Event Time Data Research Articles

Relationship between prostate-specific antigen, alkaline phosphatase levels, and time-to-tumor shrinkage: understanding the progression of prostate cancer in a longitudinal study

BackgroundThis study delves into the complex interplay among prostate-specific antigen, alkaline phosphatase, and the temporal dynamics of tumor shrinkage in prostate cancer. By investigating the longitudinal trajectories and time-to-prostate cancer tumor shrinkage, we aim to untangle the intricate patterns of these biomarkers. This understanding is pivotal for gaining profound insights into the multifaceted aspects of prostate cancer progression. The joint model approach serves as a comprehensive framework, facilitating the elucidation of intricate interactions among these pivotal elements within the context of prostate cancer .MethodsA new joint model under a shared parameters strategy is proposed for mixed bivariate longitudinal biomarkers and event time data, for obtaining accurate estimates in the presence of missing covariate data. The primary innovation of our model resides in its effective management of covariates with missing observations. Built upon established frameworks, our joint model extends its capabilities by integrating mixed longitudinal responses and accounting for missingness in covariates, thus confronting this particular challenge. We posit that these enhancements bolster the model’s utility and dependability in real-world contexts characterized by prevalent missing data. The main objective of this research is to provide a model-based approach to get full information from prostate cancer data collected with patients’ baseline characteristics (Age\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Age$$\\end{document}, body mass index (BMI\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$BMI$$\\end{document}), GleasonScore\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Gleason Score$$\\end{document}, Grade\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Grade$$\\end{document}, and Drug\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Drug$$\\end{document}) and two longitudinal endogenous covariates (Platelets\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Platelets$$\\end{document} and Bilirubin\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Bilirubin$$\\end{document}).ResultsThe results reveal a clear association between prostate-specific antigen and alkaline phosphatase biomarkers in the context of time-to-prostate cancer tumor shrinkage. This underscores the interconnected dynamics of these key indicators in gauging disease progression.ConclusionsThe analysis of the prostate cancer dataset, incorporating a joint evaluation of mixed longitudinal prostate-specific antigen and alkaline phosphatase biomarkers alongside tumor status, has provided valuable insights into disease progression. The results demonstrate the effectiveness of the proposed joint model, as evidenced by accurate estimates. The shared variables associated with both longitudinal biomarkers and event times consistently deviate from zero, highlighting the robustness and reliability of the model in capturing the complex dynamics of prostate cancer progression. This approach holds promise for enhancing our understanding and predictive capabilities in the clinical assessment of prostate cancer.

Annual survival rates of satellite-tracked adult European honey buzzards (Pernis apivorus) based on the Kaplan-Meier estimator and its probabilistic extension

Abstract The annual survival rate of adult raptors is an important parameter in population dynamics and is needed to derive measures for population stability and conservation management. Here we studied adult European honey buzzards (Pernis apivorus), a migratory land bird, using satellite telemetry throughout the year for up to three years. We used the Kaplan-Meier method of survival estimation in combination with the distribution density function for survival. This function describes the number of survivors N as a function of time t, based on the survival rate SR. This probabilistic extension of the Kaplan-Meier estimator results in a simple method that does not require a commercial statistical program to extract survival rates from event time analysis. It can be applied to analysing any event-time data, not only telemetry results but also ring recoveries, as demonstrated using European honey buzzards as an example. The average adult survival rate in our study, based on permanent satellite telemetry monitoring, was 0.44/year (linear correlation factor f = 0.99). This implies an adult mortality rate of 0.56 per year. It seems that particularly unfavourable weather conditions during the crossing of the Sahara and the Mediterranean led to this high mortality rate of our birds during migration from 2001 to 2011, but is likely to vary greatly from year to year. However, the loss rate in the wintering area was also high, at one third of the birds. More honey buzzards need to be tracked throughout the year to assess factors affecting survival and threats to populations adequately.

Estimation of trajectory of protective efficacy in infectious disease prevention trials using recurrent event times.

