key: cord-0685098-qtxwdhx6
authors: Dabbah, Mohammad A.; Reed, Angus B.; Booth, Adam T. C.; Yassaee, Arrash; Despotovic, Aleksa; Klasmer, Benjamin; Binning, Emily; Aral, Mert; Plans, David; Morelli, Davide; Labrique, Alain B.; Mohan, Diwakar
title: Machine learning approach to dynamic risk modeling of mortality in COVID-19: a UK Biobank study
date: 2021-08-19
journal: Sci Rep
DOI: 10.1038/s41598-021-95136-x
sha: 8fde7b88c774ce3da7a810648e126b75a1f36c2e
doc_id: 685098
cord_uid: qtxwdhx6

The COVID-19 pandemic has created an urgent need for robust, scalable monitoring tools supporting stratification of high-risk patients. This research aims to develop and validate prediction models, using the UK Biobank, to estimate COVID-19 mortality risk in confirmed cases. From the 11,245 participants testing positive for COVID-19, we develop a data-driven random forest classification model with excellent performance (AUC: 0.91), using baseline characteristics, pre-existing conditions, symptoms, and vital signs, such that the score could dynamically assess mortality risk with disease deterioration. We also identify several significant novel predictors of COVID-19 mortality with equivalent or greater predictive value than established high-risk comorbidities, such as detailed anthropometrics and prior acute kidney failure, urinary tract infection, and pneumonias. The model design and feature selection enables utility in outpatient settings. Possible applications include supporting individual-level risk profiling and monitoring disease progression across patients with COVID-19 at-scale, especially in hospital-at-home settings.

Leave-one-out validation. To maximise the potential of the dataset, a leave-one-out (LOO) cross-validation approach was implemented (Fig. 1C) . In this process, each data point is used as a test set while the remaining data points are used to train a Random Forest (RF) classifier using the entire feature space. This approach is the most extreme version of k-fold cross-validation and results in lower model bias and variance than the typical train/test split method. Feature importance is calculated by aggregating individual importance across all trained classifiers in the LOO experiment. The feature selection process (Fig. 1B ) ensured the combination of data-driven insights with clinical experience, shortlisting approximately 12,000 features to 64 characteristics. The shortlisted features included: 3 vital signs; 12 symptoms; 32 pre-existing clinical conditions; 5 medications and treatments; and 13 patient characteristics (Table 1) .

Model performance and comparison. The receiver operating characteristic (ROC) curves for the prediction models are presented in Fig. 2A . With an area under the curve (AUC) of 0.90, the Random Forest (RF) model showed excellent performance. A Cox Proportional Hazard (CPH) model was trained using the final set of RF-defined variables to maximize explainability of the RF, CPH model coefficients are detailed in Supplementary Table 1 . This model had improved performance, reaching a higher AUC of 0.91. Figure 2A also shows the ROC curves for both the RF and CPH 22 models against the sex-aggregated QCOVID model 11 . As shown, the ROC curves for the RF and CPH are very comparable with a slight advantage for the CPH. From Fig. 2A , it can be seen that when QCOVID is applied to the UKB dataset it performs well and achieves an AUC of 0.84, showcasing resilience to unseen data. To explore the performance further, it is essential to look at the robustness of the generated models. Figure 2B illustrates the use of F-β statistical analysis to examine the performance of the various models. As expected, despite the CPH having a slightly greater AUC score, it is clear that the RF has much more stable performance. Moreover, it can be seen that both the CPH and QCOVID models achieve optimal F-β scores when β is small. However, for the RF model, the F-β scores are considerably larger than its comparators and are more consistent across the range of thresholds, thereby demonstrating greater stability and increased capabilities regarding recall (i.e. minimizing false-negatives).

The results of this model highlighted both known and novel risk factors for mortality in COVID-19 (Fig. 3) . Age was the most important feature of the model. To test for overfitting due to this feature, and limitations in the dataset, the model was re-processed excluding age, which had minimal effect on model performance (CPH AUC: 0.90, Supplementary Fig. 2 ).

Novel features. Novel features highlighted by the CPH included demographic and lifestyle features, such as waist circumference and sleep duration (Fig. 3) . Key features in recent medical history are also elucidated, with prior acute kidney failure, respiratory failure, bacterial pneumonia, and non-bacterial pneumonia (diagnosed between one week and one month prior to COVID-19 infection) comprising the most prominent predictors of mortality. Acute kidney failure and bacterial pneumonia remain in the top features, even with a more distant diagnosis window of between one month and 12 months prior to COVID-19 infection (Fig. 3 ).

