Development and External Validation of a Machine Learning Tool to Rule Out COVID-19 Among Adults in the Emergency Department Using Routine Blood Tests: A Large, Multicenter, Real-World Study.

BACKGROUND: Conventional diagnosis of COVID-19 with reverse transcription polymerase chain reaction (RT-PCR) testing (hereafter, PCR) is associated with prolonged time to diagnosis and significant costs to run the test. The SARS-CoV-2 virus might lead to characteristic patterns in the results of widely available, routine blood tests that could be identified with machine learning methodologies. Machine learning modalities integrating findings from these common laboratory test results might accelerate ruling out COVID-19 in emergency department patients. OBJECTIVE: We sought to develop (ie, train and internally validate with cross-validation techniques) and externally validate a machine learning model to rule out COVID 19 using only routine blood tests among adults in emergency departments. METHODS: Using clinical data from emergency departments (EDs) from 66 US hospitals before the pandemic (before the end of December 2019) or during the pandemic (March-July 2020), we included patients aged ≥20 years in the study time frame. We excluded those with missing laboratory results. Model training used 2183 PCR-confirmed cases from 43 hospitals during the pandemic; negative controls were 10,000 prepandemic patients from the same hospitals. External validation used 23 hospitals with 1020 PCR-confirmed cases and 171,734 prepandemic negative controls. The main outcome was COVID 19 status predicted using same-day routine laboratory results. Model performance was assessed with area under the receiver operating characteristic (AUROC) curve as well as sensitivity, specificity, and negative predictive value (NPV). RESULTS: Of 192,779 patients included in the training, external validation, and sensitivity data sets (median age decile 50 [IQR 30-60] years, 40.5% male [78,249/192,779]), AUROC for training and external validation was 0.91 (95% CI 0.90-0.92). Using a risk score cutoff of 1.0 (out of 100) in the external validation data set, the model achieved sensitivity of 95.9% and specificity of 41.7%; with a cutoff of 2.0, sensitivity was 92.6% and specificity was 59.9%. At the cutoff of 2.0, the NPVs at a prevalence of 1%, 10%, and 20% were 99.9%, 98.6%, and 97%, respectively. CONCLUSIONS: A machine learning model developed with multicenter clinical data integrating commonly collected ED laboratory data demonstrated high rule-out accuracy for COVID-19 status, and might inform selective use of PCR-based testing.

Algorithms for Brownian first-passage-time estimation.

A class of algorithms in discrete space and continuous time for Brownian first-passage-time estimation is considered. A simple algorithm is derived that yields exact mean first-passage times (MFPTs) for linear potentials in one dimension, regardless of the lattice spacing. When applied to nonlinear potentials and/or higher spatial dimensions, numerical evidence suggests that this algorithm yields MFPT estimates that either outperform or rival Langevin-based (discrete time and continuous space) estimates.

Comment on "On the Crooks fluctuation theorem and the Jarzynski equality" [J. Chem. Phys. 129, 091101 (2008)].

It has recently been argued that a self-consistency condition involving the Jarzynski equality (JE) and the Crooks fluctuation theorem (CFT) is violated for a simple Brownian process [L. Y. Chen, J. Chem. Phys.129, 091101 (2008)]. This note adopts the definitions in the original formulation of the JE and CFT and demonstrates the contrary.

Path integral analysis of Jarzynski's equality: analytical results.

We apply path integrals to study nonequilibrium work theorems in the context of Brownian dynamics, deriving in particular the equations of motion governing the most typical and most dominant trajectories. For the analytically soluble cases of a moving harmonic potential and a harmonic oscillator with a time-dependent natural frequency, we find such trajectories, evaluate the work-weighted propagators, and validate Jarzynski's equality.

Optimized free energies from bidirectional single-molecule force spectroscopy.

An optimized method for estimating path-ensemble averages using data from processes driven in opposite directions is presented. Based on this estimator, bidirectional expressions for reconstructing free energies and potentials of mean force from single-molecule force spectroscopy-valid for biasing potentials of arbitrary stiffness-are developed. Numerical simulations on a model potential indicate that these methods perform better than unidirectional strategies.

Random-walk approach to the d-dimensional disordered Lorentz gas.

A correlated random walk approach to diffusion is applied to the disordered nonoverlapping Lorentz gas. By invoking the Lu-Torquato theory for chord-length distributions in random media [J. Chem. Phys. 98, 6472 (1993)], an analytic expression for the diffusion constant in arbitrary number of dimensions d is obtained. The result corresponds to an Enskog-like correction to the Boltzmann prediction, being exact in the dilute limit, and better or nearly exact in comparison to renormalized kinetic theory predictions for all allowed densities in d=2,3 . Extensive numerical simulations were also performed to elucidate the role of the approximations involved.