In studies of infectious disease prevention, the level of protective efficacy of medicinal products such as vaccines and prophylactic drugs tends to vary over time. Many products require administration of multiple doses at scheduled times, as opposed to one-off or continual intervention. Accurate information on the trajectory of the level of protective efficacy over time facilitates informed clinical recommendations and implementation strategies, for example, with respect to the timing of administration of the doses. Based on concepts from pharmacokinetic and pharmacodynamic modeling, we propose a non-linear function for modeling the trajectory after each dose. The cumulative effect of multiple doses of the products is captured by an additive series of the function. The model has the advantages of parsimony and interpretability, while remaining flexible in capturing features of the trajectories. We incorporate this series into the Andersen-Gill model for analysis of recurrent event time data and compare it with alternative parametric and non-parametric functions. We use data on clinical malaria disease episodes from a trial of four doses of an anti-malarial drug combination for chemoprevention to illustrate, and evaluate the performance of the methods using simulation. The proposed method out-performed the alternatives in the analysis of real data in terms of Akaike and Bayesian Information Criterion. It also accurately captured the features of the protective efficacy trajectory such as the area under curve in simulations. The proposed method has strong potential to enhance the evaluation of disease prevention measures and improve their implementation strategies.

Comprehensive modelling of prostate cancer progression: integrating continuous and binary biomarkers with event time data and missing covariates

Longitudinal studies involve recording observations at scheduled visits or time points for individuals until a predetermined event, like reaching satisfactory tumor shrinkage in cancer studies. Furthermore, dropout in longitudinal studies leads to incomplete data, which significantly increases the risk of bias. An amended joint shared-random effects model (SREM) is proposed for mixed continuous and binary longitudinal measurements and a time-to-event (TTE) outcome, incorporating missing covariates. In the proposed model, a conditional model is applied for the mixed continuous and binary longitudinal outcomes; a mixed effect model is considered for the continuous longitudinal outcome. For the binary longitudinal outcome, given the continuous longitudinal outcome, a logistic mixed effect model is considered. These models share common random effects with the model for the event time outcome. The model formulation is based on Bayesian statistical thinking via Markov Chain Monte Carlo (MCMC). The proposed joint modelling is applied to contribute to the understanding of the progression of prostate cancer (PCa) by considering a generalized linear mixed effects model for time-varying covariates that incorporate ignorable missingness. The association between prostate-specific antigen (PSA) with alkaline phosphatase (ALP) and tumor status has been studied with mixed conclusions.

Modeling and maximum likelihood based inference ofinterval-censored data with unknown upper limits andtime-dependent covariates.

Due to the nature of study design or other reasons, the upper limits of the interval-censored data with multiple visits are unknown. A naïve approach is to treat the last observed time as the exact event time, which may induce biased estimators of the model parameters. In this paper, we first develop a Cox model with time-dependent covariates for the event time and a proportional hazards model with frailty for the gap time. We then construct the upper limits using the latent gap times to resolve the issue of interval-censored event time data with unknown upper limits. A data-augmentation technique and a Monte Carlo EM (MCEM) algorithm are developed to facilitate computation. Theoretical properties of the computational algorithm are also investigated. Additionally, new model comparison criteria are developed to assess the fit of the gap time data as well as the fit of the event time data conditional on the gap time data. Our proposed method compares favorably with competing methods in both simulation study and real data analysis.

MODEL REGRESSION COX PROPORTIONAL HAZARD WITH BAYESIAN METHOD FOR SURVIVAL ANALYSIS OF COVID-19 PATIENT CASES AT RSUD Dr. PIRNGADI KOTA MEDAN

<p>Survival analysis is a statistical procedure for analyzing data by observing the response variable in the form of event time data from the beginning of recording to the end of the event. Survival analysis is used in many fields of medicine. The cox proportional hazard model aims to look at the factors of the recovery rate on patient survival. In this study using Bayesian data with Lognormal distribution in Covid-19 patients at Dr. Pirngadi, Medan City. The predictor variables are Age, gender, employment status, and other diagnose. Based on the research, the cox proportional hazard model was obtained with the influential variables based on the credible interval it is known that the age and genderare significant variables. Among the two variables that have the most influence is the age because it obtains a larger coefficient, namely</p>

Inference in the presence of likelihood monotonicity for proportional hazards regression

Proportional hazards are often used to model event time data subject to censoring. Samples involving discrete covariates with strong effects can lead to infinite maximum partial likelihood estimates. A methodology is presented for eliminating nuisance parameters estimated at infinity using approximate conditional inference. Of primary interest is testing in cases in which the parameter of primary interest has a finite estimate, but in which other parameters are estimated at infinity.

