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The Survey of Income and Program Participation (SIPP) is a survey with a longitudinal structure and complex nonignorable design, for which correct estimation requires using the weights. The longitudinal setting also suggests conditional-independence relations between survey variables and early- versus late-wave employment classifications. We state original assumptions justifying an extension of the partially model-based approach of Pfeffermann, Skinner and Humphreys [J. Roy. Statist. Soc. Ser. A 161 (1998) 13–32], accounting for the design of SIPP and similar longitudinal surveys. Our assumptions support the use of log-linear models of longitudinal survey data. We highlight the potential they offer for simultaneous bias-control and reduction of sampling error relative to direct methods when applied to small subdomains and cells. Our assumptions allow us to innovate by showing how to rigorously use only a longitudinal survey to estimate a complex log-linear longitudinal association structure and embed it in cross-sectional totals to construct estimators that can be more efficient than direct estimators for small cells.

After a brief historical survey of parametric survival models, from actuarial, biomedical, demographical and engineering sources, this paper discusses the persistent reasons why parametric models still play an important role in exploratory statistical research. The phase-type models are advanced as a flexible family of latent-class models with interpretable components. These models are now supported by computational statistical methods that make numerical calculation of likelihoods and statistical estimation of parameters feasible in theory for quite complicated settings. However, consideration of Fisher Information and likelihood-ratio type tests to discriminate between model families indicates that only the simplest phase-type model topologies can be stably estimated in practice, even on rather large datasets. An example of a parametric model with features of mixtures, multiple stages or 'hits', and a trapping-state is given to illustrate simple computational tools in R, both on simulated data and on a large SEER 1992-2002 breast-cancer dataset.

This paper develops methodology for survey estimation and small-area prediction using Fay–Herriot (1979) models in which the responses are left-censored. Parameter and small-area estimators are derived both by censored-data likelihoods and by an estimating-equation approach which adjusts a Fay–Herriot analysis restricted to the uncensored observations. Formulas for variances of estimators and mean-squared errors of small-area predictions are provided and supported by a simulation study. The methodology is applied to provide diagnostics for the left-censored Fay–Herriot model which are illustrated in the context of the Census Bureau's ongoing Small-Area Income and Poverty Estimation (SAIPE) project.

Summary The problem of accurately estimating the mean-squared error of small area estimators within a Fay–Herriot normal error model is studied theoretically in the common setting where the model is fitted to a logarithmically transformed response variable. For bias-corrected empirical best linear unbiased predictor small area point estimators, mean-squared error formulae and estimators are provided, with biases of smaller order than the reciprocal of the number of small areas. The performance of these mean-squared error estimators is illustrated by a simulation study and a real data example relating to the county level estimation of child poverty rates in the US Census Bureau's on-going ‘Small area income and poverty estimation’ project.

In many clinical trials involving survival endpoints, one has additional data on some binary indicator of'response', such as initial tumour shrinkage in cancer trials. This paper studies the case of randomised clinical trials where the response indicator is available shortly after randomisation, and where one can assume that, within each stratum defined by the response indicator, a two treatment-group proportional-hazards model holds. The same model may also describe some incompletely randomised or observational studies. Asymptotic relative efficiencies for Kaplan-Meier-based estimators versus maximum partial likelihood estimators are examined under this model for estimating either the difference in survival probabilities at a specified time or the parameter estimated by the logrank numerator. It is shown that the efficiency gains using the model are more promising when estimating the difference in survival probabilities. An example is given comparing the long-term survival experience of two groups of patients with advanced Hodgkin's disease.

The prevalence of survival analyses based on a fixed duration of time-on-test, together with the need for generally powerful two-sample censored-data rank tests against stochastically ordered but not proportional-hazard alternatives, are used to motivate an extension of ‘precedence tests’ (Nelson (1963), Lin and Sukhatme (1989)) to right-censored survival data. The idea is to compare the r -th Kaplan-Meier quantile from the first sample with the s -th Kaplan-Meier quantile from the second sample, where r and s are nearby values chosen to give size α and best power against local proportional-hazards alternatives.

This article reflects the views of the authors and should not be construed to be those of the US Food and Drug Administration. Copyright © 2015 John Wiley & Sons, Ltd.

