Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

This paper reviews a theory of causal inference based on the Structural Causal Model (SCM) described in (Pearl, 2000a). The theory unifies the graphical, potential-outcome (Neyman-Rubin), decision analytical, and structural equation approaches to causation, and provides both a mathematical foundation and a friendly calculus for the analysis of causes and counterfactuals. In particular, the paper establishes a methodology for inferring (from a combination of data and assumptions) the answers to three types of causal queries: (1) queries about the effect of potential interventions, (2) queries about counterfactuals, and (3) queries about the direct (or indirect) effect of one event on another.

What is Causal Inference

Objectives Our aim was to investigate in a real-life setting the use of machine learning for modelling the postprandial glucose concentrations in morbidly obese patients undergoing Roux-en-Y gastric bypass (RYGB) or one-anastomosis gastric bypass (OAGB). Methods As part of the prospective randomized open-label trial (RYSA), data from obese (BMI ≥35 kg/m2) non-diabetic adult participants were included. Glucose concentrations, measured with FreeStyle Libre, were recorded over 14 preoperative and 14 postoperative days. During these periods, 3-day food intake was self-reported. A machine learning model was applied to estimate glycaemic responses to the reported carbohydrate intakes before and after the bariatric surgeries. Results Altogether, 10 participants underwent RYGB and 7 participants OAGB surgeries. The glucose concentrations and carbohydrate intakes were reduced postoperatively in both groups. The relative time spent in hypoglycaemia increased regardless of the operation (RYGB, from 9.2 to 28.2%; OAGB, from 1.8 to 37.7%). Postoperatively, we observed an increase in the height of the fitted response curve and a reduction in its width, suggesting that the same amount of carbohydrates caused a larger increase in the postprandial glucose response and that the clearance of the meal-derived blood glucose was faster, with no clinically meaningful differences between the surgeries. Conclusions A detailed analysis of the glycaemic responses using food diaries has previously been difficult because of the noisy meal data. The utilized machine learning model resolved this by modelling the uncertainty in meal times. Such an approach is likely also applicable in other applications involving dietary data. A marked reduction in overall glycaemia, increase in postprandial glucose response, and rapid glucose clearance from the circulation immediately after surgery are evident after both RYGB and OAGB. Whether nondiabetic individuals would benefit from monitoring the post-surgery hypoglycaemias and the potential to prevent them by dietary means should be investigated.KEY MESSAGESThe use of a novel machine learning model was applicable for combining patient-reported data and time-series data in this clinical study.Marked increase in postprandial glucose concentrations and rapid glucose clearance were observed after both Roux-en-Y gastric bypass and one-anastomosis gastric bypass surgeries.Whether nondiabetic individuals would benefit from monitoring the post-surgery hypoglycaemias and the potential to prevent them by dietary means should be investigated.

Computational modelling of self-reported dietary carbohydrate intake on glucose concentrations in patients undergoing Roux-en-Y gastric bypass versus one-anastomosis gastric bypass.

A treatment policy defines when and what treatments are applied to affect some outcome of interest. Data-driven decision-making requires the ability to predict what happens if a policy is changed. Existing methods that predict how the outcome evolves under different scenarios assume that the tentative sequences of future treatments are fixed in advance, while in practice the treatments are determined stochastically by a policy and may depend, for example, on the efficiency of previous treatments. Therefore, the current methods are not applicable if the treatment policy is unknown or a counterfactual analysis is needed. To handle these limitations, we model the treatments and outcomes jointly in continuous time, by combining Gaussian processes and point processes. Our model enables the estimation of a treatment policy from observational sequences of treatments and outcomes, and it can predict the interventional and counterfactual progression of the outcome after an intervention on the treatment policy (in contrast with the causal effect of a single treatment). We show with real-world and semi-synthetic data on blood glucose progression that our method can answer causal queries more accurately than existing alternatives.

Causal Modeling of Policy Interventions From Sequences of Treatments and Outcomes

Policy makers need to predict the progression of an outcome before adopting a new treatment policy, which deﬁnes when and how a sequence of treatments aﬀecting the outcome occurs in continuous time. Commonly, algorithms that predict interventional future outcome trajectories take a ﬁxed sequence of future treatments as input. This excludes scenarios where the policy is unknown or a counterfactual analysis is needed. To handle these limitations, we develop a joint model for treatments and outcomes, which allows for the estimation of treatment policies and eﬀects from sequential treatment–outcome data. It can answer interventional and counterfactual queries about interventions on treatment policies, as we show with a realistic semi-synthetic simulation study.

Joint Point Process Model for Counterfactual Treatment–Outcome Trajectories Under Policy Interventions

Estimating the impact of a treatment on a given response is needed in many biomedical applications. However, methodology is lacking for the case when the response is a continuous temporal curve, treatment covariates suffer extensively from measurement error, and even the exact timing of the treatments is unknown. We introduce a novel method for this challenging scenario. We model personalized treatment-response curves as a combination of parametric response functions, hierarchically sharing information across individuals, and a sparse Gaussian process for the baseline trend. Importantly, our model accounts for errors not only in treatment covariates, but also in treatment timings, a problem arising in practice for example when data on treatments are based on user self-reporting. We validate our model with simulated and real patient data, and show that in a challenging application of estimating the impact of diet on continuous blood glucose measurements, accounting for measurement error significantly improves estimation and prediction accuracy.

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Errors-in-Variables Modeling of Personalized Treatment-Response Trajectories

Estimating the effect of a treatment on a given outcome, conditioned on a vector of covariates, is central in many applications. However, learning the impact of a treatment on a continuous temporal response, when the covariates suffer extensively from measurement error and even the timing of the treatments is uncertain, has not been addressed. We introduce a novel data-driven method that can estimate treatment-response trajectories in this challenging scenario. We model personalized treatment-response curves as a combination of parametric response functions, hierarchically sharing information across individuals, and a sparse Gaussian process for the baseline trend. Importantly, our model considers measurement error not only in treatment covariates, but also in treatment times, a problem which arises in practice for example when treatment information is based on self-reporting. In a challenging and timely problem of estimating the impact of diet on continuous blood glucose measurements, our model leads to significant improvements in estimation accuracy and prediction.

Reza A. Ashrafi

Papers

Errors-in-Variables Modeling of Personalized Treatment-Response Trajectories

Errors-in-variables Modeling of Personalized Treatment-Response Trajectories

On the distribution of the threshold voltage in multi-level cell flash memories

Short-term effect of plant-based Nordic diet versus carbohydrate-restricted diet on glucose levels in gestational diabetes – the eMOM pilot study