A semiparametric joint model for cluster size and subunit-specific interval-censored outcomes.

Clustered data frequently arise in biomedical studies, where observations, or subunits, measured within a cluster are associated. The cluster size is said to be informative, if the outcome variable is associated with the number of subunits in a cluster. In most existing work, the informative cluster size issue is handled by marginal approaches based on within-cluster resampling, or cluster-weighted generalized estimating equations. Although these approaches yield consistent estimation of the marginal models, they do not allow estimation of within-cluster associations and are generally inefficient. In this paper, we propose a semiparametric joint model for clustered interval-censored event time data with informative cluster size. We use a random effect to account for the association among event times of the same cluster as well as the association between event times and the cluster size. For estimation, we propose a sieve maximum likelihood approach and devise a computationally-efficient expectation-maximization algorithm for implementation. The estimators are shown to be strongly consistent, with the Euclidean components being asymptotically normal and achieving semiparametric efficiency. Extensive simulation studies are conducted to evaluate the finite-sample performance, efficiency and robustness of the proposed method. We also illustrate our method via application to a motivating periodontal diseasedataset.

Goodness-of-fit test for a parametric mixture cure model with partly interval-censored data.

Partly interval-censored event time data arise naturally in medical, biological, sociological and demographic studies. In practice, some patients may be immune from the event of interest, invoking a cure model for survival analysis. Choosing an appropriate parametric distribution for the failure time of susceptible patients is an important step to fully structure the mixture cure model. In the literature, goodness-of-fit tests for survival models are usually restricted to uncensored or right-censored data. We fill in this gap by proposing a new goodness-of-fit test dealing with partly interval-censored data under mixture cure models. Specifically, we investigate whether a parametric distribution can fit the susceptible part by using a Cramér-von Mises type of test, and establish the asymptotic distribution of the test . Empirically, the critical value is determined from the bootstrap resamples. The proposed test, compared to the traditional leveraged bootstrap approach, yields superior practical results under various settings in extensive simulation studies. Two clinical data sets are analyzed to illustrate our method.

Analysis and asymptotic theory for nested case-control designs under highly stratified proportional hazards models.

Nested case-control sampled event time data under a highly stratified proportional hazards model, in which the number of strata increases proportional to sample size, is described and analyzed. The data can be characterized as stratified sampling from the event time risk sets and the analysis approach of Borgan et al.(Ann Stat 23:1749-1778, 1995) is adapted to accommodate both the stratification and case-control sampling from the stratified risk sets. Conditions for the consistency and asymptotic normality of the maximum partial likelihood estimator are provided and the results are used to compare the efficiency of the stratified analysis to an unstratified analysis when the baseline hazards can be semi-parametrically modeled in two special cases. Using the stratified sampling representation of the stratified analysis, methods for absolute risk estimation described by Borgan et al.(1995) for nested case-control data are used to develop methods for absolute risk estimation under the stratified model. The methods are illustrated by a year of birth stratified analysis of radon exposure and lung cancer mortality in a cohort of uranium miners from the Colorado Plateau.

Analyzing recurrent and nonrecurrent terminal events data in discrete time.

Joint analysis of recurrent and nonrecurrent terminal events has attracted substantial attention in literature. However, there lacks formal methodology for such analysis when the event time data are on discrete scales, even though some modeling and inference strategies have been developed for discrete-time survival analysis. We propose a discrete-time joint modeling approach for the analysis of recurrent and terminal events where the two types of events may be correlated with each other. The proposed joint modeling assumes a shared frailty to account for the dependence among recurrent events and between the recurrent and the terminal terminal events. Also, the joint modeling allows for time-dependent covariates and rich families of transformation models for the recurrent and terminal events. A major advantage of our approach is that it does not assume a distribution for the frailty, nor does it assume a Poisson process for the analysis of the recurrent event. The utility of the proposed analysis is illustrated by simulation studies and two real applications, where the application to the biochemists' rank promotion data jointly analyzes the biochemists' citation numbers and times to rank promotion, and the application to the scleroderma lung study data jointly analyzes the adverse events and off-drug time among patients with the symptomatic scleroderma-related interstitial lungdisease.

