RANK-BASED INFERENCE FOR SURVEY SAMPLING DATA

For regression models where data are obtained from sampling surveies, the statistical analysis is often based on approaches that are either non-robust or inefficient. The handling of survey data requires more appropriate techniques, as the classical methods usually result in biased and inefficient estimates of the underlying model parameters. This article is concerned with the development of a new approach of obtaining robust and efficient estimates of regression model parameters when dealing with survey sampling data. Asymptotic properties of such estimators are established under mild regularity conditions. To demonstrate the performance of the proposed method, Monte Carlo simulation experiments are carried out and show that the estimators obtained from the proposed methodology are robust and more efficient than many of those obtained from existing approaches, mainly if the survey data tend to result in residuals with heavy-tailed or skewed distributions and/or when there are few gross outliers. Finally, the proposed approach is illustrated with a real data example

Estimation with Recurrent Event Data under an Informative Monitoring Period

We consider a study which monitors the occurrence of a recurrent event for n subjects or units. Of interest is the problem of parametric and semiparametric estimation of the inter-event or gap-time distribution when the data is subject to informative censoring. We first address the case where the gap-times are assumed to be independent and identically distributed with some parametric survival distribution function F¯( t,theta); where theta is some p-dimensional parameter. It is further assumed that the recurrent event is observed until some random time, tau, whose distribution G depends on that of F through the relationship G¯ = F¯beta, for some beta \u3e 0; the so-called Koziol-Green model. We present finite and asymptotic properties of the maximum likelihood estimates of beta and theta as well as the estimator F¯(t). Next, we derive Nelson-Aalen and Kaplan-Meier type estimators by embedding the problem in an appropriate counting process. Finite and asymptotic properties of the semiparametric estimators are also established. The proposed estimators in both cases are compared to those derived ignoring informative censoring to ascertain efficiency gained that results by taking into account informative censoring. It will be shown that the proposed estimators are more efficient than those derived ignoring informative censoring. Moreover, in the special case of the homogeneous Poisson process, the asymptotic relative efficiency is shown to be bounded by approximately 0.65

Semiparametric Estimation with Correlated Recurrent Event Data under Informative Monitoring

Consider a recurrent event data where frailty models are used to account for correlations among the inter-event times within each unit under study. In this talk we consider the problem of semiparametric estimation of the inter-event time distribution under informative monitoring and the Gamma frailty model. We propose a semiparametric estimator of the baseline survivor function. We show that the estimator under the i.i.d. setting is inconsistent in the presence of frailty. We present results of simulaiton study where we discuss the performence of our proposed estimator to that derived under the i.i.d. setting. Finally, these estimators will be demonstrated by applying to biomedical and engineering data sets

A General Class of Semiparametric Models for Recurrent Event Data

We propose a general class of semiparametric models for analyzing recurrent event data that takes into account the change in age of a unit due to interventions; allows for the possibility of the unit receiving a life supplement after being repaired; and provides a mechanism for researchers to incorporate time-dependent covariates. The class of models includes as special cases many other models that have been proposed for analyzing recurrent event data. Models belonging to the class can be easily generalized and new models can be created to accommodate a variety of practical considerations. A partial maximum likelihood estimator of the regression parameter and a Nelson-Aalen type estimator of the baseline cumulative intensity are given. Asymptotic properties of the estimators are established and the finite sample properties are investigated via a simulation study. The statistical analysis of a real data set is used to illustrate the class of models

A General Class of Additive Semiparametric Models for Recurrent Event Data

Recurrent event data is a special case of multivariate lifetime data that is present in a large variety of studies from numerous disciplines. Due to its pervasiveness, it is essential that appropriate models and inference procedures exist for its analysis. We propose a general class of additive semiparametric models for examining recurrent event data that uses an effective age process to take into account the impact of interventions applied to units after an event occurrence. The effect of covariates is additive instead of the common multiplicative assumption. We derive estimators of the regression parameter, baseline cumulative hazard function, and baseline survival function. We also establish the asymptotic properties of the estimators using tools from empirical process theory. Simulation studies indicate that the asymptotic properties of the regression parameter closely approximate its finite sample properties. The analysis of a real data set consisting of indolent lymphoma recurrence times provides a practical illustration of the class of models and is used to examine the impact of the effective age process. The importance of the effective age process is also demonstrated via the modeling of a data set of failure times for the hydraulic subsystems of load-haul-dump machines used in mining

