No Arabic abstract
To estimate direct and indirect effects of an exposure on an outcome from observed data strong assumptions about unconfoundedness are required. Since these assumptions cannot be tested using the observed data, a mediation analysis should always be accompanied by a sensitivity analysis of the resulting estimates. In this article we propose a sensitivity analysis method for parametric estimation of direct and indirect effects when the exposure, mediator and outcome are all binary. The sensitivity parameters consist of the correlation between the error terms of the mediator and outcome models, the correlation between the error terms of the mediator model and the model for the exposure assignment mechanism, and the correlation between the error terms of the exposure assignment and outcome models. These correlations are incorporated into the estimation of the model parameters and identification sets are then obtained for the direct and indirect effects for a range of plausible correlation values. We take the sampling variability into account through the construction of uncertainty intervals. The proposed method is able to assess sensitivity to both mediator-outcome confounding and confounding involving the exposure. To illustrate the method we apply it to a mediation study based on data from the Swedish Stroke Register (Riksstroke).
Sensitivity indices are commonly used to quantity the relative inuence of any specic group of input variables on the output of a computer code. In this paper, we focus both on computer codes the output of which is a cumulative distribution function and on stochastic computer codes. We propose a way to perform a global sensitivity analysis for these kinds of computer codes. In the rst setting, we dene two indices: the rst one is based on Wasserstein Fr{e}chet means while the second one is based on the Hoeding decomposition of the indicators of Wasserstein balls. Further, when dealing with the stochastic computer codes, we dene an ideal version of the stochastic computer code thats ts into the frame of the rst setting. Finally, we deduce a procedure to realize a second level global sensitivity analysis, namely when one is interested in the sensitivity related to the input distributions rather than in the sensitivity related to the inputs themselves. Several numerical studies are proposed as illustrations in the dierent settings.
The development of global sensitivity analysis of numerical model outputs has recently raised new issues on 1-dimensional Poincare inequalities. Typically two kind of sensitivity indices are linked by a Poincare type inequality, which provide upper bounds of the most interpretable index by using the other one, cheaper to compute. This allows performing a low-cost screening of unessential variables. The efficiency of this screening then highly depends on the accuracy of the upper bounds in Poincare inequalities. The novelty in the questions concern the wide range of probability distributions involved, which are often truncated on intervals. After providing an overview of the existing knowledge and techniques, we add some theory about Poincare constants on intervals, with improvements for symmetric intervals. Then we exploit the spectral interpretation for computing exact value of Poincare constants of any admissible distribution on a given interval. We give semi-analytical results for some frequent distributions (truncated exponential, triangular, truncated normal), and present a numerical method in the general case. Finally, an application is made to a hydrological problem, showing the benefits of the new results in Poincare inequalities to sensitivity analysis.
We introduce a general method, named the h-function method, to unify the constructions of level-alpha exact test and 1-alpha exact confidence interval. Using this method, any confidence interval is improved as follows: i) an approximate interval, including a point estimator, is modified to an exact interval; ii) an exact interval is refined to be an interval that is a subset of the previous one. Two real datasets are used to illustrate the method.
The so-called polynomial chaos expansion is widely used in computer experiments. For example, it is a powerful tool to estimate Sobol sensitivity indices. In this paper, we consider generalized chaos expansions built on general tensor Hilbert basis. In this frame, we revisit the computation of the Sobol indices and give general lower bounds for these indices. The case of the eigenfunctions system associated with a Poincar{e} differential operator leads to lower bounds involving the derivatives of the analyzed function and provides an efficient tool for variable screening. These lower bounds are put in action both on toy and real life models demonstrating their accuracy.
In this paper, we introduce new indices adapted to outputs valued in general metric spaces. This new class of indices encompasses the classical ones; in particular, the so-called Sobol indices and the Cram{e}r-von-Mises indices. Furthermore, we provide asymptotically Gaussian estimators of these indices based on U-statistics. Surprisingly, we prove the asymp-totic normality straightforwardly. Finally, we illustrate this new procedure on a toy model and on two real-data examples.