Volume 16, Issue 2

The Highly-Adaptive least absolute shrinkage and selection operator (LASSO) Targeted Minimum Loss Estimator (HAL-TMLE) is an efficient plug-in estimator of a pathwise differentiable parameter in a statistical model that at minimal (and possibly only) assumes that the sectional variation norm of the true nuisance functions (i.e., relevant part of data distribution) are finite. It relies on an initial estimator (HAL-MLE) of the nuisance functions by minimizing the empirical risk over the parameter space under the constraint that the sectional variation norm of the candidate functions are bounded by a constant, where this constant can be selected with cross-validation. In this article we establish that the nonparametric bootstrap for the HAL-TMLE, fixing the value of the sectional variation norm at a value larger or equal than the cross-validation selector, provides a consistent method for estimating the normal limit distribution of the HAL-TMLE. In order to optimize the finite sample coverage of the nonparametric bootstrap confidence intervals, we propose a selection method for this sectional variation norm that is based on running the nonparametric bootstrap for all values of the sectional variation norm larger than the one selected by cross-validation, and subsequently determining a value at which the width of the resulting confidence intervals reaches a plateau. We demonstrate our method for 1) nonparametric estimation of the average treatment effect when observing a covariate vector, binary treatment, and outcome, and for 2) nonparametric estimation of the integral of the square of the multivariate density of the data distribution. In addition, we also present simulation results for these two examples demonstrating the excellent finite sample coverage of bootstrap-based confidence intervals.

We introduce a Bayesian framework for simultaneous feature selection and outlier detection in sparse high-dimensional regression models, with a focus on quantitative trait locus (QTL) mapping in experimental crosses. More specifically, we incorporate the robust mean shift outlier handling mechanism into the multiple QTL mapping regression model and apply LASSO regularization concurrently to the genetic effects and the mean-shift terms through the flexible extended Bayesian LASSO (EBL) prior structure, thereby combining QTL mapping and outlier detection into a single sparse model representation problem. The EBL priors on the mean-shift terms prevent outlying phenotypic values from distorting the genotype-phenotype association and allow their detection as cases with outstanding mean shift values following the LASSO shrinkage. Simulation results demonstrate the effectiveness of our new methodology at mapping QTLs in the presence of outlying phenotypic values and simultaneously identifying the potential outliers, while maintaining a comparable performance to the standard EBL on outlier-free data.

In this work, we propose a spatio-temporal Markovian-like model for ordinal observations to predict in time the spread of disease in a discrete rectangular grid of plants. This model is constructed from a logistic distribution and some simple assumptions that reflect the conditions present in a series of studies carried out to understand the dissemination of a particular infection in plants. After constructing the model, we establish conditions for the existence and uniqueness of the maximum likelihood estimator (MLE) of the model parameters. In addition, we show that, under further restrictions based on Partially Ordered Markov Models (POMMs), the MLE of the model is consistent and normally asymptotic. We then employ the MLE’s asymptotic normality to propose methods for testing spatio-temporal and spatial dependencies. The model is estimated from the real data on plants that inspired the model, and we used its results to construct prediction maps to better understand the transmission of plant illness in time and space.

We consider joint selection of fixed and random effects in general mixed-effects models. The interpretation of estimated mixed-effects models is challenging since changing the structure of one set of effects can lead to different choices of important covariates in the model. We propose a stepwise selection algorithm to perform simultaneous selection of the fixed and random effects. It is based on Bayesian Information criteria whose penalties are adapted to mixed-effects models. The proposed procedure performs model selection in both linear and nonlinear models. It should be used in the low-dimension setting where the number of ovariates and the number of random effects are moderate with respect to the total number of observations. The performance of the algorithm is assessed via a simulation study, which includes also a comparative study with alternatives when available in the literature. The use of the method is illustrated in the clinical study of an antibiotic agent kinetics.

A recent paper proposed an extended trivariate generalized linear mixed model (TGLMM) for synthesis of diagnostic test accuracy studies in the presence of non-evaluable index test results. Inspired by the aforementioned model we propose an extended trivariate vine copula mixed model that includes the TGLMM as special case, but can also operate on the original scale of sensitivity, specificity, and disease prevalence. The performance of the proposed vine copula mixed model is examined by extensive simulation studies in comparison with the TGLMM. Simulation studies showed that the TGLMM leads to biased meta-analytic estimates of sensitivity, specificity, and prevalence when the univariate random effects are misspecified. The vine copula mixed model gives nearly unbiased estimates of test accuracy indices and disease prevalence. Our general methodology is illustrated by meta-analysing coronary CT angiography studies.

Survival analysis is a widely used method to establish a connection between a time to event outcome and a set of potential covariates. Accurately predicting the time of an event of interest is of primary importance in survival analysis. Many different algorithms have been proposed for survival prediction. However, for a given prediction problem it is rarely, if ever, possible to know in advance which algorithm will perform the best. In this paper we propose two algorithms for constructing super learners in survival data prediction where the individual algorithms are based on proportional hazards. A super learner is a flexible approach to statistical learning that finds the best weighted ensemble of the individual algorithms. Finding the optimal combination of the individual algorithms through minimizing cross-validated risk controls for over-fitting of the final ensemble learner. Candidate algorithms may range from a basic Cox model to tree-based machine learning algorithms, assuming all candidate algorithms are based on the proportional hazards framework. The ensemble weights are estimated by minimizing the cross-validated negative log partial likelihood. We compare the performance of the proposed super learners with existing models through extensive simulation studies. In all simulation scenarios, the proposed super learners are either the best fit or near the best fit. The performances of the newly proposed algorithms are also demonstrated with clinical data examples.