This study developed and validated machine learning models to predict mortality in patients with COVID-19 using comprehensive data from 11,245 COVID-19 patients in the UKB. The results show that by using easily accessible patient characteristics, brief medical history, symptoms, and vital signs we can predict mortality in patients with COVID-19 with excellent performance (AUC: 0.91). The features selected in the presented model mirror much of the current clinical understanding regarding risk factors associated with COVID-19 mortality, highlighting age 23 and obesity 24 as significant contributors.

In addition, we identified many novel features that may be strong predictors of mortality in patients with COVID-19. The most interesting findings concern the impact of prior inpatient diagnosis of urinary tract infection (UTI), respiratory failure, acute kidney failure, bacterial and non-bacterial pneumonias, and other bacterial infections. With the exception of UTI, dividing each feature into time groupings by their proximity to the COVID- 19 www.nature.com/scientificreports/ infections, the risk returns to approximately baseline when > 12 months prior to COVID-19 diagnosis. The outlying significance of acute kidney failure at > 12 months before COVID-19 diagnosis suggests the impact of renal damage may be more integral to COVID-19 prognosis than that of the respiratory system. This is supported by findings related to UTIs, where they appear as a less severe, but persistent, risk factor regardless of the time since diagnosis. Respiratory and renal complications are a hallmark of severe COVID-19 25 . It is, therefore, unsurprising that previous pathology of these organs effectively forecasts prognosis. To date, however, the relationship between non-severe urogenital pathology and COVID-19 has not been effectively assessed. A recent systematic review on urological manifestations of COVID-19 found urinary symptoms were absent from all included studies 26 . Where data has been collected, sample sizes have been too low to draw strong conclusions. Though the occurrence of de novo urinary symptoms has been documented without noticeable impact on prognosis 27,28 , it has been previously suggested, and recently evidenced, that the presence of pre-existing urinary conditions may be associated with a poorer disease prognosis proportional to their severity 29, 30 . Our investigation provides the first reliable evidence that a history of UTI is predictive of greater COVID-19 mortality risk, roughly equivalent to the predictive value of type 2 diabetes or a prior stroke (Fig. 3 ). We hypothesise that the underlying nature of this association reflects the effect of poorer, possibly sub-clinical, baseline health status. While this sub-clinical deterioration previously had no noticeable impact, in the context of a highly infective, fatal pathogen such as SARS-CoV-2, even a small deterioration can take on clinical significance. The unique value of the UKB can be attributed to its well-established, longitudinal background dataset. Encompassing non-traditional health data, including anthropometric measurements and lifestyle insights, allows for the assessment of commonly overlooked, yet easily collectable, variables to supplement the already-known clinical factors. The ability to capture a deeper phenotype of the individual prior to infection has proved integral to the model's performance, in line with other disease-specific prediction models developed on the UKB [31] [32] [33] . Notably, we identified baseline waist circumference, height, weight, and hip circumference to be valuable independent of BMI and obesity, accounting for four of the top-seven RF-ranked features ( Supplementary Fig. 3 ). Although the pathophysiological link between adiposity and severe COVID-19 outcomes is not fully understood, our results indicate that comprehensive body composition may provide more granular risk profiling than BMI alone 34, 35 . Moreover, while baseline sleep duration has been demonstrated to be highly predictive of all-cause mortality 36 , cardiovascular diseases 37 , and type 2 diabetes 38 , our findings mark the first instance of its significant predictive influence within COVID-19 prognosis. While we present novel features associated with severe COVID-19 outcomes, it is important to consider that correlations identified in this observational dataset often will not reflect direct causation. We encourage further investigation of these novel features, both those previously established outside of COVID-19 and those discovered de novo, in a prospective setting to establish the underlying pathophysiology conferring their predictive association with COVID-19 mortality.

