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 failure _d: readmit 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 failure _d: readmit 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.

Back to Exercise: Readmission to hospital for asthmatic children.

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Last updated: 6 February, 2008.