# Causal Mediation Pathways in Continuous Postprandial Glucose Monitoring for Type 1 Diabetes Patients

## TL;DR

This study uses causal mediation analysis to understand how carbohydrate intake affects glucose levels in Type 1 Diabetes patients, revealing important differences in how individuals respond to meals.

## Contribution

The study introduces a Causally-constrained Linear Autoencoder to adjust for confounding in causal mediation analysis of postprandial glucose.

## Key findings

- Dinner shows a direct glycemic effect exceeding insulin-mediated response, with persistent total effects of 10–14 mg/dL for increased carbohydrate intake.
- Breakfast has large but nearly canceling direct and mediated effects, while lunch and snacks show negligible mediation.
- Quantile analysis identifies a subgroup with a significant 22.03 mg/dL total carbohydrate effect at dinner, undetectable in mean-level analysis.

## Abstract

Managing postprandial glucose in Type 1 Diabetes Mellitus (T1DM) requires understanding how carbohydrate intake affects glucose through both direct pathways and insulin-mediated compensation.1,2 Standard analyses often treat insulin as a confounder rather than a mediator, obscuring the distinct roles of these two causal channels and hiding clinically important heterogeneity in how different patients respond to carbohydrate intake. Using meal-centered continuous glucose monitoring windows from twelve adults in the OhioT1DM 2018 and 2020 cohorts,3,4 we apply the causal mediation framework of Imai et al.5 to decompose the total effect of carbohydrate intake on glucose change into the Average Causal Mediation Effect (ACME, the indirect effect operating through insulin), the Average Direct Effect (ADE, the effect not mediated by insulin), and the Average Total Effect (ATE).6 We estimate these quantities by meal type over a 3.5-hour post-meal horizon and across outcome quantiles to characterize heterogeneity in glucose control mechanisms that population-average methods fail to detect.7,8 To adjust for confounding by longitudinal pre-meal physiological trajectories, we introduce a Causally-constrained Linear Autoencoder (CLAE) that learns low-dimensional pre-treatment representations satisfying the conditional independence assumptions required for valid mediation.9–11 Results reveal clinically meaningful heterogeneity in response to carbohydrate and bolus insulin intake across meal types and across the conditional glucose response distribution. At dinner, the direct glycemic effect substantially exceeds the insulin-mediated response, producing persistent total effects of 10–14 mg/dL for a +30 g carbohydrate increase that indicates systematic under-compensation by evening boluses. Breakfast, in contrast, exhibits large but nearly canceling direct and mediated effects, while lunch and snack show negligible mediation structures. Quantile-specific analysis further identifies a subgroup for whom the total carbohydrate effect at dinner reaches 22.03 mg/dL (p = 0.04), statistically significant despite being undetectable in the mean-level analysis. This distributional heterogeneity points to patients whose glycemic risk is undermined by population-average estimates and for whom current dosing recommendations are inadequate.12–14