Joint modeling of generalized scale-change models for recurrent event and failure time data.

Recurrent event and failure time data arise frequently in many clinical and observational studies. In this article, we propose a joint modeling of generalized scale-change models for the recurrent event process and the failure time, and allow the two processes to be correlated through a shared frailty. The proposed joint model is flexible in that it requires neither the Poisson assumption for the recurrent event process nor a parametric assumption on the frailty distribution. Estimating equation approaches are developed for parameter estimation, and the asymptotic properties of the resulting estimators are established. Simulation studies are conducted to evaluate the finite sample performances of the proposed method. An application to a medical cost study of chronic heart failure patients is provided.

Combining seroprevalence and capture-mark-recapture data to estimate the force of infection of brucellosis in a managed population of Alpine ibex

In wildlife, epidemiological data are often collected using cross-sectional surveys and antibody tests, and seroprevalence is the most common measure used to monitor the transmission dynamics of infectious diseases. On the contrary, the force of infection, a measure of transmission intensity that can help understand epidemiological dynamics and monitor management interventions, remains rarely used. The force of infection can be derived from age-stratified cross-sectional serological data, or from longitudinal data (although less frequently available in wildlife populations). Here, we combined seroprevalence and capture-mark-recapture data to estimate the force of infection of brucellosis in an Alpine ibex (Capra ibex) population monitored from 2012 to 2018. Because the seroprevalence of brucellosis was 38% in this population in 2012, managers conducted two culling operations in 2013 and 2015, as well as captures every year since 2012, where seronegative individuals were marked and released, and seropositive individuals were removed. We obtained two estimates of the force of infection and its changes across time, by fitting (i) a catalytic model to age-seroprevalence data obtained from unmarked animals (cross-sectional), and (ii) a survival model to event time data obtained from recaptures of marked animals (longitudinal). Using both types of data allowed us to make robust inference about the temporal dynamics of the force of infection: indeed, there was evidence for a decrease in the force of infection between mid-2014 and late 2015 in both datasets. The force of infection was estimated to be reduced from 0.115 year-1 [0.074–0.160] to 0.016 year-1 [0.001–0.057]. These results confirm that transmission intensity decreased during the study period, probably due to management interventions and natural changes in infection dynamics. Estimating the force of infection could therefore be a valuable complement to classical seroprevalence analyses to monitor the dynamics of wildlife diseases, especially in the context of ongoing disease management interventions.

Multistate analysis of multitype recurrent event and failure time data with event feedbacks in biomarkers

AbstractIn this paper we propose a class of multistate models for the analysis of multitype recurrent event and failure time data when there are past event feedbacks in longitudinal biomarkers. It can well incorporate various effects, including time‐dependent and time‐independent effects, of different event paths or the number of occurrences of events of different types. Asymptotic unbiased estimating equations based on polynomial splines approximation are developed. The consistency and asymptotic normality of the proposed estimators are provided. Simulation studies show that the naive estimators which either ignore the past event feedback or the measurement errors are biased. Our method has a better coverage probability of the time‐varying/constant coefficients, compared to the naive methods. An application to the dataset from the Atherosclerosis Risk in Communities Study, which is also the motivating example to develop the method, is presented.

Factor copula models for right-censored clustered survival data.

In this article we extend the factor copula model to deal with right-censored event time data grouped in clusters. The new methodology allows for clusters to have variable sizes ranging from small to large and intracluster dependence to be flexibly modeled by any parametric family of bivariate copulas, thus encompassing a wide range of dependence structures. Incorporation of covariates (possibly time dependent) in the margins is also supported. Three estimation procedures are proposed: both one- and two-stage parametric and a two-stage semiparametric method where marginal survival functions are estimated by using a Cox proportional hazards model. We prove that the estimators are consistent and asymptotically normally distributed, and assess their finite sample behavior with simulation studies. Furthermore, we illustrate the proposed methods on a data set containing the time to first insemination after calving in dairy cattle clustered in herds of different sizes.

