Estimation Of Hazard Function Research Articles

Stock market prices and Dividends in the US: Bubbles or Long-run equilibria relationships?

This paper presents a novel approach to identifying potential bubbles in the US stock market by employing alternative time series methods based on long memory, including fractional integration and cointegration, as well as duration dependence non-parametric models. To test for duration dependence, the paper employs a unique non-parametric hazard function estimation method, using monotonic P-splines, which enables the estimation of a coherent and sophisticated Bayesian confidence interval for the function. By analyzing historical data of real US stock index from January 1871 to November 2022, the results reveal strong evidence of bubbles in the US stock market. It is worth noting that this is the first time a fractional integration approach and a novel non-parametric hazard function have been utilized to test for rational speculative bubbles in the US stock market, making this paper a significant contribution to the field.

A Comprehensive Analysis of MSE in Estimating Conditional Hazard Functions: A Local Linear, Single Index Approach for MAR Scenarios

In unveiling the non-parametric estimation of the conditional hazard function through the local linear method, our study yields key insights into the method’s behavior. We present rigorous analyses demonstrating the mean square convergence of the estimator, subject to specific conditions, within the realm of independent observations with missing data. Furthermore, our contributions extend to the derivation of expressions detailing both bias and variance of the estimator. Emphasizing the practical implications, we underscore the applicability of two distinct models discussed in this paper for single index estimation scenarios. These findings not only enhance our understanding of survival analysis methodologies but also provide practitioners with valuable tools for navigating the complexities of missing data in the estimation of conditional hazard functions. Ultimately, our results affirm the robustness of the local linear method in non-parametrically estimating the conditional hazard function, offering a nuanced perspective on its performance in the challenging context of independent observations with missing data.

Reliability Analysis and Its Applications for a Newly Improved Type-II Adaptive Progressive Alpha Power Exponential Censored Sample

Recently, a newly improved Type-II adaptive progressive censoring plan was devised, which can successfully ensure that the test length will not surpass a particular threshold period. In this study, we explore the statistical inference of the alpha power exponential distribution in the context of improved adaptive progressive Type-II censored data. The parameters, reliability, and hazard functions were estimated from both classical and Bayesian viewpoints using this censoring plan. To begin, we applied the maximum likelihood estimation approach to obtain parameter, reliability, and hazard function estimators. Following that, the approximate confidence intervals for the aforementioned metrics were derived, assuming the asymptotic normality traits of the maximum likelihood estimators. Additionally, by employing the Bayesian method via the Markov chain Monte Carlo technique, the point estimators and highest posterior density intervals of various parameters were created based on the symmetric squared error loss. A simulation study that incorporates numerous scenarios was used to assess the effectiveness of various estimation methodologies. The optimal progressive censorship plans are then discussed based on a set of criteria. Finally, three applications from the engineering and medical domains have been offered as examples.

PT16 Impact of Data Maturity on the Estimation of the within-Trial Hazard Function: An Example from Metastatic Castration Resistant Prostate Cancer

PT16 Impact of Data Maturity on the Estimation of the within-Trial Hazard Function: An Example from Metastatic Castration Resistant Prostate Cancer

Asymptotic Results of Some Conditional Nonparametric Functional Parameters in High-Dimensional Associated Data

In this paper, we propose to study the asymptotic properties of some conditional functional parameters, such as the distribution function, the density, and the hazard function, for an explanatory variable with values in a Hilbert space (infinite dimension) and a response variable real in a quasi-associated dependency framework. We consider the non parametric estimation of the conditional distribution function by the kernel method in the presence of the quasi-associated dependence, and we establish under general hypotheses the almost complete convergence with speed of the estimator built in the associated case. The estimation of the conditional hazard function will be conducted by utilizing the two outcomes of the conditional distribution function and the conditional density. We establish the asymptotic normality of the kernel estimator as the conditional risk function of a properly normalized functional. We explicitly give the asymptotic variance. Simulation studies were conducted to investigate the behavior of the asymptotic property in the context of finite sample data. All the statistical analyses were performed using R software.

