Robust and efficient estimation of nonparametric generalized linear models.

Generalized linear models are flexible tools for the analysis of diverse datasets, but the classical formulation requires that the parametric component is correctly specified and the data contain no atypical observations. To address these shortcomings, we introduce and study a family of nonparametric full-rank and lower-rank spline estimators that result from the minimization of a penalized density power divergence. The proposed class of estimators is easily implementable, offers high protection against outlying observations and can be tuned for arbitrarily high efficiency in the case of clean data. We show that under weak assumptions, these estimators converge at a fast rate and illustrate their highly competitive performance on a simulation study and two real-data examples. Supplementary Information: The online version contains supplementary material available at 10.1007/s11749-023-00866-x.

Mixed scale joint graphical lasso.

We have developed a method for estimating brain networks from fMRI datasets that have not all been measured using the same set of brain regions. Some of the coarse scale regions have been split in smaller subregions. The proposed penalized estimation procedure selects undirected graphical models with similar structures that combine information from several subjects and several coarseness scales. Both within-scale edges and between-scale edges that identify possible connections between a large region and its subregions are estimated.

Copula based flexible modeling of associations between clustered event times.

Multivariate survival data are characterized by the presence of correlation between event times within the same cluster. First, we build multi-dimensional copulas with flexible and possibly symmetric dependence structures for such data. In particular, clustered right-censored survival data are modeled using mixtures of max-infinitely divisible bivariate copulas. Second, these copulas are fit by a likelihood approach where the vast amount of copula derivatives present in the likelihood is approximated by finite differences. Third, we formulate conditions for clustered right-censored survival data under which an information criterion for model selection is either weakly consistent or consistent. Several of the familiar selection criteria are included. A set of four-dimensional data on time-to-mastitis is used to demonstrate the developed methodology.

Multivariate mixtures of Erlangs for density estimation under censoring.

Multivariate mixtures of Erlang distributions form a versatile, yet analytically tractable, class of distributions making them suitable for multivariate density estimation. We present a flexible and effective fitting procedure for multivariate mixtures of Erlangs, which iteratively uses the EM algorithm, by introducing a computationally efficient initialization and adjustment strategy for the shape parameter vectors. We furthermore extend the EM algorithm for multivariate mixtures of Erlangs to be able to deal with randomly censored and fixed truncated data. The effectiveness of the proposed algorithm is demonstrated on simulated as well as real data sets.

Goodness-of-fit tests for the frailty distribution in proportional hazards models with shared frailty.

Frailty models account for the clustering present in event time data. A proportional hazards model with shared frailties expresses the hazard for each subject. Often a one-parameter gamma distribution is assumed for the frailties. In this paper, we construct formal goodness-of-fit tests to test for gamma frailties. We construct a new class of frailty models that extend the gamma frailty model by using certain polynomial expansions that are orthogonal with respect to the gamma density. For this extended family, we obtain an explicit expression for the marginal likelihood of the data. The order selection test is based on finding the best fitting model in such a series of expanded models. A bootstrap is used to obtain p-values for the tests. Simulations and data examples illustrate the test's performance.

Variable selection with incomplete covariate data.

SUMMARY: Application of classical model selection methods such as Akaike's information criterion (AIC) becomes problematic when observations are missing. In this article we propose some variations on the AIC, which are applicable to missing covariate problems. The method is directly based on the expectation maximization (EM) algorithm and is readily available for EM-based estimation methods, without much additional computational efforts. The missing data AIC criteria are formally derived and shown to work in a simulation study and by application to data on diabetic retinopathy.

On model selection and model misspecification in causal inference.

Standard variable selection procedures, primarily developed for the construction of outcome prediction models, are routinely applied when assessing exposure effects in observational studies. We argue that this tradition is sub-optimal and prone to yield bias in exposure effect estimators as well as their corresponding uncertainty estimators. We weigh the pros and cons of confounder-selection procedures and propose a procedure directly targeting the quality of the exposure effect estimator. We further demonstrate that certain strategies for inferring causal effects have the desirable features (a) of producing (approximately) valid confidence intervals, even when the confounder-selection process is ignored, and (b) of being robust against certain forms of misspecification of the association of confounders with both exposure and outcome.

Variable selection for logistic regression using a prediction-focused information criterion.

In biostatistical practice, it is common to use information criteria as a guide for model selection. We propose new versions of the focused information criterion (FIC) for variable selection in logistic regression. The FIC gives, depending on the quantity to be estimated, possibly different sets of selected variables. The standard version of the FIC measures the mean squared error of the estimator of the quantity of interest in the selected model. In this article, we propose more general versions of the FIC, allowing other risk measures such as the one based on L(p) error. When prediction of an event is important, as is often the case in medical applications, we construct an FIC using the error rate as a natural risk measure. The advantages of using an information criterion which depends on both the quantity of interest and the selected risk measure are illustrated by means of a simulation study and application to a study on diabetic retinopathy.