Stochastic actions for diffusive dynamics: reweighting, sampling, and minimization.

In numerical studies of diffusive dynamics, two different action functionals are often used to specify the probability distribution of trajectories, one of which requires the evaluation of the second derivative of the potential in addition to the force. Here it is argued that both actions are equivalent prescriptions for the purposes of reweighting and sampling trajectories, whereas the most probable path is more generally given by the global minimum of the action involving the second derivative term. The answer to this apparent paradox lies in the nondifferentiable character of Brownian paths, as well as in the "entropy" associated with a given trajectory.

Algebraic perturbation theory for dense liquids with discrete potentials.

A simple theory for the leading-order correction g{1}(r) to the structure of a hard-sphere liquid with discrete (e.g., square-well) potential perturbations is proposed. The theory makes use of a general approximation that effectively eliminates four-particle correlations from g{1}(r) with good accuracy at high densities. For the particular case of discrete perturbations, the remaining three-particle correlations can be modeled with a simple volume-exclusion argument, resulting in an algebraic and surprisingly accurate expression for g{1}(r). The structure of a discrete "core-softened" model for liquids with anomalous thermodynamic properties is reproduced as an application.

Free energy surfaces from nonequilibrium processes without work measurement.

Recent developments in statistical mechanics have allowed the estimation of equilibrium free energies from the statistics of work measurements during processes that drive the system out of equilibrium. Here a different class of processes is considered, wherein the system is prepared and released from a nonequilibrium state, and no external work is involved during its observation. For such "clamp-and-release" processes, a simple strategy for the estimation of equilibrium free energies is offered. The method is illustrated with numerical simulations and analyzed in the context of tethered single-molecule experiments.

Symmetry relations in chemical kinetics arising from microscopic reversibility.

It is shown that the kinetics of time-reversible chemical reactions having the same equilibrium constant but different initial conditions are closely related to one another by a directly measurable symmetry relation analogous to chemical detailed balance. In contrast to detailed balance, however, this relation does not require knowledge of the elementary steps that underlie the reaction, and remains valid in regimes where the concept of rate constants is ill defined, such as at very short times and in the presence of low activation barriers. Numerical simulations of a model of isomerization in solution are provided to illustrate the symmetry under such conditions, and potential applications in protein folding or unfolding are pointed out.

Entropy and density of states from isoenergetic nonequilibrium processes.

Two identities in statistical mechanics involving entropy differences (or ratios of densities of states) at constant energy are derived. The first provides a nontrivial extension of the Jarzynski equality to the microcanonical ensemble [C. Jarzynski, Phys. Rev. Lett. 78, 2690 (1997)], which can be seen as a "fast-switching" version of the adiabatic switching method for computing entropies [M. Watanabe and W. P. Reinhardt, Phys. Rev. Lett. 65, 3301 (1990)]. The second is a thermodynamic integration formula analogous to a well-known expression for free energies, and follows after taking the quasistatic limit of the first. Both identities can be conveniently used in conjunction with a scaling relation (herein derived) that allows one to extrapolate measurements taken at a single energy to a wide range of energy values. Practical aspects of these identities in the context of numerical simulations are discussed.

Unbiased estimators for spatial distribution functions of classical fluids.

We use a statistical-mechanical identity closely related to the familiar virial theorem, to derive unbiased estimators for spatial distribution functions of classical fluids. In particular, we obtain estimators for both the fluid density rho(r) in the vicinity of a fixed solute and the pair correlation g(r) of a homogeneous classical fluid. We illustrate the utility of our estimators with numerical examples, which reveal advantages over traditional histogram-based methods of computing such distributions.

Adiabatic invariance with first integrals of motion.

The construction of a microthermodynamic formalism for isolated systems based on the concept of adiabatic invariance is an old but seldom appreciated effort in the literature, dating back at least to P. Hertz [Ann. Phys. (Leipzig) 33, 225 (1910)]. An apparently independent extension of such formalism for systems bearing additional first integrals of motion was recently proposed by Hans H. Rugh [Phys. Rev. E 64, 055101 (2001)], establishing the concept of adiabatic invariance even in such singular cases. After some remarks in connection with the formalism pioneered by Hertz, it will be suggested that such an extension can incidentally explain the success of a dynamical method for computing the entropy of classical interacting fluids, at least in some potential applications where the presence of additional first integrals cannot be ignored.