Our model's critical component is the distinction of variables with respect to their time of onset. Classifying variables in a time-dependent fashion enables discrimination between pre-existing conditions, symptoms, and complications. This was especially important as several of our novel features are also established complications of COVID-19. Studies have emphasised the need for distinguishing pre-existing conditions from complications of COVID-19 infection and their respective impact on prognosis 39,40 but, to our knowledge, no predictive models for this disease have stratified variables in such a way. Applied in the context of patient management, and enriched by the explainability of variable time-filtering, our results could help clarify crucial aspects of patients' past medical history and their relation to predicted prognosis. Models which forecast infection risk as a component of their mortality prediction have been criticised for generalizing human behaviour, which results in underestimation of risk factors and leaves their calibration extremely vulnerable to changes in local population dynamics 41 www.nature.com/scientificreports/ high prediction accuracy for COVID-19 mortality. However, by significantly reducing the number of features through the data-driven approach and clinical refinement, the model also overcomes the curse of dimensionality, where beforehand the full feature array was far greater in size than the available samples, resulting in improved performance (AUC: 0.91). The results show that both the RF and CPH models are comparable in terms of accuracy. However, the RF was integral to the CPH's construction by searching through the large feature space and selecting the most important of the original ~ 12,000. Moreover, the RF model is more resilient to overfitting the data, and this could explain the improved F1-scores. Owing to its stability, we would recommend the RF model as the preferred implementation in clinical practice. Given the different performance characteristics of the RF and CPH models, an ensemble of the two models may be of interest for investigation to further improve stability and performance. Prior to deployment in clinical practise, calibration of the final resulting model would be required alongside external validation on a new dataset. In addition, further investigation into differing machine learning models, such as SVMs 42 or Deep Neural Networks 43 would be of merit. Such models could then be interpreted using methodologies such as the SHAP 44 or LIME 45 . Several studies have reported risk models for COVID-19 mortality. In a review of prediction models for COVID-19, Wynatts et al. report all current prediction models show high risk of bias, and lack evidence from independent external validation 46 . While this model is yet to be externally validated, we have considerably larger sample size than comparable models 46 and, by implementing LOO cross-validation, our results have reduced overall variability and bias than the traditional train-test-validate method. A recent study utilising only age, minimum oxygen saturation during encounter, and health-care setting of patient encounter as features achieved comparable results (AUC: 0.91) 47 , however, the intended use of this model differs from the one presented. While the model presented outperforms QCOVID (AUC: 0.91 vs. 0.84), and best efforts were made in the comparison, it cannot be considered a direct comparison. In replication of the QCOVID algorithms, variables were mapped to related fields in the UKB, however, we were unable to confirm these were fully paired. Moreover, as the UKB is not linked to GP databases in the same manner, there were some missing variables (Supplementary Table 2 ). Importantly, contrasting with our purpose of supporting patient management, QCOVID is designed for population risk stratification to aid public health decision-making, and was used to exemplify the necessity of specific model design for specific purposes.

The COVID-19 pandemic has resulted in extraordinary acceptance of digital technology in healthcare 48 . Risk assessment tools can support the streamlining of clinical time and resource prioritization, whether on a national, organizational, or patient level. Models such as those presented, can support the latter by monitoring patients at-scale and identifying those at-risk of severe illness, in real-time, and without requiring specialist equipment or clinical input. Algorithm performance may be further improved by inclusion of passive, continuous variables via smartphones or wearables. Establishing our model in a prospective healthcare setting may enable this when coupled with high quality, continuous vital sign information and replete data on the course of symptomatology. Similar digital phenotyping has also shown potential in predicting COVID-19 infection at early symptoms onset 49, 50 . We believe a combination of these two types of digital tools, in union with dedicated hospital-at-home services, may become considered standard practice in infectious disease management, particularly during historically resource-intense periods, such as annual influenza outbreaks.

While the use of the UKB is a key strength in the development of the model, there are associated limitations which may impact the generalizability of the model. The UKB cohort trends towards being healthier and wealthier than the general population, which poses a notable limitation when modeling noncommunicable diseases 51 . As COVID-19 acquisition, however, is determined by exposure, this limitation is minimised in our investigation. Separately, the UKB COVID-19 data subset is less likely to capture asymptomatic or non-severe cases, in part as such individuals may not have received a test or sought medical treatment, but predominantly owing to UKB's enrichment for older age resulting in lesser rates of such presentation. The restricted age distribution (51-85 years) may further limit generalization of our findings to outside of this age range, however, Office for National Statistics figures show those aged ≥ 50 have accounted for 97.97% of all COVID-19-related deaths in England and Wales (up to 19th February 2021) 52 .

