Statistics

Standard Mendelian randomization analysis can produce biased results if the genetic variant defining the instrumental variable (IV) is confounded and/or has a horizontal pleiotropic effect on the outcome of interest not mediated by the treatment. We provide novel identification conditions for the causal effect of a treatment in presence of unmeasured confounding, by leveraging an invalid IV for which both the IV independence and exclusion restriction assumptions may be violated. The proposed Mendelian Randomization Mixed-Scale Treatment Effect Robust Identification (MR MiSTERI) approach relies on (i) an assumption that the treatment effect does not vary with the invalid IV on the additive scale; and (ii) that the selection bias due to confounding does not vary with the invalid IV on the odds ratio scale; and (iii) that the residual variance for the outcome is heteroscedastic and thus varies with the invalid IV. We formally establish that their conjunction can identify a causal effect even with an invalid IV subject to pleiotropy. MiSTERI is shown to be particularly advantageous in presence of pervasive heterogeneity of pleiotropic effects on additive scale, a setting in which two recently proposed robust estimation methods MR GxE and MR GENIUS can be severely biased. In order to incorporate multiple, possibly correlated and weak IVs, a common challenge in MR studies, we develop a MAny Weak Invalid Instruments (MR MaWII MiSTERI) approach for strengthened identification and improved accuracy MaWII MiSTERI is shown to be robust to horizontal pleiotropy, violation of IV independence assumption and weak IV bias. Both simulation studies and real data analysis results demonstrate the robustness of the proposed MR MiSTERI methods.

While there have been a lot of recent developments in the context of Bayesian model selection and variable selection for high dimensional linear models, there is not much work in the presence of change point in literature, unlike the frequentist counterpart. We consider a hierarchical Bayesian linear model where the active set of covariates that affects the observations through a mean model can vary between different time segments. Such structure may arise in social sciences/ economic sciences, such as sudden change of house price based on external economic factor, crime rate changes based on social and built-environment factors, and others. Using an appropriate adaptive prior, we outline the development of a hierarchical Bayesian methodology that can select the true change point as well as the true covariates, with high probability. We provide the first detailed theoretical analysis for posterior consistency with or without covariates, under suitable conditions. Gibbs sampling techniques provide an efficient computational strategy. We also consider small sample simulation study as well as application to crime forecasting applications.

A new bivariate copula is proposed for modeling negative dependence between two random variables. We show that it complies with most of the popular notions of negative dependence reported in the literature and study some of its basic properties. Specifically, the Spearman's rho and the Kendall's tau for the proposed copula have a simple one-parameter form with negative values in the full range. Some important ordering properties comparing the strength of negative dependence with respect to the parameter involved are considered. Simple examples of the corresponding bivariate distributions with popular marginals are presented. Application of the proposed copula is illustrated using a real data set.

We propose a new L 2 -type goodness-of-fit test for the family of beta distributions based on a conditional moment characterisation. The asymptotic null distribution is identified, and since it depends on the underlying parameters, a parametric bootstrap procedure is proposed. Consistency against all alternatives that satisfy a convergence criterion is shown, and a Monte Carlo simulation study indicates that the new procedure outperforms most of the classical tests. Finally, the procedure is applied to a real data set related to air humidity.

We propose to study quantile oriented sensitivity indices (QOSA indices) and quantile oriented Shapley effects (QOSE). Some theoretical properties of QOSA indices will be given and several calculations of QOSA indices and QOSE will allow to better understand the behaviour and the interest of these indices.

Popular measures of meta-analysis heterogeneity, such as I 2 , cannot be considered measures of population heterogeneity since they are dependant on samples sizes within studies. The coefficient of variation (CV) recently introduced and defined to be the heterogeneity variance divided by the absolute value of the overall mean effect does not suffer such shortcomings. However, very large CV values can occur when the effect is small making interpretation difficult. The purpose of this paper is two-fold. Firstly, we consider variants of the CV that exist in the interval (0, 1] making interpretation simpler. Secondly, we provide interval estimators for the CV and its variants with excellent coverage properties. We perform simulation studies based on simulated and real data sets and draw comparisons between the methods.

Penalized logistic regression methods are frequently used to investigate the relationship between a binary outcome and a set of explanatory variables. The model performance can be assessed by measures such as the concordance statistic (c-statistic), the discrimination slope and the Brier score. Often, data resampling techniques, e.g. crossvalidation, are employed to correct for optimism in these model performance criteria. Especially with small samples or a rare binary outcome variable, leave-one-out crossvalidation is a popular choice. Using simulations and a real data example, we compared the effect of different resampling techniques on the estimation of c-statistics, discrimination slopes and Brier scores for three estimators of logistic regression models, including the maximum likelihood and two maximum penalized-likelihood estimators. Our simulation study confirms earlier studies reporting that leave-one-out crossvalidated c-statistics can be strongly biased towards zero. In addition, our study reveals that this bias is more pronounced for estimators shrinking predicted probabilities towards the observed event rate, such as ridge regression. Leave-one-out crossvalidation also provided pessimistic estimates of the discrimination slope but nearly unbiased estimates of the Brier score. We recommend to use leave-pair-out crossvalidation, five-fold crossvalidation with repetition, the enhanced or the .632+ bootstrap to estimate c-statistics and leave-pair-out or five-fold crossvalidation to estimate discrimination slopes.

We discuss issues of structural and practical identifiability of partially observed differential equations which are often applied in systems biology. The development of mathematical methods to investigate structural non-identifiability has a long tradition. Computationally efficient methods to detect and cure it have been developed recently. Practical non-identifiability on the other hand has not been investigated at the same conceptually clear level. We argue that practical identifiability is more challenging than structural identifiability when it comes to modelling experimental data. We discuss that the classical approach based on the Fisher information matrix has severe shortcomings. As an alternative, we propose using the profile likelihood, which is a powerful approach to detect and resolve practical non-identifiability.

Suppose that we are interested in the average causal effect of a binary treatment on an outcome when this relationship is confounded by a binary confounder. Suppose that the confounder is unobserved but a non-differential binary proxy of it is observed. We identify conditions under which adjusting for the proxy comes closer to the incomputable true average causal effect than not adjusting at all. Unlike other works, we do not assume that the average causal effect of the confounder on the outcome is in the same direction among treated and untreated.

In Bayesian inference, an unknown measurement uncertainty is often quantified in terms of a Gamma distributed precision parameter, which is impractical when prior information on the standard deviation of the measurement uncertainty shall be utilised during inference. This paper thus introduces a method for transforming between a gamma distributed precision parameter and the distribution of the associated standard deviation. The proposed method is based on numerical optimisation and shows adequate results for a wide range of scenarios.