Efficient and Ad Hoc Estimation in the Bivariate Censoring Model

A large number of proposals for estimating the bivariate survival function under random censoring has been made. In this paper we discuss nonparametric maximum likelihood estimation and the bivariate Kaplan-Meier estimator of Dabrowska. We show how these estimators are computed, present their intuitive background and compare their practical performance under different levels of dependence and censoring, based on extensive simulation results, which leads to a practical advise.

Locally Efficient Estimation with Current Status Data and High Dimensional Covariates

In biostatistical applications, interest often focuses on the estimation of the distribution of time T between two consecutive events. If the initial event time is observed and the subsequent event time is only known to be larger or smaller than an observed monitoring time, then the data is described by the well known singly-censored current status model, also known as interval censored data, case I. We extend this current status model by allowing the presence of a time-dependent process, which is partly observed and allowing C to depend on T through the observed part of this time-dependent process. Because of the high dimension of the covariate process, no globally efficient estimators exist with a good practical performance at moderate sample sizes. We follow the approach of Robins and Rotnitzky (1992) by modeling the censoring variable, given the time-variable and the covariate-process, i.e., the missingness process, under the restriction that it satisfied coarsening at random. We propose a generalization of the simple current status estimator of the distribution of T and of smooth functionals of the distribution of T, which is based on an estimate of the missingness. In this estimator the covariates enter only through the estimate of the missingness process. Due to the coarsening at random assumption, the estimator has the interesting property that if we estimate the missingness process more nonparametrically, then we improve its efficiency. We show that by local estimation of an optimal model or optimal function of the covariates for the missingness process, the generalized current status estimator for smooth functionals become locally efficient; meaning it is efficient if the right model or covariate is consistently estimated and it is consistent and asymptotically normal in general. Estimation of the optimal model requires estimation of the conditional distribution of T, given the covariates. Any (prior) knowledge of this conditional distribution can be used at this stage without any risk of losing root-n consistency. We also propose locally efficient one step estimators. Finally, we show some simulation results.

Smooth Hazard Function Estimation for Interval Censored Data with Time Varying Covariates

In this paper we propose methods for smooth hazard estimation of a time variable where that variable is interval censored. These methods allow one to model the transformed hazard in terms of either smooth (smoothing splines) or linear functions of time and other relevant time varying predictor variables. We illustrate the use of this method on a dataset of hemophiliacs where the outcome, time to seroconversion for HIV, is interval censored and left-truncated.

The Two-Interval Line-Segment Problem

In this paper, the NPMLE in the one-dimensional line segment problem is defined and studied, where line segments on the real line through two non-overlapping intervals are observed. The self-consistency equations for the NPMLE are defined and a quick algorithm for solving them is provided. Supnorm weak convergence to a Gaussian process and efficiency of the NPMLE is proved. The problem has a strong geological application in the study of the lifespan of species.

Semiparametric Methods for Semi-competing Risks Problem with Censoring and Truncation

Studies of chronic life-threatening diseases often involve both mortality and morbidity. In observational studies, the data may also be subject to administrative left truncation and right censoring. Since mortality and morbidity may be correlated and mortality may censor morbidity, the Lynden-Bell estimator for left truncated and right censored data may be biased for estimating the marginal survival function of the non-terminal event. We propose a semiparametric estimator for this survival function based on a joint model for the two time-to-event variables, which utilizes the gamma frailty specification in the region of the observable data. Firstly, we develop a novel estimator for the gamma frailty parameter under left truncation. Using this estimator, we then derive a closed form estimator for the marginal distribution of the non-terminal event. The large sample properties of the estimators are established via asymptotic theory. The methodology performs well with moderate sample sizes, both in simulations and in an analysis of data from a diabetes registry.

Mixture Cure Survival Models with Dependent Censoring

A number of authors have studies the mixture survival model to analyze survival data with nonnegligible cure fractions. A key assumption made by these authors is the independence between the survival time and the censoring time. To our knowledge, no one has studies the mixture cure model in the presence of dependent censoring. To account for such dependence, we propose a more general cure model which allows for dependent censoring. In particular, we derive the cure models from the perspective of competing risks and model the dependence between the censoring time and the survival time using a class of Archimedean copula models. Within this framework, we consider the parameter estimation, the cure detection, and the two-sample comparison of latency distribution in the presence of dependent censoring when a proportion of patients is deemed cured. Large sample results using the martingale theory are obtained. We applied the proposed methodologies to the SEER prostate cancer data.

Measurement of the 1s-2s energy interval in muonium

The 1s-2s interval has been measured in the muonium (;mgr;(+)e(-)) atom by Doppler-free two-photon pulsed laser spectroscopy. The frequency separation of the states was determined to be 2 455 528 941.0(9.8) MHz, in good agreement with quantum electrodynamics. The result may be interpreted as a measurement of the muon-electron charge ratio as -1-1.1(2.1)x10(-9). We expect significantly higher accuracy at future high flux muon sources and from cw laser technology.

The performance of computer-aided detection when analyzing prior mammograms of newly detected breast cancers with special focus on the time interval from initial imaging to detection

PURPOSE: The clinical role of CAD systems to detect breast cancer, which have not been on cancer containing mammograms not detected by the radiologist was proven retrospectively. METHODS: All patients from 1992 to 2005 with a histologically verified malignant breast lesion and a mammogram at our department, were analyzed in retrospect focussing on the time of detection of the malignant lesion. All prior mammograms were analyzed by CAD (CADx, USA). The resulting CAD printout was matched with the cancer containing images yielding to the radiological diagnosis of breast cancer. CAD performance, sensitivity as well as the association of CAD and radiological features were analyzed. RESULTS: 278 mammograms fulfilled the inclusion criteria. 111 cases showed a retrospectively visible lesion (71 masses, 23 single microcalcification clusters, 16 masses with microcalcifications, in one case two microcalcification clusters). 54/87 masses and 34/41 microcalcifications were detected by CAD. Detection rates varied from 9/20 (ACR 1) to 5/7 (ACR 4) (45% vs. 71%). The detection of microcalcifications was not influenced by breast tissue density. CONCLUSION: CAD might be useful in an earlier detection of subtle breast cancer cases, which might remain otherwise undetected.

Influence of antibiotic dose, dosing interval, and duration of therapy on outcome in experimental pneumococcal meningitis in rabbits

We examined the influence of several pharmacokinetic parameters on cure rates in rabbits with experimental pneumococcal meningitis. When the duration of treatment was kept constant, cure rates improved as the individual dose of ampicillin was increased. On the other hand, when four doses of ampicillin at 60 mg/kg of body weight, producing peak concentrations in cerebrospinal fluid (CSF) of approximately 40 times the MBC, were administered at intervals of 24 instead of 4 h and the duration of therapy was thus prolonged from 12 to 72 h, cure rates also increased (85 versus 25%; P less than 0.01). These high cure rates were achieved even though bacterial titers in CSF 24 h after the first dose had reached levels similar to those present at the beginning of therapy. Cure in these animals was explained by the fact that the second ampicillin dose reduced bacterial titers in CSF significantly more than did the first dose (5.2 versus 2.5 log10 CFU/ml; P less than 0.02). The clinical relevance of these observations remains to be determined.