SURVIVAL FUNCTION AND HAZARD FUNCTION ANALYSIS OF EXPONENTIAL DISTRIBUTION IN TYPE I CENSORED SURVIVAL DATA: A CASE STUDY OF BREAST CANCER PATIENTS

Breast cancer is the most common cancer in women and the leading cause of cancer-related death in Indonesia. Analysis of survival data is important for improving the treatment and care of breast cancer patients. This study aims to estimate the parameters, find the survival function, and hazard function of breast cancer patients using a parametric method with an exponential distribution. Previous studies have shown that the Maximum Likelihood Estimation (MLE) method is suitable for estimating the survival function from exponential survival data by censoring. In this study, the exponential distribution was found to be the best for data on breast cancer patients from Surabaya Ontology Hospital. The estimated parameters are θ = 33.9157, and the survival function is calculated using The estimated hazard function for patient death or failure is 0.0295. The results of this study can contribute to the development of better treatment and care strategies for breast cancer patients. However, further research is needed because this study only used monthly time units.

Improved estimation of hazard function when failure information is missing not at random

ABSTRACT Hazard function plays a crucial role in survival analysis. Its estimation has garnered a lot of attention when the survival time variable suffers from right-censoring. Most of the existing works focus on the cases that failure information is complete or missing at random (MAR). When the censoring information is missing not at random (MNAR), statistical inferences on hazard function are very challenging. In this study, estimation of hazard function is addressed under the MNAR mechanism of the failure information. Three estimators are proposed by employing the techniques of correcting biases and adjusting weighting probabilities. These estimators are validated to be consistent and asymptotically normal. Simulation studies and two real-data analyses are performed to assess the proposed methods.

The Association Between Tobacco and Cannabis Use and the Age of Onset of Depression and Anxiety Symptoms: Among Adolescents and Young Adults.

No studies have prospectively explored the association between the use of tobacco or cannabis use and the age of onset of depressive or anxiety symptoms, and no studies have identified the peak ages and ranges of onset of these symptoms among tobacco and/or cannabis users. This is a secondary analysis of Texas Adolescent Tobacco and Marketing Surveillance System data, waves 9-14 (2019-20121). Participants were in 10th grade, 12th grade, and 2 years post-high school (HS) at baseline (wave 9). Interval-censoring multivariable Cox proportional hazards models were fit to assess differences in the estimated age of onset of depression and anxiety by tobacco and cannabis use while adjusting for covariates. We found that lifetime or ever cigarette, e-cigarette, and cannabis use had an increased risk of an earlier age of onset of depressive and anxiety symptoms across the three cohorts, and the youngest cohort was the most differentially impacted by substance use. Between ages 18 to 19 years in the 10th-grade cohort, between ages 20 to 21 years in the 12th-grade cohort, and between ages 22 to 23 years in the post-HS cohort, the estimated hazard function (or cumulative incidence) for reporting depressive and anxiety symptoms almost doubled among lifetime cigarette, e-cigarette, and cannabis users. Tobacco and cannabis users should be screened for mental health problems at an earlier age, especially those aged 18 years and younger, and provided with age- and culturally appropriate resources to prevent or delay the onset of anxiety and/or depression symptoms. The study's findings indicate that tobacco and cannabis use is directly linked to the early onset of depressive and anxiety symptoms among youth. This highlights the significance of early screening and substance use interventions, particularly for youth aged 18 years and younger, as they are disproportionately affected by both substance use and mental health problems. School-based interventions that are age- and culturally appropriate hold promise as they enable youth to seek professional help early, and in a supportive environment. Intervening early in substance shows promise in reducing the likelihood of developing mental health problems at a young age.

UNIFORM CONVERGENCE OF NONPARAMETRIC CONDITIONAL HAZARD FUNCTION IN THE SINGLE FUNCTIONAL INDEX MODELING FOR DEPENDENT DATA

We study the nonparametric local linear estimation of the conditional hazard function of a scalar response variable given a functional explanatory variable, when the functional data are α-mixing dependency and we give the uniform almost complete convergence with rates of this function.

Strong asymptotic properties of kernel smoothing estimation for NA random variables with right censoring

Most studies for negatively associated (NA) random variables consider the complete-data situation, which is actually a relatively ideal condition in practice. The article relaxes this condition to the incomplete-data setting and considers kernel smoothing density and hazard function estimation in the presence of right censoring based on the Kaplan–Meier estimator. We establish the strong asymptotic properties for these two estimators to assess their asymptotic behavior and justify their practical use.

