Kernel machines for current status data

This paper considers joint analysis of current status and marker data using a threshold model based on first hitting times. A failure time is defined as the time at which a subject's latent health status process first decreases to zero. We extend the bivariate Wiener process model in Whitmore et al. (1998) to the case when only current status data are available. We develop maximum likelihood estimation procedures and provide simulation studies. We apply our methods to a motivating example involving liver tumors in mice.

SUMMARY A great deal of recent attention has focused on the estimation of survival distributions based on current status data, an extreme form of interval censored data. This particular data structure arises in a wide variety of applications where cross-sectional observation either naturally occurs or is preferred to more traditional forms of follow-up. Here we consider current status data in the context of competing risks. We briefly consider simple parametric models as a backdrop to nonparametric procedures. We make some brief comparisons and remarks regarding the nonparametric maximum likelihood estimator. The ideas are illustrated on the data of Krailo & Pike (1983) which considers estimation of the age distribution at both natural and operative menopause. We also consider the case where there is exact observation of failure times due to one of the competing risks when failure occurs prior to the monitoring time. Basic techniques of survival analysis focus on estimation of the survival distribution based on various forms of censored data. An extreme form of censoring arises where the only information on studied individuals is their survival status at a single monitoring time. This particular data structure is known as current status data. Nonparametric estimation of the survival function and semiparametric techniques for related regression models, based on current status data, have been much studied of late. Here, we consider estimation of sub-survival functions based on current status observations in the presence of competing risks. For simplicity, we describe only two competing risks, but the ideas are easily extended when there are more than two possible causes of failure. Let )j denote the cause-specific hazard function for cause j = 1, 2 (Kalbfleisch & Prentice, 2002, p. 252). If T and J are the random variables that measure time to failure and cause of failure, respectively, the two sub-distribution functions of interest are

We consider a varying-coefficient partially linear proportional odds model with current status data. This model enables one to examine the extent to which some covariates interact nonlinearly with an exposure variable, while other covariates present linear effects. B-spline approach and sieve maximum likelihood estimation method are used to get an integrated estimate for the linear coefficients, the varying-coefficient functions and the baseline function. The proposed parameter estimators are proved to be semiparametrically efficient and asymptotically normal, and the estimators for the nonparametric functions achieve the optimal rate of convergence. Simulation studies and a real data analysis are used for assessment and illustration.

ABSTRACTIn this paper, we introduce a partially linear single-index additive hazards model with current status data. Both the unknown link function of the single-index term and the cumulative baseline hazard function are approximated by B-splines under a monotonicity constraint on the latter. The sieve method is applied to estimate the nonparametric and parametric components simultaneously. We show that, when the nonparametric link function is an exact B-spline, the resultant estimator of regression parameter vector is asymptotically normal and achieves the semiparametric information bound and the rate of convergence of the estimator for the cumulative baseline hazard function is optimal. Simulation studies are presented to examine the finite sample performance of the proposed estimation method. For illustration, we apply the method to a clinical dataset with current status outcome.

We investigate empirical likelihood for the additive hazards model with current status data. An empirical log-likelihood ratio for a vector or subvector of regression parameters is defined and its limiting distribution is shown to be a standard chi-squared distribution. The proposed inference procedure enables us to make empirical likelihood-based inference for the regression parameters. Finite sample performance of the proposed method is assessed in simulation studies to compare with that of a normal approximation method, it shows that the empirical likelihood method provides more accurate inference than the normal approximation method. A real data example is used for illustration.

In studies involving subclinical events, times of events are often subject to interval censoring since their occurrence is only detected at inspection times. When individuals are event-free at an initial time and a single follow-up inspection is made, current status data are obtained. In many settings, however, the population comprised a susceptible and a nonsusceptible subpopulation, where only susceptible individuals will go on to experience the event. Then interest often lies primarily in identifying prognostic variables for susceptibility, and secondarily in the event time distribution among the susceptible individuals. We give a simple mixture model that facilitates estimation of the proportion of susceptible individuals, covariate effects on the odds of susceptibility, and the event time distribution under a current status observation scheme. Asymptotic relative efficiency of maximum likelihood estimators is considered based on the Fisher information for a variety of settings. EM algorithms are proposed for parametric, weakly parametric, and nonparametric estimation of the event time distribution. The methods are applied to motivating studies examining an immunological response to low molecular weight heparin in patients undergoing orthopedic surgery.

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.

Current status data arise when each study subject is observed only once and the survival time of interest is known only to be either less or greater than the observation time. Such data often occur in, for example, cross-sectional studies, demographical investigations and tumorigenicity experiments and several semi-parametric and non-parametric methods for their analysis have been proposed. However, most of these methods deal only with the situation where observation time is independent of the underlying survival time completely or given covariates. This paper discusses regression analysis of current status data when the observation time may be related to the underlying survival time and inference procedures are presented for estimation of regression parameters under the additive hazards regression model. The procedures can be easily implemented and are applied to two motivating examples.

The current status and panel count data frequently arise from cancer and tumorigenicity studies when events currently occur. A common and widely used class of two sample tests, for current status and panel count data, is the permutation class. We manipulate the double saddlepoint method to calculate the exact mid-p-values of the underlying permutation distributions of this class of tests. Permutation simulations are replaced by analytical saddlepoint computations which provide extremely accurate mid-p-values that are exact for most practical purposes and almost always more accurate than normal approximations. The method is illustrated using two real tumorigenicity panel count data. To compare the saddlepoint approximation with the normal asymptotic approximation, a simulation study is conducted. The speed and accuracy of the saddlepoint method facilitate the calculation of the confidence interval for the treatment effect. The inversion of the mid-p-values to calculate the confidence interval for the mean rate of development of the recurrent event is discussed.

