Semiparametric regression estimation in the presence of dependent censoring

We propose a semiparametric estimation procedure for estimatingthe regression of an outcome Y, measured at the end of a fixedfollow-up period, on baseline explanatory variables X, measuredprior to start of follow-up, in the presence of dependent censoringgiven X. The proposed estimators are consistent when the dataare ‘missing at random’ but not ‘missing completelyat random’ (Rubin, 1976), and do not require full specificationof the complete data likelihood. Specifically, we assume thatthe probability of censoring at time t is independent of theoutcome Y conditional on the recorded history up to t of a vectorof time-dependent covariates that are correlated with Y. Ourestimators can be used to adjust for dependent censoring andnonrandom noncompliance in randomised trials studying the effectof a treatment on the mean of a response variable of interest.Even with independent censoring, our methods allow the investigatorto increase efficiency by exploiting the correlation of theoutcome with a vector of time-dependent covariates.     

Nonparametric comparison of two survival-time distributions in the presence of dependent censoring

When testing the null hypothesis that treatment arm-specific survival-time distributions are equal, the log-rank test is asymptotically valid when the distribution of time to censoring is conditionally independent of randomized treatment group given survival time. We introduce a test of the null hypothesis for use when the distribution of time to censoring depends on treatment group and survival time. This test does not make any assumptions regarding independence of censoring time and survival time. Asymptotic validity of this test only requires a consistent estimate of the conditional probability that the survival event is observed given both treatment group and that the survival event occurred before the time of analysis. However, by not making unverifiable assumptions about the data-generating mechanism, there exists a set of possible values of corresponding sample-mean estimates of these probabilities that are consistent with the observed data. Over this subset of the unit square, the proposed test can be calculated and a rejection region identified. A decision on the null that considers uncertainty because of censoring that may depend on treatment group and survival time can then be directly made. We also present a generalized log-rank test that enables us to provide conditions under which the ordinary log-rank test is asymptotically valid. This generalized test can also be used for testing the null hypothesis when the distribution of censoring depends on treatment group and survival time. However, use of this test requires semiparametric modeling assumptions. A simulation study and an example using a recent AIDS clinical trial are provided.     

Nonparametric estimation of a multivariate distribution in the presence of censoring

This paper presents examples of situations in which one wishes to estimate a multivariate distribution from data that may be right-censored. A distinction is made between what we term 'homogeneous' and 'heterogeneous' censoring. It is shown how a multivariate empirical survivor function must be constructed in order to be considered a (nonparametric) maximum likelihood estimate of the underlying survivor function. A closed-form solution, similar to the product-limit estimate of Kaplan and Meier, is possible with homogeneous censoring, but an iterative method, such as the EM algorithm, is required with heterogeneous censoring. An example is given in which an anomaly is produced if censored multivariate data are analyzed as a series of univariate variables; this anomaly is shown to disappear if the methods of this paper are used.     

RDCurve: a nonparametric method to evaluate the stability of ranking procedures

Great concerns have been raised about the reproducibility of gene signatures based on high-throughput techniques such as microarray. Studies analyzing similar samples often report poorly overlapping results, and the p-value usually lacks biological context. We propose a nonparametric ReDiscovery Curve (RDCurve) method, to estimate the frequency of rediscovery of gene signature identified. Given a ranking procedure and a data set with replicated measurements, the RDCurve bootstraps the data set and repeatedly applies the ranking procedure, selects a subset of k important genes, and estimates the probability of rediscovery of the selected subset of genes. We also propose a permutation scheme to estimate the confidence band under the Null hypothesis for the significance of the RDCurve. The method is nonparametric and model-independent. With the RDCurve, we can assess the signal-to-noise ratio of the data, compare the performance of ranking procedures in term of their expected rediscovery rates, and choose the number of genes to be reported.     

Semiparametric model-based inference in the presence of missing responses

We consider a semiparametric model that parameterizes the conditionaldensity of the response, given covariates, but allows the marginaldistribution of the covariates to be completely arbitrary. Responsesmay be missing. A likelihood-based imputation estimator anda semi-empirical-likelihood-based estimator for the parametervector describing the conditional density are defined and provedto be asymptotically normal. Semi-empirical loglikelihood functionsfor the parameter vector and the response mean are derived.It is shown that the two semi-empirical loglikelihood functionsare distributed asymptotically as weighted ² and scaled ², respectively.     

Semiparametric analysis of survival data with left truncation and dependent right censoring

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. Because 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. First, 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.     

Causal inference for non-mortality outcomes in the presence of death

Evaluation of the causal effect of a baseline exposure on a morbidity outcome at a fixed time point is often complicated when study participants die before morbidity outcomes are measured. In this setting, the causal effect is only well defined for the principal stratum of subjects who would live regardless of the exposure. Motivated by gerontologic researchers interested in understanding the causal effect of vision loss on emotional distress in a population with a high mortality rate, we investigate the effect among those who would live both with and without vision loss. Since this subpopulation is not readily identifiable from the data and vision loss is not randomized, we introduce a set of scientifically driven assumptions to identify the causal effect. Since these assumptions are not empirically verifiable, we embed our methodology within a sensitivity analysis framework. We apply our method using the first three rounds of survey data from the Salisbury Eye Evaluation, a population-based cohort study of older adults. We also present a simulation study that validates our method.     

Quantifying the impact of dependent evolution among sites in phylogenetic inference

Nearly all commonly used methods of phylogenetic inference assume that characters in an alignment evolve independently of one another. This assumption is attractive for simplicity and computational tractability but is not biologically reasonable for RNAs and proteins that have secondary and tertiary structures. Here, we simulate RNA and protein-coding DNA sequence data under a general model of dependence in order to assess the robustness of traditional methods of phylogenetic inference to violation of the assumption of independence among sites. We find that the accuracy of independence-assuming methods is reduced by the dependence among sites; for proteins this reduction is relatively mild, but for RNA this reduction may be substantial. We introduce the concept of effective sequence length and its utility for considering information content in phylogenetics.     

Parametric inference of neuronal response latency in presence of a background signal

Neurons are commonly characterized by spontaneous generation of action potentials (spikes), which appear without any apparent or controlled stimulation. When a stimulus is applied, the spontaneous firing may prevail and hamper identification of the effect of the stimulus. Therefore, for any rigorous analysis of evoked neuronal activity, the presence of spontaneous firing has to be taken into account. If the background signal is ignored, however small it is compared to the response activity, and however large is the delay, estimation of the response latency will be wrong, and the error will persist even when sample size is increasing. The first question is: what is the response latency to the stimulus? Answering this question becomes even more difficult if the latency is of a complex nature, for example composed of a physically implied deterministic part and a stochastic part. This scenario is considered here, where the response time is a sum of two components; the delay and the relative latency. Parametric estimators for the time delay and the response latency are derived. These estimators are evaluated on simulated data and their properties are discussed. Finally, we show that the mean of the response latency is always satisfactorily estimated, even assuming a wrong distribution for the response latency.