arXiv subjects

Md. Niamul Islam Sium

Publications and source records attributed to Md. Niamul Islam Sium.

5 recordsLinked to original sources

arXiv2026

Quantifying Inconsistent Mediation: The Mediated Magnitude Share and the Degree of Suppression

The proportion mediated (PM), defined as the indirect effect divided by the total effect, is intuitive when direct and indirect effects operate in the same direction. Under inconsistent mediation, however, opposing pathways partially cancel each other, causing PM to fall outside the unit interval or become unstable as the total effect approaches zero. We introduce two complementary effect-scale measures: the Mediated Magnitude Share (MMS), which quantifies the absolute magnitude of an indirect pathway relative to the combined absolute magnitudes of the direct and indirect pathways, and the degree of suppression, which quantifies the fraction of this combined magnitude that is cancelled by opposing pathways. We establish the bounds and limiting behavior of both measures in the two-pathway case, show that MMS reduces to PM under consistent mediation, and extend both measures to settings with multiple indirect pathways. For binary outcomes, we extend the framework to odds-ratio and risk-ratio scales by using logarithms to convert multiplicative effects into additive ones, enabling direct application of MMS and the degree of suppression. Together, these measures provide bounded and interpretable characterizations of mediation systems in which pathway directions are not uniform.

stat.ME↗

arXiv2026

G-computation for causal effect estimation from observational hierarchical data with unmeasured cluster context

Observational studies frequently involve hierarchical data structures in which individuals are nested within higher-level units. In such settings, unmeasured cluster-level factors may confound the treatment-outcome relationship and may additionally induce treatment effect heterogeneity across clusters, complicating causal effect estimation. We formalize the use of g-computation for hierarchical observational data by incorporating random-effects models (REM) as outcome models and propose a within-group g-computation strategy designed to reduce bias arising from unmeasured cluster context. The approach groups clusters according to their observed treatment prevalence and performs g-computation within groups before aggregating group-specific estimates. Through extensive Monte Carlo simulations, we compare the standard and within-group implementations of g-computation using both linear models and REM. Results show that both standard and within-group REM-based implementations substantially reduce bias when the unmeasured cluster-level variable acts solely as a confounder, whereas the proposed within-group REM estimator achieves the lowest RMSE when the unmeasured cluster-level factor acts as both a confounder and a source of treatment effect heterogeneity. We apply the proposed within-group REM estimator to estimate the causal effect of adolescent pregnancy on the child height-for-age Z-score using 2019 Bangladesh MICS data, obtaining an estimated effect of -0.12 (95% bootstrap CI: [-0.18, -0.06]). The proposed within-group g-computation framework offers a strategy for reducing bias from unmeasured cluster-level confounding and treatment effect heterogeneity in hierarchical observational studies.

stat.ME↗

arXiv2026

Quantifying Robustness to Unmeasured Confounding in Time-Varying Treatment Confounder Settings: An Extension of E-value Approach

Background: The E-value has become widely used for assessing robustness to unmeasured confounding in observational studies, but the original framework was developed for single time-point exposure-outcome settings. This study extends the E-value methodology to longitudinal set up with time-varying treatments and confounders, where treatment-confounder feedback occurs. Methods: A combined bias factor accounting for unmeasured confounding at multiple time points was extended, with three reporting scenarios presented: equal bias distribution across time points, confounding at a single time point, and a general case visualizing all possible confounder strength combinations. Results: In simulations with an observed risk ratio of 1.73, unmeasured confounders with 1.96-fold associations at each time point could nullify the effect under equal distribution-substantially lower than the single time-point E-value of 2.85. Re-analysis of a published insulin resistance and cardiovascular disease study yielded similar patterns, with time-varying E-values of 1.63 at each time point compared to the originally reported 2.09. Conclusions: Studies more like longitudinal set up may be more vulnerable to unmeasured confounding than single time-point E-values suggest. This extension provides accessible tools for transparent sensitivity analysis in time-varying settings while preserving the simplicity and minimal assumptions that make E-values widely applicable.

stat.AP↗

arXiv2026

Causal Inference with MNAR Self-Masking Confounders: A Stratified Delta-Imputed Propensity Estimation Method

In observational studies, causal inference becomes difficult when confounders are missing-not-at-random (MNAR), particularly where the missingness depends on the confounder's own unreported value (self-masking). Existing methods for handling MNAR confounders often rely on strong, unverifiable assumptions, leading to biased estimates. We propose a simple approach with Stratified Delta-Imputed Propensity Estimator (SDIPE) in the presence of self-masking confounders. SDIPE first stratifies data into observed and missing groups, imputes missing confounders via delta-adjusted multiple imputation. Then, within each group, average-treatment-effects (ATEs) are estimated by stabilized-inverse-probability-weights. The final ATE is obtained by combining the subgroup-specific estimates, weighted by respective proportions in the sample. Simulation study shows that SDIPE achieves low bias and near-nominal coverage (94-96%) across varying missingness, sample sizes, and treatment prevalence. In contrast, conventional sensitivity-based multiple imputation exhibits substantial bias and poor coverage (18-89%). Additionally, SDIPE is robust to the choice of the delta parameter. Applied to NHANES-2017-2018, SDIPE estimates that married individuals have a 1.19-point lower depression score than unmarried individuals (95% CI: -1.76, -0.64), adjusting for MNAR income data. SDIPE provides a practical and robust approach for causal inference with self-masking MNAR confounders, offering improved performance over existing methods without requiring restrictive assumptions about the missingness mechanism.

stat.ME↗

arXiv2026

Central limit theorem for the global clustering coefficient of random geometric graphs

The global clustering coefficient serves as a powerful metric for the structural analysis and comparison of complex networks. Random geometric graphs offer a realistic framework for representing the spatial constraints and geometry often found in real-world network datasets. In this paper, we establish a central limit theorem for the global clustering coefficient of random geometric graphs. Our main result identifies the centering and scaling sequences required for convergence in law to the standard normal distribution. Our approach varies by regime: in the dense case, we employ the Lyapunov CLT; in the intermediate case, we utilize the asymptotic theory of $U$-statistics with sample-size-dependent kernels; and in the sparse regime, we use the method of moments to derive the asymptotic distribution. Notably, the convergence rates for non-uniform and uniform random geometric graphs diverge in the dense regime, yet they coincide in the sparse regime. In addition, we find that the global clustering coefficient for both uniform and non-uniform RGGs is asymptotically equal to $3/4$

math.ST↗