Hazard rate estimation from associated and contaminated data: strong uniform consistency

In survival analysis, it is possible to have some data which are both positively dependent and corrupted by additive noise. This occurs due to the presence of measurement errors. The main focus of this paper is the nonparametric estimation of the hazard rate function in terms of the deconvolution kernel density estimator f n ( x ) and the distribution function estimator obtained by integrating f n ( x ) . We aim at establishing a strong uniform consistency with rates. The performance quality of the hazard function estimator is evaluated numerically. Finally, the approach is implemented to estimate the length of pregnancy from a real data set.

Uniformly complete consistency of frequency polygon estimation for dependent samples and an application

ABSTRACT The frequency polygon estimation, which is based on histogram technique, has a similar convergence rate as those of modern non-negative kernel estimators and the advantage of computational simplicity. This paper will study the uniformly complete consistency and the rates of uniformly complete consistency of frequency polygon estimation for widely orthant dependent samples under some general conditions, which improve and extend the corresponding ones in the literature. As an application, the uniformly complete consistency and the corresponding rates of hazard rate function estimator are also obtained.

Inference for Local Parameters in Convexity Constrained Models

ABSTRACT In this article, we develop automated inference methods for “local” parameters in a collection of convexity constrained models based on the natural constrained tuning-free estimators. A canonical example is given by the univariate convex regression model, in which automated inference is drawn for the function value, the function derivative at a fixed interior point, and the anti-mode of the convex regression function, based on the widely used tuning-free, piecewise linear convex least squares estimator (LSE). The key to our inference proposal in this model is a pivotal joint limit distribution theory for the LS estimates of the local parameters, normalized appropriately by the length of certain data-driven linear piece of the convex LSE. Such a pivotal limiting distribution instantly gives rise to confidence intervals for these local parameters, whose construction requires almost no more effort than computing the convex LSE itself. This inference method in the convex regression model is a special case of a general inference machinery that covers a number of convexity constrained models in which a limit distribution theory is available for model-specific estimators. Concrete models include: (i) log-concave density estimation, (ii) s-concave density estimation, (iii) convex nonincreasing density estimation, (iv) concave bathtub-shaped hazard function estimation, and (v) concave distribution function estimation from corrupted data. The proposed confidence intervals for all these models are proved to have asymptotically exact coverage and oracle length, and require no further information than the estimator itself. We provide extensive simulation evidence that validates our theoretical results. Real data applications and comparisons with competing methods are given to illustrate the usefulness of our inference proposals. Supplementary materials for this article are available online.

Analysis with Applications of the Generalized Type-II Progressive Hybrid Censoring Sample from Burr Type-XII Model

In this article, based on the generalized Type-II progressive hybrid censoring sample from the Burr Type-XII distribution, maximum likelihood and Bayesian inference are discussed. Point and interval estimates of unknown parameters, reliability, and hazard functions are developed. We employed several loss functions, such as squared error, LINEX, and general entropy, as symmetric and asymmetric loss functions and various prior distributions as informative and non-informative priors for Bayesian inference of unknown parameters. Under a generalized Type-II progressive hybrid censoring sample, we also propose a Bayesian one-sample prediction for unobserved failures. We conduct simulation study using the MCMC algorithm for the Bayesian approach based on several prior distributions. Finally, we apply the results of the theoretical research to real data.

Nonparametric inference in the accelerated failure time model using restricted means.

We propose a nonparametric estimate of the scale-change parameter for characterizing the difference between two survival functions under the accelerated failure time model using an estimating equation based on restricted means. Advantages of our restricted means based approach compared to current nonparametric procedures is the strictly monotone nature of the estimating equation as a function of the scale-change parameter, leading to a unique root, as well as the availability of a direct standard error estimate, avoiding the need for hazard function estimation or re-sampling to conduct inference. We derive the asymptotic properties of the proposed estimator for fixed and for random point of restriction. In a simulation study, we compare the performance of the proposed estimator with parametric and nonparametric competitors in terms of bias, efficiency, and accuracy of coverage probabilities. The restricted means based approach provides unbiased estimates and accurate confidence interval coverage rates with efficiency ranging from 81% to 95% relative to fitting the correct parametric model. An example from a randomized clinical trial in head and neck cancer is provided to illustrate an application of the methodology in practice.