The research uses data from a representative national survey to explore the determinants of age at sexual debut among South African youths in the age group 15–24 years. A random sample of 5 708 youths were interviewed and 92% responded to questions on whether or not they had ever had sex and their age at first sex for those who had. The research used survival analyses techniques to combine ‘current status data’ and ‘recall data’ for respondents who reported ever having had sex. The females were more likely than the males to report ever having had sex (p≤0.001). The median age at sexual debut was 18 years for both males and females. The hazard ratio pertaining to early sexual debut was 0.81-times less for those in the age group 15–19 as compared to those in the age group 20–24 (p≤0.001). Age, race, geographical location, and level of education were found to be important determinants of age at sexual debut. The ‘hazards of sexual debut’ (θ=0.112; p≤0.001) varied significantly between geographical areas (rural or urban). Youths with an earlier age of sexual debut were less likely to have used condoms, a behaviour which increases their risk of HIV infection. HIV prevalence was consistently higher among the females than among the males. We recommend that HIV-prevention interventions target community sets rather than only individuals at higher risk of exposure to HIV.

Current status data occur in many fields including demographical, epidemiological, financial, medical, and sociological studies. We consider the regression analysis of current status data with latent variables. The proposed model consists of a factor analytic model for characterizing latent variables through their multiple surrogates and an additive hazard model for examining potential covariate effects on the hazards of interest in the presence of current status data. We develop a borrow-strength estimation procedure that incorporates the expectation-maximization algorithm and correlated estimating equations. The consistency and asymptotic normality of the proposed estimators are established. A simulation study is conducted to evaluate the finite sample performance of the proposed method. A real-life study on the chronic kidney disease of type 2 diabetic patients is presented.

On efficient estimation in additive hazards regression with current status data

Interval-censored data is a common type of failure time data in survival analysis. However, in practice, there is often a dependent relationship between the failure time and the observation time, and ignoring this dependency can lead to biased inferences. To address this issue, this study describes the dependent relationship between the failure time and the observation time using the copula model and establishes a copula-based joint model. Existing research on dependent censored data has focused on cases where covariate effects take relatively simple forms, however, in practical studies, it has been observed that the effects of covariates are more complex. Consequently, this study assumes that the failure time follows an additive-multiplicative hazards model, which includes covariates with multiplicative effects as well as covariates with additive effects, providing greater flexibility. Additionally, we propose a penalized sieve maximum likelihood estimation method. Furthermore, a Newton Multiple Iteration (Newton-MI) algorithm, adept at handling parameter non-negativity constraints, is employed to estimate the model parameters. Extensive simulations validate the proposed method's favorable statistical properties. Finally, we apply the proposed model and methods to a tumor dataset.

Bivariate failure time data is widely used in survival analysis, for example, in twins study. This article presents a class of chi2-type tests for independence between pairs of failure times after adjusting for covariates. A bivariate accelerated failure time model is proposed for the joint distribution of bivariate failure times while leaving the dependence structures for related failure times completely unspecified. Theoretical properties of the proposed tests are derived and variance estimates of the test statistics are obtained using a resampling technique. Simulation studies show that the proposed tests are appropriate for practical use. Two examples including the study of infection in catheters for patients on dialysis and the diabetic retinopathy study are also given to illustrate the methodology.

Cost-effectiveness research is an essential tool in healthcare decision-making, enabling the comparison of interventions based on their incremental costs and effects. While traditionally conducted alongside Randomized Controlled Trials (RCTs), there is a growing interest in complementary Real-World Data (RWD) analysis for Cost-Effectiveness Analysis (CEA). In order for healthcare decision-makers to make valid reimbursement decisions, it is essential that the results of CEAs are both valid and applicable to a broader context. While RCTs offer high internal validity, their generalizability can be limited. Therefore, RWD is increasingly being recognized as a valuable source of information that can complement RCT data. RWD offers advantages over RCTs, such as better generalizability because of less strict patient selection and reflection of actual treatment patterns, but come with complexities, like confounding and missing observations. Confounding, stemming from the non-random allocation of treatment, presents a significant challenge in RWD analysis and requires careful adjustment to avoid biased estimates. In this thesis, the concepts of time-fixed and time-dependent confounding are distinguished, with the latter being more common in longitudinal studies. Various methods for dealing with confounding have been proposed, but their performance in different scenarios remains unclear. Within the context of CEA, this thesis aims to clarify terminology, review methods for adjusting confounding, and compare the performance of different techniques in CEA studies using RWD. Firstly, this thesis aimed to bridge the gap between epidemiologists and economists by providing a glossary that equips participants in interdisciplinary collaborations with the essential shared vocabulary (Chapter 2). Next, the thesis provides a scoping review of methods available for addressing time-invariant confounding (Chapter 3). Following the identification of a wide range of methods, the aim was to evaluate the most promising ones and compare them with current research practices in the context of CEA (Chapter 4). This exploration expanded the research question by building upon the time-invariant confounding study. It introduced time-dependent confounding to the simulation setup by adding an extra time point (Chapter 5). Finally, in the general discussion, insights and recommendations for improving the validity and reliability of CEA using RWD are provided based on the scoping review and simulation studies included in this thesis (Chapter 6).