Sensitivity analysis for unobserved confounding in causal mediation analysis allowing for effect modification, censoring and truncation

Causal mediation analysis is used to decompose the total effect of an exposure on an outcome into an indirect effect, taking the path through an intermediate variable, and a direct effect. To estimate these effects, strong assumptions are made about unconfoundedness of the relationships between the exposure, mediator and outcome. These assumptions are difficult to verify in a given situation and therefore a mediation analysis should be complemented with a sensitivity analysis to assess the possible impact of violations. In this paper we present a method for sensitivity analysis to not only unobserved mediator-outcome confounding, which has largely been the focus of previous literature, but also unobserved confounding involving the exposure. The setting is estimation of natural direct and indirect effects based on parametric regression models. We present results for combinations of binary and continuous mediators and outcomes and extend the sensitivity analysis for mediator-outcome confounding to cases where the continuous outcome variable is censored or truncated. The proposed methods perform well also in the presence of interactions between the exposure, mediator and observed confounders, allowing for modeling flexibility as well as exploration of effect modification. The performance of the method is illustrated through simulations and an empirical example.

Trends in COVID-19 Infected Cases and Deaths Based on Parametric and Nonparametric Regression Models

The present investigation was carried out to study the trends in COVID-19 infected cases and deaths based on the parametric, exponential smoothing and non-parametric regression models by using COVID-19 cumulative infected cases and deaths due to infections The statistically most suited parametric models are selected based on the highest adjusted R2, significant regression co-efficient and co-efficient of determination (R2). Appropriate model is selected based on the model performance measures such as, Root Mean Square Error, Mean Absolute Error, Mean Absolute Percentage Error, assumptions of normality and independence of residuals. Nonparametric estimates of underlying growth functions are computed at each and every time points.

Common Permutation Methods in Animal Social Network Analysis Do Not Control for Non-independence

The non-independence of social network data is a cause for concern among behavioural ecologists conducting social network analysis. This has led to the adoption of several permutation-based methods for testing common hypotheses. One of the most common types of analysis is nodal regression, where the relationships between node-level network metrics and nodal covariates are analysed using a permutation technique known as node-label permutation. We show that, contrary to accepted wisdom, node-label permutations do not account for the types of non-independence assumed to exist in network data, because regression-based permutation tests still assume exchangeability of residuals. The same theoretical condition also applies to the quadratic assignment procedure (QAP), a permutation-based method often used for conducting dyadic regression. We highlight that node-label permutations produce the same p-values as equivalent parametric regression models, but that in the presence of confounds, parametric regression models produce more accurate effect size estimates. We also note that QAP only controls for a specific type of non-independence between edges that are connected to the same nodes, and that appropriate parametric regression models are also able to account for this type of non-independence. Based on this, we advocate the retirement of permutation tests for regression analyses, in favour of well-specified parametric models. Moving away from permutation-based methods will reduce over-reliance on p-values, generate more reliable estimates of effect sizes, and facilitate the adoption of more powerful types of statistical analysis.

Trees and forests. Recursive partitioning as an alternative to parametric regression models in social sciences

Parametric regression models became the dominant tool of quantitative sociology. This dominance is not without its challenges and many criticisms have been expressed, both statistically and epistemologically. Still, the development of data mining, and then of machine learning, has led to the emergence of methodological approaches that make it possible to overcome most of the limitations of parametric regression models, for the various types of use that are of interest to the social sciences. We argue that recursive partitioning in particular may be highly vauable for social sciences. Indeed, this approach has a number of technical advantages over parametric regression and, above all, it is consistent with a conception of social determinations in terms of configurations of interdependent factors (and not of additions of independent factors). In a second step, we review a range of tools for interpreting the results obtained from recursive partitioning algorithms. Together, they form a very complete toolbox for the social sciences and show that recursive partitioning is no longer a black box as soon as the appropriate interpretative tools are mobilized. Finally, we illustrate the methods presented using sociological examples from the world of cinema. In doing so, we will show that these methods make it possible to deal with the different types of problems that arise in the social sciences when parametric regressions are usually used, in this case the study of structure effects and the ranking of explanatory factors.

Performance Comparison of Parametric and Non-Parametric Regression Models for Uncertainty Analysis of Sheet Metal Forming Processes

This work aims to compare the performance of various parametric and non-parametric metamodeling techniques when applied to sheet metal forming processes. For this, the U-Channel and the Square Cup forming processes were studied. In both cases, three steel grades were considered, and numerical simulations were performed, in order to establish a database for each combination of forming process and material. Each database was used to train and test the various metamodels, and their predictive performances were evaluated. The best performing metamodeling techniques were Gaussian processes, multi-layer perceptron, support vector machines, kernel ridge regression and polynomial chaos expansion.