This paper discusses two mechanisms with time-dependent covariates for dependence between competing-risk latent failure times under which the marginal survival functions are identifiable. The first is the finite-state nonhomogeneous Markov chain with two absorbing failure states, A and B, where “marginal survival function for A” is the probability that failure due to A does not occur before t when transitions to B are suppressed. Even in highly stratified models, the nonparametric survival estimator due to Aalen & Johansen (1978) is readily computable when transitions between each pair (i,j) states can occur only in one direction.

It is well known that survival data randomly censored from the right by deaths from a competing risk do not allow nonparametric identifiability of marginal survival distributions when survival times and competing-risk censoring times are dependent (Tsiatis 1975). Parametric models for the joint distribution of survival and competing-risk censoring times cannot solve the problem since the goodness of fit of such models cannot be tested with observable data. Nevertheless, there are many such settings where marginal “latent” survival distributions are a desirable object of inference, expressing most clearly the underlying biological failure mechanism disentangled from physiologically distinct effects. One hope to overcome the obstacle of nonidentifiability is to make use of observable covariate data which are prognostic only for the latent survival times and not for the competing risk. In this paper, it is shown how the marginal distribution of the latent survival time T can be nonparametrically identifiable when only the data min(T, C), I[T≤C], and V are observed, where C is a latent competing-risk censoring time and V is an observed covariate such that C and V are conditionally independent given T.

Several new methodological issues that arise within two-way factorial designs for survival experiments are discussed within the framework of asymptotic theory for the proportional hazards model with two binary treatment covariates. These issues include: the proper formulation of null hypotheses and alternatives, the choice among log-rank and adjusted or stratified log-rank statistics, the asymptotic correlation between test statistics for the separate main effects, the asymptotic power (under the various possible methods of analysis) of tests to detect main effects and interactions, the comparison of power to detect main effects within a 2 x 2 factorial design with power in a three-group trial where no patients are randomized simultaneously to both treatments, and the problems of analysis arising when accrual or exposure to one of the treatments is terminated early for ethical reasons.

A new class of reliability point-process models for dependent components is introduced. The dependence is expressed through a regression, following a form suggested by Cox (1972) for survival data analysis involving the current life-length of the components. After formulating the current-life process as a Markov process with stationary transitions and stating some general results on asymptotic behavior, we describe the stationary distributions in some bivariate examples. Finally, we discuss statistical inference for the new models, exhibiting and justifying full- and partial-likelihood methods for their analysis.

SUMMARY In many contexts where there is interest in inferring the marginal distribution of a survival time T subject to censoring embodied in a latent waiting time C, the times T and C may not be independent. This paper presents a new class of nonparametric assumptions on the conditional distribution of T given C and shows how they lead to consistent generalizations of the Kaplan & Meier (1958) survival curve estimator. The new survival curve estimators are used under weak assumptions to construct bounds on the marginal survival which can be much narrower than those of Peterson (1976). In stratified populations where T and C are independent only within strata examples indicate that the Kaplan-Meier estimator is often approximately consistent.

In two-sample semiparametric survival models other than the Cox proportional-hazards regression model, it is shown that partial-likelihood inference of structural parameters in the presence of fully nonpararnetric nuisance-hazards typically has relative efficiency zero compared with fuii-Iikelihood infer -ence. The practical Interpretation of efficiencies in the pres-ence of infinite-dimensional nuisance-parameters is discussed, with reference to two important examples, namely a recent sur-vival regression-model of Clayton and Cuzick and a class of additive excess-risk models. Under the excess-risk models, a formula is derived for the large-sample information [which here is the same as the limiting Fisher information when the nuisance-parameter dimension gets large] for estimating the parameter of difference between two samples, as the nuisance function becomes fully nonpararnetric.

The small-sample performance of some recently proposed nonparametric methods of constructing confidence intervals for the median survival time, based on randomly right-censored data, is compared with that of two new methods. Most of these methods are equivalent for large samples. All proposed intervals are either 'test-based' or 'reflected' intervals, in the sense defined in the paper. Coverage probabilities for the interval estimates were obtained by exact calculation for uncensored data, and by stimulation for three life distributions and four censoring patterns. In the range of situations studied, 'test-based' methods often have less than nominal coverage, while the coverage of the new 'reflected' confidence intervals is closer to nominal (although somewhat conservative), and these intervals are easy to compute.