The following table shows the results of a survival study for patients following

Question

The following table shows the results of a survival study for patients following a diagnosis of sepsis, based on the APACHE II score used as a measure of severity. Here the data are observations on the total number in each group (mi ,i = I , ,7); on yi (the number of deaths in group i, i = I , ,7); and also on xi,i = I, , 7, the APACHE II severity score at the time of diagnosis. Note that the xi values here have been used as the basis for forming the seven groups. 123 4 5 6 7 x (APACHE II) 4 8 12 16 20 24 28 mi (no. in group1 22 17 24 13 3 yi (no. deaths) 0 5 5 8 6 81 (a) Propose an appropriate logistic regression model with linear predictor +Dixi. [3 Marks] (b) Write down the log-likelihood in terms of Bo and ßi hased on the model given in (a). 14 Marks

Explanation / Answer

As yi is dependent variable.. Here if death occurs put 1 and if not then put 0. now we got the datast..

Run logistic regression model on new data

> data<-read.csv("D://chegg2.csv",header=T)
> data
i yi xi
1 1 0 4
2 2 1 8
3 3 1 12
4 4 1 16
5 5 1 20
6 6 1 24
7 7 1 28
> yi<-data[,2]
> yi
[1] 0 1 1 1 1 1 1
> xi<-data[,3]
> xi
[1] 4 8 12 16 20 24 28
> model<-glm(yi~xi,family=binomial(logit))
Warning messages:
1: glm.fit: algorithm did not converge
2: glm.fit: fitted probabilities numerically 0 or 1 occurred
> model

Call: glm(formula = yi ~ xi, family = binomial(logit))

Coefficients:
(Intercept) xi  
-67.98 11.30  

Degrees of Freedom: 6 Total (i.e. Null); 5 Residual
Null Deviance: 5.742
Residual Deviance: 6.288e-10 AIC: 4
>

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