Although age is clearly an important feature, our sensitivity analysis ( Supplementary Fig. 2 ) demonstrated negligible performance drop, likely because much of the risk associated with older age is captured within other included features. One reason for using uniform leave-one-out (LOO) training is to overcome such issues of feature reliance and generalize the model as much as possible. The F-score in Fig. 2B illustrates this robustness, however, this must be tested on a separate representative dataset for a conclusive answer. Our robust development approach, paired with deep individual phenotyping, strengthens the evidence towards effective COVID-19 risk profiling. Granular symptoms and vital measurements are significant in determining deterioration. However, owing to the nature of this dataset, we could not model trajectories at this resolution but encourage further investigation in an appropriate dataset. In addition to the limitations of the dataset, it is likely that there are regional variances in COVID-19 outcomes. As such, the model would strongly benefit from external validation, especially with the continued emergence of disruptive SARS-CoV-2 variants 53 . Evidence of real-world utility, with the associated incomplete and missing data, is lacking for COVID-19 risk models. Further research is required to both establish prospective, real-world model performance and to understand the maximal data quality reduction, with respect to advanced techniques to handle missing data, which still produces clinically acceptable performance.

In conclusion, we present a comprehensive, robust model based on readily accessible factors (AUC: 0.91). In our analysis, we combine data-driven model development and clinical refinement to produce a model that uniquely incorporates time-to-event, symptoms, and vital signs. We identify several significant novel predictors of COVID-19 mortality with equivalent or greater predictive value than established high-risk comorbidities, www.nature.com/scientificreports/ such as detailed anthropometrics, lifestyle factors, and prior acute kidney failure, urinary tract infection, and pneumonias. The design and feature selection of the framework lends itself for deployment at-scale in a digital setting. Possible applications of this include supporting individual-level risk profiling and monitoring deterioration in high volumes of COVID-19 patients, particularly in hospital-at-home settings.

Online methods Study population. The development and validation of the risk model was carried out using the UKB. The UKB is a large cohort study with rich phenotype mapping of participants, including over 500,000 individuals aged between 40-and 69-years-old at recruitment, between 2006 and 2010, from across England, Scotland, and Wales 54 . The open dataset contains detailed health data and outcomes obtained prospectively from electronic health records and self-reported health measures from on-site testing over the past 15- COVID-19 mortality model. Feature selection. The data ingestion pipeline, Fig. 1A , generates an array of ~ 12,000 dimensions (including patient characteristics, pre-existing conditions, symptoms, and vital signs).

Owing to the disparity in size between the survivor and non-survivors population in the dataset and the importance of obtaining an unbiased model, a LOO cross-validation experiment 56 , which is also closely related to the jack-knife estimation method 57 , was used to search the full feature array for the most relevant features. LOO iterates through every sample in the dataset, whereby at each step the current sample was used to evaluate the model trained on the remaining dataset (Fig. 1C) . At each iteration the samples of all classes were balanced to ensure unbiased training and, following evaluation, the model was discarded and a new model trained. A RF model was chosen due to its inherent ability to extract features, handle high dimensionality data, and generalize well to unseen data 58 . During each step of the LOO cross-validation, a ranked list of features was extracted and averaged across the entire experiment to obtain a final shortlist of features that produced the highest accuracy, further cross-checked by clinical expertise. Figure 1B illustrates the production of shortlisted features driven by data, and their validation and review based on clinical judgement. Clinical feature selection was informed by a review of ranked feature importance in RF model. The highest ranked 1,000 features were screened by at least two reviewers. Any disagreements were settled by consensus with input of additional reviewers. Features were excluded where: (i) they could not be readily obtained through self-reporting or measured outside of the clinical setting; (ii) there was high confounding with higher ranked features; (iii) clinical consensus concluded that the feature's rank was more likely to be explained by database bias. Subsequently, features which were closely related (e.g. cancer diagnoses) were grouped together. Supplementary ICD-10 codes were included and, where possible, generalized (Supplementary Table 3) .

Model construction and validation. The LOO evaluation was selected to maximize the value of the available datasets. The LOO is used in this case to quantitatively evaluate the model; it is not used for hyperparameter tuning of the model. In essence, at each iteration of the LOO, there is a hold-out test set, which is a single sample of unseen data. At each iteration, a completely new model is trained from scratch on a randomly selected set of samples and tested on a single hold-out sample. At the end of the experiment, following iteration over all dataset samples, the results of each of these hold-out sets are aggregated to provide the final evaluation performance of www.nature.com/scientificreports/ the model. None of the models at each iteration are used in any other iteration and they are completely discarded once the iteration is complete. Specifically, this is equivalent to a k-fold evaluation, where k = n − 1 , with n being the total number of samples in the set. Moreover, LOO has been chosen to be as objective as possible when reporting on the outcome of the model. A single hold-out set could potentially provide a different benchmark depending on the random split of this set. Conversely, the LOO exhaustively tests against every sample in the dataset.

