1
$\begingroup$

I' ve been reading some scientific works and I don't understand how nomograms are constructed from logistic regression models. In the article:

Development and Validation of an Early Scoring System for Prediction of Disease Severity in COVID-19 Using Complete Blood Count Parameters

Source -> https://pubmed.ncbi.nlm.nih.gov/34786318/

I also provide link to download from my Google Drive -> https://drive.google.com/file/d/1xEoYh6RZJ3bsqdaCbfE943E11xFtgmeP/view?usp=sharing

In the article they work with COVID19 dataset describing two target values. Patient died from covid or survived. Along with preprocessing phase and feature selection as well as statistical characteristics they choose 10 blood parameters on which the algorithms will be trained and evaluated. [well not only blood as age is here too] enter image description here
After training it turns out that Logistic Regression model has the best results, so it is chosen for nomogram creation.

So.. logistic regression model is used to create nomogram for covid19 mortality prediction.
enter image description here If the score < 0.05 there is low probability od death. If score > 0.5 there is high probality.

The point I can't undestand is how they come up with Death probability and this:

enter image description here

I get all the part conserning preprocessing, feature selection and statistical characterictics.

$\endgroup$

1 Answer 1

1
$\begingroup$

The maths if very simples for this :

Step 1: Lets Assume your Logistics equation is
 log(p/(1-p) = BO + B1X + B2X + B3X

Step 2: Exponentiate and take the multiplicative inverse of both sides    
 (1-p)/p = 1/ exp(BO + B1X + B2X + B3X. )

Step 3: Partial out the fraction on the left-hand side of the equation and add one to both sides


 1/p = 1 + 1/ exp(BO + B1X + B2X + B3X )

Step 4: Take the sum on RHS

 1/p = (exp(BO + B1X + B2X + B3X ) + 1)/exp(BO + B1X + B2X + B3X )

Step 5: Finally, take the multiplicative inverse again to obtain the formula for the probability p(y=1):
 p = exp(BO + B1X + B2X + B3X ) / (1+exp(BO + B1X + B2X + B3X ))

Formula to calulate probability is :
probability = exp(BO + B1X + B2X + B3X ) / (1+exp(BO + B1X + B2X + B3X ))

If you substiture your equation in this you can get the probability of death assuming death was 1 in target variable

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.