Karim Anaya-Izquierdo

Self-Controlled Case Series Analysis With Event-Dependent Observation Periods

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 event-dependent 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.

Antipsychotic drugs and risks of myocardial infarction: a self-controlled case series study

Aim Antipsychotics 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 results All 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. Conclusion We 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.

Local mixture models of exponential families

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.

Estimation of basic reproduction numbers: Individual heterogeneity and robustness to perturbation of the contact function

The basic reproduction number of an infection in a given population, R0, is inflated by individual heterogeneity in contact rates. Recently, new methods for estimating R0 using social contact data and serological survey data have been proposed. These methods, like most of their predecessors, ignore individual heterogeneity, and are sensitive to perturbation of the contact function. Using a frailty framework, we derive expressions for R0 in the presence of age-varying heterogeneity. In this case, R0 is the spectral radius of a population version of the next generation operator, which involves the variance function of the age-dependent frailty. This variance can be estimated within a shared frailty framework from paired data on two infections transmitted by the same route. We propose two estimators of R0 for infections in endemic equilibrium. We investigate their performance by simulation, and find that one is generally less efficient but more robust than the other to perturbation of the effective contact function. These methods are applied to data on varicella zoster virus infection from two European countries.

Computational information geometry in statistics: foundations

This paper lays the foundations for a new framework for numerically and computationally applying information geometric methods to statistical modelling.

Comments on 'Log transformation: application and interpretation in biomedical research'.

1. Feng C, Wang H, Lu N, Tu XM. Log transformation: application and interpretation in biomedical research. Statistics in Medicine 2013; 32:230–239. 2. Bland JM, Altman DG. Transformations, means, and confidence intervals. British Medical Journal 1996; 312:1079. 3. Steyermark AC, Miamen AG, Feghahati HS, Lewno AW. Physiological and morphological correlates of among-individual variation in standard metabolic rate in the leopard frog Rana pipiens. The Journal of Experimental Biology 2005; 208:1201–1208. 4. Sokal RR, Rohlf FJ. Biometry: The Principles and Practices of Statistics in Biological Research, 3rd ed. W. H. Freeman and Co: New York, 1995. 5. Sokal RR, Rohlf FJ. Biometry: The Principles and Practices of Statistics in Biological Research, 4th ed. W. H. Freeman and Co: New York, 2012.

Computational Information Geometry in Statistics: Mixture Modelling

This paper applies the tools of computation information geometry [3] – in particular, high dimensional extended multinomial families as proxies for the ‘space of all distributions’ – in the inferentially demanding area of statistical mixture modelling. A range of resultant benefits are noted.

On the Geometric Interplay Between Goodness-of-Fit and Estimation: Illustrative Examples

We show how information geometry throws new light on the interplay between goodness-of-fit and estimation, a fundamental issue in statistical inference. A geometric analysis of simple, yet representative, models involving the same population parameter compellingly establishes the main theme of the paper: namely, that goodness-of-fit is necessary but not sufficient for model selection. Visual examples vividly communicate this. Specifically, for a given estimation problem, we define a class of least-informative models, linking these to both nonparametric and maximum entropy methods. Any other model is then seen to involve an informative rotation, often embodying extra-data considerations. We also look at the way that translation of models generates a form of bias-variance trade-off. Overall, our approach is a global extension of pioneering local work by Copas and Eguchi which, we note, was also geometrically inspired.

Towards the Geometry of Model Sensitivity: An Illustration

In statistical practice model building, sensitivity and uncertainty are major concerns of the analyst. This paper looks at these issues from an information geometric point of view. Here, we define sensitivity to mean understanding how inference about a problem of interest changes with perturbations of the model. In particular it is an example of what we call computational information geometry. The embedding of simple models in much larger information geometric spaces is shown to illuminate these critically important issues.

Using Geometry to Select One Dimensional Exponential Families That Are Monotone Likelihood Ratio in the Sample Space, Are Weakly Unimodal and Can Be Parametrized by a Measure of Central Tendency

One dimensional exponential families on finite sample spaces are studied using the geometry of the simplex Δn°-1 and that of a transformation Vn-1 of its interior. This transformation is the natural parameter space associated with the family of multinomial distributions. The space Vn-1 is partitioned into cones that are used to find one dimensional families with desirable properties for modeling and inference. These properties include the availability of uniformly most powerful tests and estimators that exhibit optimal properties in terms of variability and unbiasedness.