In this study, the prediction classes were two: COVID-19 survivors (n = 11,245) and non-survivors (n = 640). At each LOO iteration, two groups of equal sample size were randomly selected without replacement for training. The evaluation sample outcome and RF likelihood value were aggregated from all iterations. After aggregating all the evaluation results from the LOO experiment, the ROC curve analysis was carried out, and the AUC computed as a measure of accuracy 58 . Furthermore, the F-β statistic was used to evaluate the robustness of the model. When β is 1, this becomes the F1-score, which gives equal weights to recall and precision. A smaller β value gives more weight to precision, minimising false-positive errors, while a larger β value gives more weight to recall, minimising false-negative errors. The F-score range is [0, 1], where a score of 1 is a perfect performance.

The machine learning algorithm used in this study is the RF, which is an ensemble meta-estimator constructed from several decision trees 58 . These trees were fitted to the data using the bootstrap aggregation method (or bagging), which is robust and resilient to over-fitting 59 . The Gini impurity was used to compute the model likelihood of prediction. To quantify the prediction uncertainty of the RF model, a Monte Carlo approach was used to compute the confidence interval of each prediction. A CPH model 22 , predicting survival time to death from the first confirmed COVID-19 positive test result, was trained on the same subset of features selected by the RF feature selection process and tested on in the same manner as the RF to maximise its explainability. We did not carry out censoring of the data, as such, the AUROC can be considered the same as concordance probability (Harrel's C) for binary outcomes-which in this case is COVID-19 mortality and survival.

QCOVID comparison. We compared our model against QCOVID, a leading risk prediction model for infection and subsequent death due to COVID-19, which was developed by fitting a sub-distribution hazard model on the QResearch database 11 . Predictor variables reported in QCOVID were mapped to comparable features in the UKB dataset. The UKB dataset did not include all of the relevant variables used in the QCOVID algorithm, hence chemotherapy grades and medication variables were excluded in our analysis (Supplementary Table 2 ). QCOVID risk equations for mortality were then implemented for both male and female cohorts. To ensure a fair comparison between models, QCOVID risk equations were evaluated on the UKB dataset using the same methods described above.

All methods within this article were performed in accordance with and was written following the TRIPOD (Transparent Reporting of a Multivariable Prediction Model for Individual Prognosis or Diagnosis) guidelines 60 , which are further elaborated in Supplementary Table 4. 

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Prevalence of Asymptomatic SARS-CoV-2 Infection

Estimating the extent of asymptomatic COVID-19 and its potential for community transmission: Systematic review and meta-analysis

COVID-19 case-fatality rate and demographic and socioeconomic influencers: worldwide spatial regression analysis based on country-level data

Preexisting comorbidities predicting COVID-19 and mortality in the UK biobank community cohort

The association between symptom onset and length of hospital stay in 2019 novel coronavirus pneumonia cases without epidemiological trace

Population risk factors for severe disease and mortality in COVID-19: A global systematic review and meta-analysis

Vital signs assessed in initial clinical encounters predict COVID-19 mortality in an NYC hospital system

Clinical course and risk factors for mortality of adult inpatients with COVID-19 in Wuhan, China: a retrospective cohort study

Association of red blood cell distribution width with mortality risk in hospitalized adults with SARS-CoV-2 infection

Living risk prediction algorithm (QCOVID) for risk of hospital admission and mortality from coronavirus 19 in adults: National derivation and validation cohort study

Individual and community-level risk for COVID-19 mortality in the United States

Developing a COVID-19 mortality risk prediction model when individual-level data are not available

Factors associated with COVID-19-related death using OpenSAFELY

COVID-19 mortality risk assessment: An international multi-center study

An interpretable mortality prediction model for COVID-19 patients

Risk stratification of patients admitted to hospital with covid-19 using the ISARIC WHO Clinical Characterisation Protocol: development and validation of the 4C Mortality Score