Optimal Goodness-of-Fit Tests for Recurrent Event Data

A class of tests for the hypothesis that the baseline intensity belongs to a parametric class of intensities is given in the recurrent event setting. Asymptotic properties of a weighted general class of processes that compare the non-parametric versus parametric estimators for the cumulative intensity are presented. These results are given for a sequence of Pitman alternatives. Test statistics are proposed and methods of obtaining critical values are examined. Optimal choices for the weight function are given for a class of chi-squared tests. Based on Khmaladze\u27s transformation we propose distributional free tests. These include the types of Kolmogorov-Smirnov and Cramér-von Mises. The tests are used to analyze two different data sets

Optimal Rejection Curves for Exact False Discovery Rate Control

Finner et al. (2012) provided multiple hypothesis testing procedures based on a nonlinear rejection curve for exact false discovery rate control. This paper constructs classes of such procedures and compares the most powerful procedure in each class to competing procedures

Parameter estimation for correlated recurrent events under informative monitoring

When subjects are monitored for a recurrent event over a period of time, each individual behaves like an experimental unit within which measurements may be correlated. The subject-specific observation window (i.e. monitoring period) constitutes another factor controlling the accumulation of events and censoring. We develop a procedure for estimating survivor parameters in the presence of joint effect of correlation and informative monitoring; specifically, for studies in which the survival time for a subject is censored because of deterioration of their physical condition or due to the accumulation of their event occurrences. In this manuscript, we approach the survivor parameter estimation problem by a fully parametric baseline hazard model where the intensity functions of the inter-event time and the duration of the monitoring period are reconciled through the generalized Koziol-Green (KG) model (Koziol and Green (1976) [12]), and the within experimental unit correlation modeled through frailty. We outline the Expectation Maximization (EM) steps for estimating Weibull parameters with correlated recurrent event data under informative monitoring. We apply our method to a real life data

A Khmaladze-Transformed Test of Fit with ML Estimation in the Presence of Recurrent Events

This article provides a goodness-of-fit test for the distribution function or the survival function in a recurrent event setting, when the inter-event time parametric structure F( · ; θ) is estimated from the observed data. Of concern is the null hypothesis that the inter-event time distribution is absolutely continuous and belongs to a parametric family ℱ = {F(· ; θ) : θ ∈ Θ ⊆ ℜq} where the q-dimensional parameter space is neither known nor specified. We proposed a Khmaladze martingale-transformed type of test (Khmaladze, 1981), adapted to recurrent events. The test statistic combines two likelihood sources of estimation to form a parametric empirical process: (1) a product-limit nonparametric maximum likelihood estimator (NPMLE; Pena et al., 2001a) that is a consistent estimator of F, [F hat] say, and (2) a point process likelihood estimator F( · ;[θ hat] ) (Jacod, 1974/1975). These estimators are combined to construct a Kolmogorov-Smirnov (KS) type of test (Kolmogorov 1933; Smirnov, 1933). Empirical process and martingale weak convergence frameworks are utilized for theoretical derivations and motivational justification of the proposed transformation. A simulation study is conducted for performance assessment, and the test is applied to a problem investigated by Proschan (1963) on air-conditioning failure in a fleet of Boeing 720 jets

On Corrected Phase-Type Approximations of the Time Value of Ruin with Heavy Tails

We approximate Gerber-Shiu functions with heavy-tailed claims in a recently introduced risk model having both interclaim times and premiums depending on the claim sizes. We apply a technique known as corrected phase-type approximations . This results in adding a correction term to the Gerber-Shiu function with phase-type claim sizes. The correction term contains the heavy-tailed behavior at most once per convolution and captures the tail behavior of the true Gerber-Shiu function. We make the tail behavior specific in the classical case of one class of risk insured. After illustrating a use of such approximations, we study numerically the approximations\u27 relative errors for some specific penalty functions and claims distributions