The SOFA score is a widely used measurement of disease severity [1] - [4] . SOFA has 6 integer subscores ranging from 0 to 4 for different organ systems, added up to obtain a total score [1] . Advantages of SOFA include simplicity, interpretability, wide applicability due to reliance on commonly available measurements, ability to track illness temporally, and correlation with mortality.

However, the SOFA score has drawbacks: it discards information by discretizing analog values; it was designed by consensus rather than optimization; its categories are arbitrarily given equal weight; and it does not include age, which is strongly associated with mortality and arguably should be part of a disease severity score. Finally, it is common for variables required by SOFA to be missing, particularly in retrospective studies such as large-scale medical records data studies [4] - [8] . As SOFA does not accommodate missing data, investigators have proposed a variety of ad hoc imputation methods, including median imputation, zero imputation, multiple imputation, and last observation carried forward [3] [4] [6] [7] [9] .

Here, we develop an illness severity score suitable for large-scale studies that involve missing data, such as the IMPS (immediate mortality prediction score). IMPS retains the strengths of SOFA score while addressing the weaknesses described above. IMPS is based on the same variables as SOFA plus age and sex, and allows for missing variables. IMPS also has a stronger association with mortality, enhancing its value as an illness severity score.

This study follows the STROBE (Strengthening the Reporting of Observational Studies in Epidemiology) statement. The Mass General Brigham IRB reviewed and approved the study (protocol#: 2013P001024), and waived the requirement for informed consent. All study procedures followed were in accordance with the ethical standards of the responsible committee on human experimentation (the institutional IRB) and with the Helsinki Declaration of 1975, as most recently amended. Data were from inpatients (age ≥ 18) admitted to intensive care units at a single center between Jan 18, 2016 - Dec 31, 2022. For each patient we collected SOFA component variables from the first 24 hours of hospital admission, plus age, sex, and for those who died, time of death. Where multiple measurements were available, the worst measurements were considered (i.e., minimum Glasgow Coma Score (GCS), mean arterial blood pressure (MAP), platelets, percent arterial oxygen to fraction of inspired oxygen ratio (PaO2/FiO2), and maximum bilirubin, creatinine, dopamine, epinephrine, norepinephrine). Outliers (99^th percentile values for PaO2/FiO2 ratio, bilirubin, platelets, creatinine, urine output, dopamine dosage, and pressor doses, and first percentile values for PaO2/FiO2, platelets, creatinine, and urine output) were assumed to be errors because most such values were clinically implausible, and were therefore treated as missing after looking at box plots. Data was randomly split into training and testing sets of equal size (50:50).

IMPS was created by logistic regression with SOFA components, age, sex, and “missingness” indicators for all variables except age, sex, ventilator status, and amounts of medication, which were never missing. The target variable was death within 10 days. These variables were included to keep IMPS close to the spirit and simplicity of SOFA, while addressing it’s drawbacks.

For comparison, we also calculated conventional SOFA scores [1] . Missing values were median imputed, as this is commonly done in the literature. We converted SOFA scores to a [0, 1] scale by fitting a logistic regression model with death within 10 days as the target variable. We also fit a logistic regression model that included SOFA plus age and sex as predictors.

All logistic regression models (SOFA, SOFA + age + sex, IMPS) were trained using LASSO regularization with 5-fold internal cross validation to select the regularization parameter.

Performance Evaluation:

Models were compared using area under the receiver operating characteristic curves (AUROC). We also evaluated calibration of the IMPS model: how closely predicted risk of death matches the observed rate [10] . The calibration curve was computed by dividing IMPS mortality predictions into 100 bins, with bin centers at regular intervals between 0.05 and 0.95, and calculating the percentage of patients who died (within 10 days) whose predictions were in ±0.05 of the bin center. Uncertainty for ROC and calibration curves was quantified by 95% confidence intervals (CIs), calculated via using 10,000 iterations of bootstrapping. Model evaluation was done exclusively using testing data.

IMPS integrates measurements from multiple organ systems that are readily available and easily repeatable, and thus represents a general-purpose hospital illness severity score that can be tracked over time. IMPS is designed via optimization (machine learning), and shows both excellent predictive validity and calibration. IMPS explicitly allows for missing values, making it suitable for retrospective studies that leverage large-scale electronic health records.

IMPS is an optimized alternative to the SOFA score. IMPS incorporates strengths of SOFA including simplicity and reliance on commonly available data, while exhibiting a stronger association with short-term mortality and ability to handle missing data. IMPS represents a promising and versatile replacement for the SOFA score.

All code and data necessary to reproduce the results, including figures, are made available in a GitHub repository https://github.com/bdsp-core/IMPS .

Dr Zafar was supported by a grant from the NIH (K23NS114201). Dr. Westover was supported by grants from the NIH (R01NS102190, R01NS102574, R01NS107291, RF1AG064312, RF1NS120947, R01AG073410, R01HL161253, R01NS126282, R01AG073598), and NSF (2014431).

Dr. Zafar is a consultant for Corticare and receives royalties from Springer for the Acute Neurology Survival Guide. Dr. Westover is a co-founder, scientific advisor, consultant, and has personal equity interest in Beacon Biosignals. Other authors report no disclosures.

*Co-first authors.

^#Corresponding author.