Development and external validation of a dynamic risk score for early prediction of cardiogenic shock in cardiac intensive care units using machine learning.

AIMS: Myocardial infarction and heart failure are major cardiovascular diseases that affect millions of people in the USA with morbidity and mortality being highest among patients who develop cardiogenic shock. Early recognition of cardiogenic shock allows prompt implementation of treatment measures. Our objective is to develop a new dynamic risk score, called CShock, to improve early detection of cardiogenic shock in the cardiac intensive care unit (ICU). METHODS AND RESULTS: We developed and externally validated a deep learning-based risk stratification tool, called CShock, for patients admitted into the cardiac ICU with acute decompensated heart failure and/or myocardial infarction to predict the onset of cardiogenic shock. We prepared a cardiac ICU dataset using the Medical Information Mart for Intensive Care-III database by annotating with physician-adjudicated outcomes. This dataset which consisted of 1500 patients with 204 having cardiogenic/mixed shock was then used to train CShock. The features used to train the model for CShock included patient demographics, cardiac ICU admission diagnoses, routinely measured laboratory values and vital signs, and relevant features manually extracted from echocardiogram and left heart catheterization reports. We externally validated the risk model on the New York University (NYU) Langone Health cardiac ICU database which was also annotated with physician-adjudicated outcomes. The external validation cohort consisted of 131 patients with 25 patients experiencing cardiogenic/mixed shock. CShock achieved an area under the receiver operator characteristic curve (AUROC) of 0.821 (95% CI 0.792-0.850). CShock was externally validated in the more contemporary NYU cohort and achieved an AUROC of 0.800 (95% CI 0.717-0.884), demonstrating its generalizability in other cardiac ICUs. Having an elevated heart rate is most predictive of cardiogenic shock development based on Shapley values. The other top 10 predictors are having an admission diagnosis of myocardial infarction with ST-segment elevation, having an admission diagnosis of acute decompensated heart failure, Braden Scale, Glasgow Coma Scale, blood urea nitrogen, systolic blood pressure, serum chloride, serum sodium, and arterial blood pH. CONCLUSION: The novel CShock score has the potential to provide automated detection and early warning for cardiogenic shock and improve the outcomes for millions of patients who suffer from myocardial infarction and heart failure.

DIET: Conditional independence testing with marginal dependence measures of residual information.

Conditional randomization tests (CRTs) assess whether a variable x is predictive of another variable y, having observed covariates z. CRTs require fitting a large number of predictive models, which is often computationally intractable. Existing solutions to reduce the cost of CRTs typically split the dataset into a train and test portion, or rely on heuristics for interactions, both of which lead to a loss in power. We propose the decoupled independence test (DIET), an algorithm that avoids both of these issues by leveraging marginal independence statistics to test conditional independence relationships. DIET tests the marginal independence of two random variables: Fx∣z(x∣z) and Fy∣z(y∣z) where F⋅∣z(⋅∣z) is a conditional cumulative distribution function (CDF) for the distribution p(⋅∣z). These variables are termed "information residuals." We give sufficient conditions for DIET to achieve finite sample type-1 error control and power greater than the type-1 error rate. We then prove that when using the mutual information between the information residuals as a test statistic, DIET yields the most powerful conditionally valid test. Finally, we show DIET achieves higher power than other tractable CRTs on several synthetic and real benchmarks.

Beyond Distribution Shift: Spurious Features Through the Lens of Training Dynamics.

Deep Neural Networks (DNNs) are prone to learning spurious features that correlate with the label during training but are irrelevant to the learning problem. This hurts model generalization and poses problems when deploying them in safety-critical applications. This paper aims to better understand the effects of spurious features through the lens of the learning dynamics of the internal neurons during the training process. We make the following observations: (1) While previous works highlight the harmful effects of spurious features on the generalization ability of DNNs, we emphasize that not all spurious features are harmful. Spurious features can be "benign" or "harmful" depending on whether they are "harder" or "easier" to learn than the core features for a given model. This definition is model and dataset dependent. (2) We build upon this premise and use instance difficulty methods (like Prediction Depth (Baldock et al., 2021)) to quantify "easiness" for a given model and to identify this behavior during the training phase. (3) We empirically show that the harmful spurious features can be detected by observing the learning dynamics of the DNN's early layers. In other words, easy features learned by the initial layers of a DNN early during the training can (potentially) hurt model generalization. We verify our claims on medical and vision datasets, both simulated and real, and justify the empirical success of our hypothesis by showing the theoretical connections between Prediction Depth and information-theoretic concepts like 𝒱-usable information (Ethayarajh et al., 2021). Lastly, our experiments show that monitoring only accuracy during training (as is common in machine learning pipelines) is insufficient to detect spurious features. We, therefore, highlight the need for monitoring early training dynamics using suitable instance difficulty metrics.

Learning Invariant Representations with Missing Data.

Spurious correlations allow flexible models to predict well during training but poorly on related test populations. Recent work has shown that models that satisfy particular independencies involving correlation-inducing nuisance variables have guarantees on their test performance. Enforcing such independencies requires nuisances to be observed during training. However, nuisances, such as demographics or image background labels, are often missing. Enforcing independence on just the observed data does not imply independence on the entire population. Here we derive MMD estimators used for invariance objectives under missing nuisances. On simulations and clinical data, optimizing through these estimates achieves test performance similar to using estimators that make use of the full data.

Individual treatment effect estimation in the presence of unobserved confounding using proxies: a cohort study in stage III non-small cell lung cancer.

