The self-controlled case series method may be used to study the association between a time-varying exposure and a health event. It is based only on cases, and it controls for fixed confounders. Exposure and event histories are collected for each case over a predefined observation period. The method requires that observation periods should be independent of event times. This requirement is violated when events increase the mortality rate, since censoring of the observation periods is then event dependent. In this article, the case series method for rare nonrecurrent events is extended to remove this independence assumption, thus introducing an additional term in the likelihood that depends on the censoring process. In order to remain within the case series framework in which only cases are sampled, the model is reparameterized so that this additional term becomes estimable from the distribution of intervals from event to end of observation. The exposure effect of primary interest may be estimated unbiasedly. The age effect, however, takes on a new interpretation, incorporating the effect of censoring. The model may be fitted in standard loglinear modeling software; this yields conservative standard errors. We describe a detailed application to the study of antipsychotics and stroke. The estimates obtained from the standard case series model are shown to be biased when eventdependent observation periods are ignored. When they are allowed for, antipsychotic use remains strongly positively associated with stroke in patients with dementia, but not in patients without dementia. Two detailed simulation studies are included as Supplemental Material.

General multivariate distributions are notoriously expensive to sample from, particularly the high-dimensional posterior distributions in PDE-constrained inverse problems. This paper develops a sampler for arbitrary continuous multivariate distributions that is based on low-rank surrogates in the tensor-train format, a methodology that has been exploited for many years for scalable, high-dimensional density function approximation in quantum physics and chemistry. We build upon recent developments of the cross approximation algorithms in linear algebra to construct a tensor-train approximation to the target probability density function using a small number of function evaluations. For sufficiently smooth distributions the storage required for accurate tensor-train approximations is moderate, scaling linearly with dimension. In turn, the structure of the tensor-train surrogate allows sampling by an efficient conditional distribution method since marginal distributions are computable with linear complexity in dimension. Expected values of non-smooth quantities of interest, with respect to the surrogate distribution, can be estimated using transformed independent uniformly-random seeds that provide Monte Carlo quadrature, or transformed points from a quasi-Monte Carlo lattice to give more efficient quasi-Monte Carlo quadrature. Unbiased estimates may be calculated by correcting the transformed random seeds using a Metropolis-Hastings accept/reject step, while the quasi-Monte Carlo quadrature may be corrected either by a control-variate strategy, or by importance weighting. We show that the error in the tensor-train approximation propagates linearly into the Metropolis-Hastings rejection rate and the integrated autocorrelation time of the resulting Markov chain; thus the integrated autocorrelation time may be made arbitrarily close to 1, implying that, asymptotic in sample size, the cost per effectively independent sample is one target density evaluation plus the cheap tensor-train surrogate proposal that has linear cost with dimension. These methods are demonstrated in three computed examples: fitting failure time of shock absorbers; a PDE-constrained inverse diffusion problem; and sampling from the Rosenbrock distribution. The delayed rejection adaptive Metropolis (DRAM) algorithm is used as a benchmark. In all computed examples, the importance-weight corrected quasi-Monte Carlo quadrature performs best, and is more efficient than DRAM by orders of magnitude across a wide range of approximation accuracies and sample sizes. Indeed, all the methods developed here significantly outperform DRAM in all computed examples.

Summary.  The relative frailty variance among survivors provides a readily interpretable measure of how the heterogeneity of a population, as represented by a frailty model, evolves over time. We discuss the properties of the relative frailty variance, show that it characterizes frailty distributions and that, suitably rescaled, it may be used to compare patterns of dependence across models and data sets. In shared frailty models, the relative frailty variance is closely related to the cross‐ratio function, which is estimable from bivariate survival data. We investigate the possible shapes of the relative frailty variance function for the purpose of model selection, and we review available frailty distribution families in this context. We introduce several new families with contrasting properties, including simple but flexible time varying frailty models. The benefits of the approach that we propose are illustrated with two applications to bivariate current status data obtained from serological surveys.

AimAntipsychotics increase the risk of stroke. Their effect on myocardial infarction remains uncertain because people prescribed and not prescribed antipsychotic drugs differ in their underlying vascular risk making between-person comparisons difficult to interpret. The aim of our study was to investigate this association using the self-controlled case series design that eliminates between-person confounding effects.Methods and resultsAll the patients with a first recorded myocardial infarction and prescription for an antipsychotic identified in the Clinical Practice Research Datalink linked to the Myocardial Ischaemia National Audit Project were selected for the self-controlled case series. The incidence ratio of myocardial infarction during risk periods following the initiation of antipsychotic use relative to unexposed periods was estimated within individuals. A classical case–control study was undertaken for comparative purposes comparing antipsychotic exposure among cases and matched controls. We identified 1546 exposed cases for the self-controlled case series and found evidence of an association during the first 30 days after the first prescription of an antipsychotic, for first-generation agents [incidence rate ratio (IRR) 2.82, 95% confidence interval (CI) 2.0–3.99] and second-generation agents (IRR: 2.5, 95% CI: 1.18–5.32). Similar results were found for the case–control study for new users of first- (OR: 3.19, 95% CI: 1.9–5.37) and second-generation agents (OR: 2.55, 95% CI: 0.93–7.01) within 30 days of their myocardial infarction.ConclusionWe found an increased risk of myocardial infarction in the period following the initiation of antipsychotics that was not attributable to differences between people prescribed and not prescribed antipsychotics.

Exponential families are the workhorses of parametric modelling theory. One reason for their popularity is their associated inference theory, which is very clean, both from a theoretical and a computational point of view. One way in which this set of tools can be enriched in a natural and interpretable way is through mixing. This paper develops and applies the idea of local mixture modelling to exponential families. It shows that the highly interpretable and flexible models which result have enough structure to retain the attractive inferential properties of exponential families. In particular, results on identification, parameter orthogonality and log-concavity of the likelihood are proved.Comment: Published at http://dx.doi.org/10.3150/07-BEJ6170 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Orthogonal and partly orthogonal reparametrisations are provided for certain wide and important families of univariate continuous distributions. First, the orthogonality of parameters in location-scale symmetric families is extended to symmetric distributions involving a third parameter. This sets the scene for consideration of the four-parameter situation in which skewness is also allowed. It turns out that one specific approach to generating such fourparameter families, that of two-piece distributions with a certain parametrisation restriction, has some attractive features with regard to parameter orthogonality. This work also affords partly orthogonal parametrisations of three-parameter two-piece models.

This paper looks at boundary effects on inference in an important class of models including, notably, logistic regression. Asymptotic results are not uniform across such models. Accordingly, whatever their order, methods asymptotic in sample size will ultimately “break down” as the boundary is approached, in the sense that effects such as infinite skewness, discreteness and collinearity will dominate. In this paper, a highly interpretable diagnostic tool is proposed, allowing the analyst to check if the boundary is going to have an appreciable effect on standard inferential techniques. Copyright © 2014 John Wiley & Sons Ltd.

No abstract