# Suggested answer to exercise: Readmission to hospital for asthmatic children, 6

Question 6: What is the best estimate of the effect of the crisis plan? Give a confidence interval for the estimate. How do the other variables predict readmission?

We will use Cox's proportional hazards regression method to fit a model using crisis plan, sex, age, number of previous admissions, and respiration rate as predictors.

We use Analyze, Survival, Cox Regression. The time variable is "Follow-up time (days)" and the Status variable is "Readmitted". We define the event as "1", the code for a readmission. We put "Crisis plan", "Age", "Previous admissions", and "Respiration" into the covariates box. The only categorical variables are sex and crisis plan. As these each have only two categories, we do not need to create dummy variables and do not need to click Categorical.

Because we want to estimate the hazard ratio, we want a confidence interval for it. We go to Options and check CI for exp(B):. (Exp(B) is the hazard ratio). Click Continue, OK.

We get the following output:

Omnibus Tests of Model Coefficientsa,b
-2 Log
Likelihood
Overall (score) Change From Previous Step Change From Previous Block
Chi-square     df     Sig. Chi-square     df     Sig. Chi-square     df     Sig.
6794.498 148.467 5 .000 110.882 5 .000 108.557 6 .000
a. Beginning Block Number 0, initial Log Likelihood function: -2 Log likelihood: 6905.380
b. Beginning Block Number 1. Method = Enter

Variables in the Equation
B SE Wald     df     Sig. Exp(B) 95.0% CI for Exp(B)
Lower Upper
crisis .543 .115 22.309 1 .000 1.721 1.374 2.155
sex -.185 .089 4.266 1 .039 .831 .698 .991
age -.124 .019 41.338 1 .000 .883 .851 .917
admiss .043 .005 85.695 1 .000 1.044 1.035 1.054
resp -.002 .004 .312 1 .576 .998 .990 1.006

We can remove the non-significant predictors, one at a time. We start with the least significant, respiration rate:

Omnibus Tests of Model Coefficientsa,b
-2 Log
Likelihood
Overall (score) Change From Previous Step Change From Previous Block
Chi-square     df     Sig. Chi-square     df     Sig. Chi-square     df     Sig.
6930.453 162.772 4 .000 116.411 5 .000 116.411 4 .000
a. Beginning Block Number 0, initial Log Likelihood function: -2 Log likelihood: 7046.864
b. Beginning Block Number 1. Method = Enter

Variables in the Equation
B SE Wald     df     Sig. Exp(B) 95.0% CI for Exp(B)
Lower Upper
crisis .565 .112 25.530 1 .000 1.760 1.413 2.192
sex -.201 .088 5.167 1 .023 .818 .688 .973
age -.113 .017 44.165 1 .000 .893 .864 .923
admiss .044 .005 93.541 1 .000 1.045 1.035 1.054

You may notice that the standard errors get smaller as the variables with no predictive power are removed, showing that the model has improved.

The best estimate of the effect of the crisis plan is that children with a crisis plan have an increased risk of readmission at any time, by a factor estimated to be 1.76 (95% confidence interval 1.41 to 2.19).

The other variables affect the chance of readmission as follows:

• readmission is less likely for a boy than for a girl, by a factor = 0.82,
• older children are less likely to be readmitted, by a factor = 0.89 for every year difference in age,
• children with a history of previous admission are more likely to be readmitted, by a factor = 1.045 for every previous admission.