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 Coefficients^{a,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 Coefficients^{a,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.

Back to Exercise: Readmission to hospital for asthmatic children.

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Last updated: 5 April, 2007.