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.

Seasonal forecasts of Indian summer monsoon rainfall using local polynomial based non-parametric regression model

In this paper, details of new statistical models for forecasting southwest monsoon (June-September) rainfall over India (ISMR) and for northwest India summer monsoon rainfall (NWISMR) are discussed. These models are based on the local polynomial based non-parametric regression method. Two predictor sets (SET-I & SET-II consisting of 4 and 5 predictors respectively) were selected for developing two separate models for making predictions in April and late June respectively. Another predictor set (SET-III) was selected for developing model for monsoon rainfall over NW India (NWISMR). Principle Component Analysis (PCA) of predictor data set was done and the first two principal components were selected for model development. Data for the period 1977-2005 have been used for developing the model and the Jackknife method was used to assess the skill of the model. Both the models showed useful skill in predicting ISMR and showed better performance than the model based on pure climatology. The Hit scores for the three category forecasts during the verification period by April and June models are 0.65 and 0.66 respectively. Root Mean Square Error (RMSE) of these models during the verification period is 5.99 and 6.0% respectively from the Long Period Average (LPA) as against 10.0% from the LPA of the model based on climatology alone. RMSE of the Northwest India model during the independent period is 11.5% from LPA as against 18.5% from the LPA of the model based on the climatology alone. Hit score for the three category forecast for NW India during the verification period is 0.55.

Causal simulation experiments: Lessons from bias amplification

Recent theoretical work in causal inference has explored an important class of variables which, when conditioned on, may further amplify existing unmeasured confounding bias (bias amplification). Despite this theoretical work, existing simulations of bias amplification in clinical settings have suggested bias amplification may not be as important in many practical cases as suggested in the theoretical literature. We resolve this tension by using tools from the semi-parametric regression literature leading to a general characterization in terms of the geometry of OLS estimators which allows us to extend current results to a larger class of DAGs, functional forms, and distributional assumptions. We further use these results to understand the limitations of current simulation approaches and to propose a new framework for performing causal simulation experiments to compare estimators. We then evaluate the challenges and benefits of extending this simulation approach to the context of a real clinical data set with a binary treatment, laying the groundwork for a principled approach to sensitivity analysis for bias amplification in the presence of unmeasured confounding.

Determination of Reactivity Ratios from Binary Copolymerization Using the k-Nearest Neighbor Non-Parametric Regression

This paper proposes a new method for calculating the monomer reactivity ratios for binary copolymerization based on the terminal model. The original optimization method involves a numerical integration algorithm and an optimization algorithm based on k-nearest neighbour non-parametric regression. The calculation method has been tested on simulated and experimental data sets, at low (<10%), medium (10–35%) and high conversions (>40%), yielding reactivity ratios in a good agreement with the usual methods such as intersection, Fineman–Ross, reverse Fineman–Ross, Kelen–Tüdös, extended Kelen–Tüdös and the error in variable method. The experimental data sets used in this comparative analysis are copolymerization of 2-(N-phthalimido) ethyl acrylate with 1-vinyl-2-pyrolidone for low conversion, copolymerization of isoprene with glycidyl methacrylate for medium conversion and copolymerization of N-isopropylacrylamide with N,N-dimethylacrylamide for high conversion. Also, the possibility to estimate experimental errors from a single experimental data set formed by n experimental data is shown.

Statistical Inference on Nonparametric Spline Models and its Applications

One of the components of the Human Development Index which is still a problem and concern in the world today is the Life Expectancy Rate (LER). United Nations Development Program (UNDP). United Nations Development Program (UNDP) uses the LER to measure community health status as well as a benchmark for development success. LER in Indonesia continues to increase almost throughout the year. That is, the hope of a newborn baby to be able to live longer is getting higher. LER data modelling with parametric regression is not necessarily suitable to be applied because the LER relationship pattern has a pattern that varies at certain age intervals. Spline regression is a regression method that can handle data whose pattern changes at certain intervals. Spline is one of the models in nonparametric regression that has a very special and very good visual statistical interpretation. In addition, splines are also able to handle data characters or functions that are smooth (smooth). This study aims to derive the form of the estimator and the shortest confidence interval for the quadratic spline model and model the LER data in Indonesia.