingale estimating equation (MEE) setting observed and expected counts of failures equal, conditional on the past history. Despite much successful theoretical and computational development, the simpler Breslow estimator continues to be commonly used as a compromise between simplicity and perceived loss of full efficiency. In this paper we derive the relative efficiency of the Breslow estimator and consider the properties of the two estimators using simulations and real data on prostate cancer survival.
PubDate: 2023-11-26
DOI: 10.1007/s10985-023-09611-w
- Bias reduction for semi-competing risks frailty model with rare events:
application to a chronic kidney disease cohort study in South Korea-
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Abstract: Abstract In a semi-competing risks model in which a terminal event censors a non-terminal event but not vice versa, the conventional method can predict clinical outcomes by maximizing likelihood estimation. However, this method can produce unreliable or biased estimators when the number of events in the datasets is small. Specifically, parameter estimates may converge to infinity, or their standard errors can be very large. Moreover, terminal and non-terminal event times may be correlated, which can account for the frailty term. Here, we adapt the penalized likelihood with Firth’s correction method for gamma frailty models with semi-competing risks data to reduce the bias caused by rare events. The proposed method is evaluated in terms of relative bias, mean squared error, standard error, and standard deviation compared to the conventional methods through simulation studies. The results of the proposed method are stable and robust even when data contain only a few events with the misspecification of the baseline hazard function. We also illustrate a real example with a multi-centre, patient-based cohort study to identify risk factors for chronic kidney disease progression or adverse clinical outcomes. This study will provide a better understanding of semi-competing risk data in which the number of specific diseases or events of interest is rare.
PubDate: 2023-11-13
DOI: 10.1007/s10985-023-09612-9
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