Asymptotic properties of penalized spline estimators in concave extended linear models: Rates of convergence

This paper develops a general theory on rates of convergence of penalized spline estimators for function estimation when the likelihood functional is concave in candidate functions, where the likelihood is interpreted in a broad sense that includes conditional likelihood, quasi-likelihood and pseudo-likelihood. The theory allows all feasible combinations of the spline degree, the penalty order and the smoothness of the unknown functions. According to this theory, the asymptotic behaviors of the penalized spline estimators depends on interplay between the spline knot number and the penalty parameter. The general theory is applied to obtain results in a variety of contexts, including regression, generalized regression such as logistic regression and Poisson regression, density estimation, conditional hazard function estimation for censored data, quantile regression, diffusion function estimation for a diffusion type process and estimation of spectral density function of a stationary time series. For multidimensional function estimation, the theory (presented in the Supplementary Material) covers both penalized tensor product splines and penalized bivariate splines on triangulations.

Survival Analysis: Alternate Approach

Existing models of survival analysis dealing with group data have advantages and limitations too. Assumptions of the models need to be verified. Problem arises when one or more assumptions of a model are not satisfied. Methods of survival analysis, inter alia assumes homogeneity of treatment and related factors during the follow-up periods. However, in practice, such assumptions do not hold. The proposed method (Geometric mean approach) is non-parametric, simple and satisfies desired properties from measurement theory angle. Focusing on individual patient, it helps in mathematical diagnosis of disease like cancer of a particular type, disease intensity in terms of the chosen measurable factors/variables, identification of bad prognosis factors of an individual and quantification of progress or deterioration of a patient over time (analogous to hazard function of an individual). The method can help the researchers and practitioners to make meaningful analysis and drawing meaningful conclusions including estimation of hazard function of sample patients without making any assumption. Empirical verifications of the proposed method along with its robustness and estimation of hazard function and clinical validations are proposed as future studies.

Non-parametric estimation of reciprocity and triadic effects in relational event networks

Relational event networks arise naturally from social interactions: interactions can be considered time-stamped edges between vertices of social actors. By studying the factors that influence the interaction inter-arrival times we can get insight in the drivers of interaction dynamics. Relational event models provide a succinct way to analyse a broad family of interactional patterns and their influence on network dynamics. These models can easily incorporate a wide range of mechanisms involving both endogenous and exogenous network effects. It has been typical for quantitive models to assume that endogenous network mechanisms, such as reciprocity or triadic effects, remain stable over time. However, a number of studies argued that reciprocity has a strong tendency to decay over time.This paper proposes to model the dynamic structure of reciprocal and triadic effects in relational event networks via stratified baseline hazards. This avoids having to define arbitrary temporal windows for what can be considered reciprocity or triadic closure. A two-step estimation framework is used, based on the stratified Cox proportional hazards model, followed by non-parametric estimation of the stratified cumulative hazard functions. This framework is illustrated by a simulation study and its application to two studies involving email communication and classroom interactions.

The price adjustment hazard function: Evidence from high inflation periods

The price adjustment hazard function - the probability of a good’s price changing as a function of its price misalignment - enables the examination of the relationship between price stickiness and monetary non-neutrality without specifying a micro-founded model, as discussed by Caballero and Engel (1993a, 2007). Using the micro data underlying the U.S. Consumer Price Index going back to the 1970s, we estimate the hazard function relying on empirical patterns from high and low inflation periods. We find that the relation between inflation and higher moments of the price change distribution is particularly informative for the shape of the hazard function. Our estimated hazard function is relatively flat with positive values at zero. It implies weak price selection and a high degree of monetary non-neutrality: about 60% of the degree implied by the Calvo model, and much higher than what menu cost models imply. In addition, our estimated function is asymmetric: price increases are considerably more likely to occur than price decreases of the same magnitude.

New methods for the additive hazards model with the informatively interval-censored failure time data.

The additive hazards model is one of the most commonly used models for regression analysis of failure time data and many inference procedures have been developed for it under various situations. In particular, Wang etal. (2018a, Computational Statistics and Data Analysis, 125, 1-9) discussed the situation where one observes informatively interval-censored data and proposed a likelihood estimation approach. However , it involves estimation of the unknown baseline cumulative hazard function and thus may be time-consuming . Corresponding to this, we propose two new procedures, an estimating equation-based one and an empirical likelihood-based one, and both do not need estimation of the cumulative hazard function and can be easily implemented. The asymptotic properties of the proposed methods are established and an extensive simulation study suggests that they work well in practical situations. An application is alsoprovided.