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Random left truncation is modelled by the conditional distribution of the random variable $X$ of interest, given that it is larger than the truncating random variable $Y$; usually $X$ and $Y$ are assumed independent. The present paper is based on a simple reparametrization of the left truncation model as a three-state Markov process. The derivation of a nonparametric estimator is a distribution function under random truncation is then a special case of results on the statistical theory of counting processes by Aalen and Johansen. This framework also clarifies the status of the estimator as a nonparametric maximum likelihood estimator, and consistency, asymptotic normality and efficiency may be derived directly as special cases of Aalen and Johansen's general theorems and later work. Although we do not carry through these here, we note that the present framework also allows several generalizations: censoring may be incorporated; the independence hypothesis underlying the truncation models may be tested; ties (occurring when the distributions of $F$ and $G$ have discrete components) may be handled.

On definit un nouveau test de tendance qui peut etre vu comme une generalisation du test de regression isotonique de Chako (1963)

In survival analysis, as in other branches of applied statistics, confirmatory analysis is often requested before an initial finding can be cleared of suspicion of being due just to mass significance. This paper points out that the special temporal structure of the classical clinical trial with staggered entry allows re-use of the initial survivors by left-truncating their remaining survival times. This procedure can often save a considerable amount of calendar time. The procedure is illustrated by data from the Danish Breast Cancer Cooperative Group.

Let denote k (k > 2) independent populations with distribution functions respectively, where F(0) = 0 so that are the left truncation parameters of the respective distributions. The function F and the parameters are considered to be unknown. Let be the ordered parameters and let Π(k) be the unknown "best" population, i.e. the population having distribution function . In case more than one population has a θ-value which is tied for the largest then exactly one of these tied populations is defined to be the "best" population Π(k) according to some fixed rule. This paper is concerned with the problem of constructing sequential and two-stage procedures for selecting the best population Π(k), which are in some sense nonparametric. Asymptotic expressions are obtained for the expected sample sizes of the procedures and comparisons with other procedures are discussed.

SUMMARY The use of a mixture model to estimate the probability of developing AIDS after HIV infection and the distribution of incubation time is investigated. The possibility of left truncation and an uncertain time of infection is incorporated into the analysis. The efficiency losses associated with uncertain infection times are investigated. An example is given.

SUMMARY In some areas of life testing, subjects may enter or leave the study after they have been put on test. Statistics are presented for testing the hypothesis that the lifetimes have a given distribution for both the discrete and continuous cases. They are shown to be asymptotically normal by associating a martingale with the life process and using basic results about stopping times. There is some discussion of the effect of weight functions on power. An example of the test is provided.

Summary It is shown that when estimating tbe mean μ of a normal population, the standard deviation σ being known. the BAN estimate of μ based on a truncated sample of size n is less efficient than that based on a complete sample of the same size whatever be the point of truncation xa. On the contrary, when estimating σ alone μ being known, the BAN estimate of σ based on the truncated sample is substantially more efficient than that based on the complete sample whenever xa> μ in the case of left truncation, and xa< μ in the case of right truncation.

Existing evidence on the relationship between RD (ii) RD and (iii) creative destruction as proxied by median R&D intensity in the industry and the premium on business lending have negative effects on firm survival. Other findings concerning age, size, productivity, relative growth, Pavitt technology classes and the macroeconomic environment are in line with the existing literature. The results are strongly or moderately robust to different samples, stepwise estimations, and controls for frailty and left truncation.

Survival models can support the estimation of the resources needed for future renovations of sewer systems. They are particularly useful, when a large share of network will need renovation. This paper studies modelling sewer deterioration in a context, where data are available for pipes selected for inspections due to suspected or experienced poor condition. We compare the random survival forest and the Weibull regression for modelling survival and find that both methods yield similar results, but the random survival forest performs slightly better. We propose a method for estimating the range in which the actual network survival curve lies. We conclude that in order to reach reliable results, a life span model needs to be constructed based on a random sample of pipes, which are then consecutively inspected and in addition, censoring and left truncation need to be accounted for. The inspection data applied in this paper had been collected with the aim of finding pipes in poor condition in the network. As a result, the data were biased towards poor condition and unrepresentative in terms of pipe ages.

BackgroundSome scholars posit that attempts to avert stillbirth among extremely preterm gestations may result in a live birth but an early neonatal death. The literature, however, reports no empirical test of this potential form of left truncation. We examine whether annual cohorts delivered at extremely preterm gestational ages show an inverse correlation between their incidence of stillbirth and early neonatal death.MethodsWe retrieved live birth and infant death information from the California Linked Birth and Infant Death Cohort Files for years 1989 to 2015. We defined the extremely preterm period as delivery from 22 to ResultsCalifornia reported 89,276 extremely preterm deliveries (live births and stillbirths) to Hispanic, non-Hispanic (NH) Black, and NH white mothers from 1989 to 2015. Findings indicate an inverse correlation between stillbirth and early neonatal death in the same cohort year (coefficient: -0.27, 95% CI of − 0.11; − 0.42). Results remain robust to alternative specifications and falsification tests.ConclusionsFindings support the notion that cohorts with an elevated risk of stillbirth also show a reduced risk of early neonatal death among extremely preterm deliveries. Results add to the evidence base that selectionin uteromay influence the survival characteristics of live-born cohorts.

Reinforced Urn Processes (RUPs) represent a flexible class of Bayesian nonparametric models suitable for dealing with possibly right-censored and left-truncated observations. A reliable estimation of their hyper-parameters is however missing in the literature. We therefore propose an extension of the Expectation-Maximization (EM) algorithm for RUPs, both in the univariate and the bivariate case. Furthermore, a new methodology combining EM and the prior elicitation mechanism of RUPs is developed: the Expectation-Reinforcement algorithm. Numerical results showing the performance of both algorithms are presented for several analytical examples as well as for a large dataset of Canadian annuities.

Two unbiased estimators of the Poisson parameter are given for a truncation situation in whirh Cohen has suggested a near-efficient procedure. The situation is one in which each observation has its own distinctive left. truncation point, ci , and its own distinctive Poisson parameter λt i — it is the common λ which is to be estimated. The proposed estimators are obtained as adaptations of a pltblished simple estimator for the case all ci = c, all ti = 1. Illustrative data from Cohen are used for intercomparing the various estimators. including the maximum likelihood estimator.