Estimating individual treatment effect on disability progression in multiple sclerosis using deep learning

Fig. 1. Average treatment difference curve for the anti-CD20-Abs held-out test set. Represents the difference in the ground-truth restricted mean survival time (RMST), calculated at 2 years using time-to-CDP24, between anti-CD20-Abs and placebo, among predicted responders defined using various thresholds. The conditional average treatment effect (CATE) percentile threshold is the minimum CATE (expressed as a percentile among all CATE estimates in the test set) that is used to define an individual as a responder (i.e. a threshold of 0.7 means the 30% predicted to be most responsive are considered responders).

Fig. 2. Kaplan–Meyer curves ±95% confidence intervals (CI) for predicted responders and non-responders to anti-CD20-Abs in the held-out test set, defined at two thresholds of predicted effect size. These are compared to the whole group (top). The placebo group is displayed in blue, and the treatment (anti-CD20-Abs) group is displayed in orange. Survival probability is measured in terms of time-to-CDP24 using the EDSS. p values are calculated using log-rank tests. 95% CIs are estimated using Greenwood's Exponential formula.

Fig. 3. Multi-headed multilayer perceptron (MLP) architecture for CATE estimation. The MLP was first pre-trained on a relapsing-remitting multiple sclerosis dataset (top), followed by fine tuning on a primary progressive multiple sclerosis dataset (bottom). Subtraction symbols indicate which treatment and control are being subtracted for the CATE estimate. Gray-colored layers indicate the common layers that are transferred from the pre-trained MLP to the fine-tuning MLP, at which point their parameters are frozen and only the parameters of the blue-colored layers are updated. The orange-colored layers are discarded after the pre-training step. x: Feature vector. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\hat{\tau }}_{t}(x)$$\end{document}τ^t(x): CATE estimate for treatment t given feature vector x. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}…