CPAS: the UK's national machine learning-based hospital capacity planning system for COVID-19

An external validation of the QCovid risk prediction algorithm for risk of mortality from COVID-19 in adults: national validation cohort study in England

COVID-19) risk assessment

Mobile App-Based Remote Patient Monitoring in Acute Medical Conditions: Prospective Feasibility Study Exploring Digital Health Solutions on Clinical Workload During the COVID Crisis

Regression Models and Life-Tables

The Effect of Age on Mortality in Patients With COVID-19: A Meta-Analysis With 611,583 Subjects

Global pandemics interconnected-obesity, impaired metabolic health and COVID-19

A Review of Coronavirus Disease-2019 (COVID-19)

A systematic review on COVID-19: urological manifestations, viral RNA detection and special considerations in urological conditions

De novo urinary symptoms associated With COVID-19: COVID-19-associated cystitis

Urinary frequency as a possibly overlooked symptom in COVID-19 patients: Does SARS-CoV-2 cause viral cystitis?

Focus on the Crosstalk between COVID-19 and Urogenital Systems

The Effect of the Presence of Lower Urinary System Symptoms on the Prognosis of COVID-19: Preliminary Results of a Prospective Study

Cardiovascular disease risk prediction using automated machine learning: A prospective study of 423,604 UK Biobank participants

Development and validation of risk prediction models for multiple cardiovascular diseases and Type 2 diabetes

Anthropometry, body fat composition and reproductive factors and risk of oesophageal and gastric cancer by subtype and subsite in the UK Biobank cohort

The role of visceral adiposity in the severity of COVID-19: Highlights from a unicenter cross-sectional pilot study in Germany

Obesity and SARS-CoV-2: A population to safeguard

Sleep Duration and All-Cause Mortality: A Systematic Review and Meta-Analysis of Prospective Studies

Sleep duration predicts cardiovascular outcomes: a systematic review and meta-analysis of prospective studies

Sleep Duration as a Risk Factor for Diabetes Incidence in a Large US Sample

Comorbidity and its impact on 1590 patients with COVID-19 in China: A nationwide analysis

Clinical symptoms, comorbidities and complications in severe and non-severe patients with COVID-19

Prediction models for covid-19 outcomes

Support vector methods for survival analysis: a comparison between ranking and regression approaches

DeepSurv: personalized treatment recommender system using a Cox proportional hazards deep neural network

A Unified Approach to Interpreting Model Predictions

Model-Agnostic Interpretability of Machine Learning

Prediction models for diagnosis and prognosis of covid-19: systematic review and critical appraisal

Clinical features of COVID-19 mortality: development and validation of a clinical prediction model

Applications of digital technology in COVID-19 pandemic planning and response

Pre-symptomatic detection of COVID-19 from smartwatch data

Analyzing changes in respiratory rate to predict the risk of COVID-19 infection

Comparison of Sociodemographic and Health-Related Characteristics of UK Biobank Participants With Those of the General Population

SARS-CoV-2 evolution and vaccines: cause for concern?

UK Biobank: An Open Access Resource for Identifying the Causes of a Wide Range of Complex Diseases of Middle and Old Age

Dynamic linkage of COVID-19 test results between Public Health England's Second Generation Surveillance System and UK

Leave-One-Out Cross-Validation

The jackknife, the bootstrap, and other resampling plans

Random Forests

Transparent reporting of a multivariable prediction model for individual prognosis or diagnosis (TRIPOD): the TRIPOD Statement

This research has been conducted using data from UK Biobank, a major biomedical database (www. ukbio bank. ac. uk).

All authors have approved the final version of the manuscript submitted. All authors agree to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved. M.A.D. conceived and designed the study, interpreted the results, developed the computation models, analysed the data, and wrote and reviewed the manuscript. A.B.R. and A.T.C.B. conceived and designed the study, interpreted the results, and wrote and reviewed the manuscript. B.K. interpreted the results, developed the computation models, analysed the data, and wrote and reviewed the manuscript. D. MOR developed the computation models, analysed the data, and wrote and reviewed the manuscript. A.Y. and A.D. interpreted the results and wrote and reviewed the manuscript. E.B. and M.A. conceived and designed the study and reviewed the manuscript. D.MOH., A.L., and D.P. interpreted the results and reviewed the manuscript.

This research was funded by Huma Therapeutics Ltd. Correspondence and requests for materials should be addressed to D.P.

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