# Suggested answer to exercise: Readmission to hospital for asthmatic children using Stata 9, 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. The command is stcox, followed by the list of predictor variables. 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 use xi:. We get:

```. stcox crisis sex age admiss resp

analysis time _t:  time

Iteration 0:   log likelihood = -3452.6902
Iteration 1:   log likelihood = -3414.4126
Iteration 2:   log likelihood = -3397.9027
Iteration 3:   log likelihood = -3397.2584
Iteration 4:   log likelihood =  -3397.249
Iteration 5:   log likelihood =  -3397.249
Refining estimates:
Iteration 0:   log likelihood =  -3397.249

Cox regression -- Breslow method for ties

No. of subjects =         1013                     Number of obs   =      1013
No. of failures =          524
Time at risk    =       523136
LR chi2(5)      =    110.88
Log likelihood  =    -3397.249                     Prob > chi2     =    0.0000

------------------------------------------------------------------------------
_t | Haz. Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
crisis |   1.720545   .1976694     4.72   0.000     1.373641    2.155056
sex |   .8312987   .0743663    -2.07   0.039     .6976062    .9906126
age |    .883351    .017041    -6.43   0.000     .8505748    .9173902
admiss |   1.044303   .0048903     9.26   0.000     1.034762    1.053932
resp |   .9978036   .0039263    -0.56   0.576     .9901378    1.005529
------------------------------------------------------------------------------
```

We can remove the non-significant predictors, one at a time:

```. stcox crisis sex age admiss

analysis time _t:  time

Iteration 0:   log likelihood = -3523.4318
Iteration 1:   log likelihood = -3484.7497
Iteration 2:   log likelihood =   -3466.22
Iteration 3:   log likelihood = -3465.2474
Iteration 4:   log likelihood = -3465.2266
Iteration 5:   log likelihood = -3465.2266
Refining estimates:
Iteration 0:   log likelihood = -3465.2266

Cox regression -- Breslow method for ties

No. of subjects =         1025                     Number of obs   =      1025
No. of failures =          534
Time at risk    =       525762
LR chi2(4)      =    116.41
Log likelihood  =   -3465.2266                     Prob > chi2     =    0.0000

------------------------------------------------------------------------------
_t | Haz. Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
crisis |   1.760005   .1969156     5.05   0.000     1.413444     2.19154
sex |   .8177965    .072362    -2.27   0.023     .6875867    .9726645
age |    .892974   .0152103    -6.65   0.000     .8636545    .9232889
admiss |   1.044526   .0047048     9.67   0.000     1.035346    1.053789
------------------------------------------------------------------------------
```

As all predictors are now significant, this is the final model.

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.