Randomized Controlled Trials (RCT) are the gold standard for estimating treatment effects but some important situations in cancer care require treatment effect estimates from observational data. We developed "Proxy based individual treatment effect modeling in cancer" (PROTECT) to estimate treatment effects from observational data when there are unobserved confounders, but proxy measurements of these confounders exist. We identified an unobserved confounder in observational cancer research: overall fitness. Proxy measurements of overall fitness exist like performance score, but the fitness as observed by the treating physician is unavailable for research. PROTECT reconstructs the distribution of the unobserved confounder based on these proxy measurements to estimate the treatment effect. PROTECT was applied to an observational cohort of 504 stage III non-small cell lung cancer (NSCLC) patients, treated with concurrent chemoradiation or sequential chemoradiation. Whereas conventional confounding adjustment methods seemed to overestimate the treatment effect, PROTECT provided credible treatment effect estimates.

Contra: Contrarian statistics for controlled variable selection.

The holdout randomization test (HRT) discovers a set of covariates most predictive of a response. Given the covariate distribution, HRTs can explicitly control the false discovery rate (FDR). However, if this distribution is unknown and must be estimated from data, HRTs can inflate the FDR. To alleviate the inflation of FDR, we propose the contrarian randomization test (CONTRA), which is designed explicitly for scenarios where the covariate distribution must be estimated from data and may even be misspecified. Our key insight is to use an equal mixture of two "contrarian" probabilistic models in determining the importance of a covariate. One model is fit with the real data, while the other is fit using the same data, but with the covariate being tested replaced with samples from an estimate of the covariate distribution. CONTRA is flexible enough to achieve a power of 1 asymptotically, can reduce the FDR compared to state-of-the-art CVS methods when the covariate distribution is misspecified, and is computationally efficient in high dimensions and large sample sizes. We further demonstrate the effectiveness of CONTRA on numerous synthetic benchmarks, and highlight its capabilities on a genetic dataset.

Inverse-Weighted Survival Games.

Deep models trained through maximum likelihood have achieved state-of-the-art results for survival analysis. Despite this training scheme, practitioners evaluate models under other criteria, such as binary classification losses at a chosen set of time horizons, e.g. Brier score (BS) and Bernoulli log likelihood (BLL). Models trained with maximum likelihood may have poor BS or BLL since maximum likelihood does not directly optimize these criteria. Directly optimizing criteria like BS requires inverse-weighting by the censoring distribution. However, estimating the censoring model under these metrics requires inverse-weighting by the failure distribution. The objective for each model requires the other, but neither are known. To resolve this dilemma, we introduce Inverse-Weighted Survival Games. In these games, objectives for each model are built from re-weighted estimates featuring the other model, where the latter is held fixed during training. When the loss is proper, we show that the games always have the true failure and censoring distributions as a stationary point. This means models in the game do not leave the correct distributions once reached. We construct one case where this stationary point is unique. We show that these games optimize BS on simulations and then apply these principles on real world cancer and critically-ill patient data.

General Control Functions for Causal Effect Estimation from Instrumental Variables.

Causal effect estimation relies on separating the variation in the outcome into parts due to the treatment and due to the confounders. To achieve this separation, practitioners often use external sources of randomness that only influence the treatment called instrumental variables (IVs). We study variables constructed from treatment and IV that help estimate effects, called control functions. We characterize general control functions for effect estimation in a meta-identification result. Then, we show that structural assumptions on the treatment process allow the construction of general control functions, thereby guaranteeing identification. To construct general control functions and estimate effects, we develop the general control function method (GCFN). GCFN's first stage called variational decoupling (VDE) constructs general control functions by recovering the residual variation in the treatment given the IV. Using VDE's control function, GCFN's second stage estimates effects via regression. Further, we develop semi-supervised GCFN to construct general control functions using subsets of data that have both IV and confounders observed as supervision; this needs no structural treatment process assumptions. We evaluate GCFN on low and high dimensional simulated data and on recovering the causal effect of slave export on modern community trust [30].

Causal Estimation with Functional Confounders.

Causal inference relies on two fundamental assumptions: ignorability and positivity. We study causal inference when the true confounder value can be expressed as a function of the observed data; we call this setting estimation with functional confounders (EFC). In this setting ignorability is satisfied, however positivity is violated, and causal inference is impossible in general. We consider two scenarios where causal effects are estimable. First, we discuss interventions on a part of the treatment called functional interventions and a sufficient condition for effect estimation of these interventions called functional positivity. Second, we develop conditions for nonparametric effect estimation based on the gradient fields of the functional confounder and the true outcome function. To estimate effects under these conditions, we develop Level-set Orthogonal Descent Estimation (LODE). Further, we prove error bounds on LODE's effect estimates, evaluate our methods on simulated and real data, and empirically demonstrate the value of EFC.

X-CAL: Explicit Calibration for Survival Analysis.

Survival analysis models the distribution of time until an event of interest, such as discharge from the hospital or admission to the ICU. When a model's predicted number of events within any time interval is similar to the observed number, it is called well-calibrated. A survival model's calibration can be measured using, for instance, distributional calibration (D-CALIBRATION) [Haider et al., 2020] which computes the squared difference between the observed and predicted number of events within different time intervals. Classically, calibration is addressed in post-training analysis. We develop explicit calibration (X-CAL), which turns D-CALIBRATION into a differentiable objective that can be used in survival modeling alongside maximum likelihood estimation and other objectives. X-CAL allows practitioners to directly optimize calibration and strike a desired balance between predictive power and calibration. In our experiments, we fit a variety of shallow and deep models on simulated data, a survival dataset based on MNIST, on length-of-stay prediction using MIMIC-III data, and on brain cancer data from The Cancer Genome Atlas. We show that the models we study can be miscalibrated. We give experimental evidence on these datasets that X-CAL improves D-CALIBRATION without a large decrease in concordance or likelihood.