Solution
Q-1 A surgeon wish to predict the live or death (status) of a CABG patient through their pulse rate, systolic blood pressure, sugar level, hemoglobin etc. He got the data from last 1600 surgeries held in a local hospital and applied an analysis. He got the following result
Identification: It is binary logistic regression (LOIGT)
Coding
0 = Death
1 = Alive
The two post-operative status of the patients are death and alive coded by 0 and 1 respectively to use in binary logistic regression.
Hosmer and Lemshow goodness of fit test sig value = 0.896
The analysis is fitted that means the analysis is compatible with the data and the logit model is expected to predict the post-operative status of the patient
Block 0
Accuracy = 29%
This shows the fluke accuracy about the post-operative status of the patient if none of the indicators are used as predictors.
Variables not in equation with sig. values
Pulse Rate 0.004
Systolic BP 0.000
Sugar Level 0.001
HB 0.450
The table shows that if Pulse rate, systolic BP and Sugar level are used for prediction it will help to predict the post-operative status of the patient more accurately while HB does not matter
Block 1
Omnibus sig 0.0000
Neglekark R square 0.548 Cox & Snell R-square 0.458
The omnibus test is showing that the logit model is expected to have enough better accuracy then fluke while Neglekarke R square is showing that about 55% increase in accuracy is expected if we use logit model to predict post-operative status of the patient
Variables in equation with B coefficients, Sig. value and Exp (B)
Pulse Rate 1.245 0.004 1.45
Systolic BP 4.658 0.000 1.104
Sugar Level -0.568 0.001 0.846
HB 0.168 0.450 1.000
Accuracy = 78%
Therefor the logit model is
Link function = 1.245 (PR) + 4.658 (SBP) – 0.568 (SL)
Where, Link function = post-operative status of the patient
The accuracy of above model is 78%
The Exp (B) shows that :
The chance of life increase by 45% if the Pulse rate of a patient after operation
Identification: It is binary logistic regression (LOIGT)
Coding
0 = Death
1 = Alive
The two post-operative status of the patients are death and alive coded by 0 and 1 respectively to use in binary logistic regression.
Hosmer and Lemshow goodness of fit test sig value = 0.896
The analysis is fitted that means the analysis is compatible with the data and the logit model is expected to predict the post-operative status of the patient
Block 0
Accuracy = 29%
This shows the fluke accuracy about the post-operative status of the patient if none of the indicators are used as predictors.
Variables not in equation with sig. values
Pulse Rate 0.004
Systolic BP 0.000
Sugar Level 0.001
HB 0.450
The table shows that if Pulse rate, systolic BP and Sugar level are used for prediction it will help to predict the post-operative status of the patient more accurately while HB does not matter
Block 1
Omnibus sig 0.0000
Neglekark R square 0.548 Cox & Snell R-square 0.458
The omnibus test is showing that the logit model is expected to have enough better accuracy then fluke while Neglekarke R square is showing that about 55% increase in accuracy is expected if we use logit model to predict post-operative status of the patient
Variables in equation with B coefficients, Sig. value and Exp (B)
Pulse Rate 1.245 0.004 1.45
Systolic BP 4.658 0.000 1.104
Sugar Level -0.568 0.001 0.846
HB 0.168 0.450 1.000
Accuracy = 78%
Therefor the logit model is
Link function = 1.245 (PR) + 4.658 (SBP) – 0.568 (SL)
Where, Link function = post-operative status of the patient
The accuracy of above model is 78%
The Exp (B) shows that :
The chance of life increase by 45% if the Pulse rate of a patient after operation