We study and compare several variants of random forests tailored to prognostic models for ordinal outcomes. Models of the conditional odds function are employed to understand the various random forest flavours. Existing random forest variants for ordinal outcomes, such as Ordinal Forests and Conditional Inference Forests, are evaluated in the presence of a non-proportional odds impact of prognostic variables. We propose two novel random forest variants in the model-based transformation forest family, only one of which explicitly assumes proportional odds. These two novel transformation forests differ in the specification of the split procedures for the underlying ordinal trees. One of these split criteria is able to detect changes in non-proportional odds situations and the other one focuses on finding proportional-odds signals. We empirically evaluate the performance of the existing and proposed methods using a simulation study and illustrate the practical aspects of the procedures by a re-analysis of the respiratory sub-item in functional rating scales of patients suffering from Amyotrophic Lateral Sclerosis (ALS).

For more than 50 years the Mean Measure of Divergence (MMD) has been one of the most prominent tools used in anthropology for the study of non-metric traits. However, one of the problems, in anthropology including palaeoanthropology (more often there), is the lack of big enough samples or the existence of samples without sufficiently measured traits. Since 1969, with the advent of bootstrapping techniques, this issue has been tackled successfully in many different ways. Here, we present a parametric bootstrap technique based on the fact that the transformed θ , obtained from the Anscombe transformation to stabilize the variance, nearly follows a normal distribution with standard deviation $\sigma = 1 / \sqrt{N + 1/2}$ σ = 1 / N + 1 / 2 , where N is the size of the measured trait. When the probabilistic distribution is known, parametric procedures offer more powerful results than non-parametric ones. We profit from knowing the probabilistic distribution of θ to develop a parametric bootstrapping method. We explain it carefully with mathematical support. We give examples, both with artificial data and with real ones. Our results show that this parametric bootstrap procedure is a powerful tool to study samples with scarcity of data.

It is shown how Passing’s and Bablok’s robust regression method may be derived from the condition that Kendall’s correlation coefficient tau shall vanish upon a scaling and rotation of the data. If the ratio of the standard deviations of the regressands is known, a similar procedure leads to a robust alternative to Deming regression, which is known as the circular median of the doubled slope angle in the field of directional statistics. The derivation of the regression estimates from Kendall’s correlation coefficient makes it possible to give analytical estimates of the variances of the slope, intercept, and of the bias at medical decision point, which have not been available to date. Furthermore, it is shown that using Knight’s algorithm for the calculation of Kendall’s tau makes it possible to calculate the Passing–Bablok estimator in quasi-linear time. This makes it possible to calculate this estimator rapidly even for very large data sets. Examples with data from clinical medicine are also provided.

Exact formulae relating parameters in conditional and reduced generalized linear models are introduced where the reduced model omits a continuous mediator from the conditional model. For certain link functions including logit, the natural direct effect and the natural indirect effect of the counterfactual method are smaller in magnitude than, respectively, the direct effect used by the difference method and the indirect effect by the product method. Contrary to what is implicitly assumed in Jiang and VanderWeele [11] for logit link, the total effect of the counterfactual method and the total effect used for the difference method are generally not the same. They are equal to each other only under special situations. For accelerated failure time models the difference method and the product method are equivalent regardless of censoring or not, a result stated in VanderWeele [6] in the absence of censorship but proved in a misleading manner. For proportional hazards models, maximum likelihood analysis indicates that these two methods can be equivalent in the absence of censorship. In the case of logit link, one can focus on the treatment effect on the marginalized odds instead of the odds of the marginalized event so that the product method would be equivalent to the difference method. Similarly, for the proportional hazards model, one can focus on the treatment effect on the marginalized hazards instead of the hazards for the reduced model.

This article aims to provide rigorous and convenient statistical models for dealing with high-variability phenomena. The presence of discrepance in variance represents a substantial issue when it is not possible to reduce variability before analysing the data, leading to the possibility to estimate an inadequate model. In this paper, the application of Generalized Additive Model for Location, Scale and Shape (GAMLSS) and the use of finite mixture model for GAMLSS will be proposed as a solution to the problem of overdispersion. An application to Liver fibrosis data is illustrated in order to identify potential risk factors for patients, which could determine the presence of the disease but also its levels of severity.

This paper discusses variable or covariate selection for high-dimensional quadratic Cox model. Although many variable selection methods have been developed for standard Cox model or high-dimensional standard Cox model, most of them cannot be directly applied since they cannot take into account the important and existing hierarchical model structure. For the problem, we present a penalized log partial likelihood-based approach and in particular, generalize the regularization algorithm under marginality principle (RAMP) proposed in Hao et al. (J Am Stat Assoc 2018;113:615–25) under the context of linear models. An extensive simulation study is conducted and suggests that the presented method works well in practical situations. It is then applied to an Alzheimer’s Disease study that motivated this investigation.