Linear Prediction: Principles and Methods[^3^]

As a linear model, the QuantileRegressor gives linear predictions\(\haty(w, X) = Xw\) for the \(q\)-th quantile, \(q \in (0, 1)\).The weights or coefficients \(w\) are then found by the followingminimization problem:

We performed stepwise logistic regression in the UK cohort, by randomly dividing it into training and test sets (ratio: 80:20) to identify independent symptoms most strongly correlated with COVID-19, adjusting for age, sex and BMI. A combination of loss of smell and taste, fatigue, persistent cough and loss of appetite resulted in the best model (with the lowest Akaike information criterion). We therefore generated a linear model for symptoms that included loss of smell and taste, fatigue, persistent cough and loss of appetite to obtain a symptoms prediction model for COVID-19:

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Baseline characteristics are presented as the number (percentage) for categorical variables and the mean (standard deviation) for continuous variables. Multivariate logistic regression adjusting for age, sex and BMI was applied to investigate the correlation between loss of smell and taste and COVID-19 in 15,368 UK users of the symptom tracker app who were also tested in the laboratory for SARS-CoV-2 (6,452 UK individuals tested positive and 9,186 tested negative). The results were replicated in 726 US individuals who tested positive and 2,037 US individuals who tested negative. We then randomly split the UK sample into training and test sets with a ratio of 80:20. In the training set, we performed stepwise logistic regression combining forward and backward algorithms, to identify other symptoms associated with COVID-19 independent of loss of smell and taste. We included in the model ten other symptoms (fever, persistent cough, fatigue, shortness of breath, diarrhea, delirium, skipped meals, abdominal pain, chest pain and hoarse voice) as well as age, sex and BMI, and chose as the best model the one with the lowest Akaike information criterion. We then assessed the performance of the model both in the test set and via tenfold cross-validation in the entire UK sample of 15,638 individuals using the R package cvAUC13. We further validated the prediction model in the US cohort. 2ff7e9595c