Joint model for survival and multivariate sparse functional data with application to a study of Alzheimer's Disease.

Studies of Alzheimer's disease (AD) often collect multiple longitudinal clinical outcomes, which are correlated and predictive of AD progression. It is of great scientific interest to investigate the association between the outcomes and time to AD onset. We model the multiple longitudinal outcomes as multivariate sparse functional data and propose a functional joint model linking multivariate functional data to event time data. In particular, we propose a multivariate functional mixed model to identify the shared progression pattern and outcome-specific progression patterns of the outcomes, which enables more interpretable modeling of associations between outcomes and AD onset. The proposed method is applied to the Alzheimer's Disease Neuroimaging Initiative study (ADNI) and the functional joint model sheds new light on inference of five longitudinal outcomes and their associations with AD onset. Simulation studies also confirm the validity of the proposed model. Data used in preparation of this article were obtained from the ADNIdatabase.

Maximum approximate Bernstein likelihood estimation in proportional hazard model for interval-censored data.

Maximum approximate Bernstein likelihood estimates of the baseline density function and the regression coefficients in the proportional hazard regression models based on interval-censored event time data result in smooth estimates of the survival functions which enjoys an almost n1/2 -rate of convergence faster than the n1/3 -rate for the existing estimates. The proposed method was shown by a simulation to have better finite sample performance than its main competitors. Some examples including real data are used to illustrate the usage of the proposed method.

Estimation on conditional restricted mean survival time with counting process

ABSTRACT In a comparative longitudinal clinical study, multiple clinical events of interest are typically collected in timing and occurrence during the follow-up period. These clinical events are often indicative of disease burden over the study period and provide overall evidence of benefit/risk of one treatment relative to another. While these clinical events are usually used to form a composite endpoint, only the first occurrence of the composite endpoint event is considered in primary efficacy analysis. This type of analysis is commonly performed but it may not be ideal. Most of the existing methods for analyzing multiple event-time data were developed, relying on certain model assumptions. However, the assumptions may greatly affect the inferences for treatment effect. In this paper, we propose a simple, non-parametric estimator of conditional mean survival time for multiple events to quantify treatment effect which has clinically meaningful interpretation. We use simulation studies to evaluate the performance of the new method. Further, we apply this method to analyze the data from a cardiovascular clinical trial as an illustration.

Classification of periodic arrivals in event time data for filtering computer network traffic

Periodic patterns can often be observed in real-world event time data, possibly mixed with non-periodic arrival times. For modelling purposes, it is necessary to correctly distinguish the two types of events. This task has particularly important implications in computer network security; there, separating automated polling traffic and human-generated activity in a computer network is important for building realistic statistical models for normal activity, which in turn can be used for anomaly detection. Since automated events commonly occur at a fixed periodicity, statistical tests using Fourier analysis can efficiently detect whether the arrival times present an automated component. In this article, sequences of arrival times which contain automated events are further examined, to separate polling and non-periodic activity. This is first achieved using a simple mixture model on the unit circle based on the angular positions of each event time on the p-clock, where p represents the main periodicity associated with the automated activity; this model is then extended by combining a second source of information, the time of day of each event. Efficient implementations exploiting conjugate Bayesian models are discussed, and performance is assessed on real network flow data collected at Imperial College London.

Goodness-of-fit test for a parametric survival function with cure fraction

We consider the survival function for univariate right-censored event time data, when a cure fraction is present. This means that the population consists of two parts: the cured or non-susceptible group, who will never experience the event of interest versus the non-cured or susceptible group, who will undergo the event of interest when followed up sufficiently long. When modeling the data, a parametric form is often imposed on the survival function of the susceptible group. In this paper, we construct a simple novel test to verify the aptness of the assumed parametric form. To this end, we contrast the parametric fit with the nonparametric fit based on a rescaled Kaplan–Meier estimator. The asymptotic distribution of the two estimators and of the test statistic are established. The latter depends on unknown parameters, hence a bootstrap procedure is applied to approximate the critical values of the test. An extensive simulation study reveals the good finite sample performance of the developed test. To illustrate the practical use, the test is also applied on two real-life data sets.