Question 4: Is the presence of a crisis plan related to other variables which might increase the risk of readmission, such as age, sex, number of previous admissions, pulse rate, or respiration rate? How do children given a crisis plan differ from the other children?
Sex is a qualitative variable, so we will use a cross-tabulation and chi-squared test:
. tab sex crisis, chi2
| crisis plan
sex | absent present | Total
-----------+----------------------+----------
girl | 337 77 | 414
boy | 539 80 | 619
-----------+----------------------+----------
Total | 876 157 | 1,033
Pearson chi2(1) = 6.1989 Pr = 0.013
Clearly girls are more likely to have crisis plans than boys.
The other variables are all quantitative and, in view of the large sample size, a z test is indicated. In Stata, this is done using a t test with unequal variances:
. ttest age, by(crisis) unequal
Two-sample t test with unequal variances
------------------------------------------------------------------------------
Group | Obs Mean Std. Err. Std. Dev. [95% Conf. Interval]
---------+--------------------------------------------------------------------
absent | 874 3.709382 .102038 3.016598 3.509114 3.909651
present | 157 5.343949 .3004859 3.765078 4.750403 5.937495
---------+--------------------------------------------------------------------
combined | 1031 3.958293 .0994898 3.194535 3.763067 4.153519
---------+--------------------------------------------------------------------
diff | -1.634567 .3173382 -2.260451 -1.008683
------------------------------------------------------------------------------
diff = mean(absent) - mean(present) t = -5.1509
Ho: diff = 0 Satterthwaite's degrees of freedom = 193.592
Ha: diff < 0 Ha: diff != 0 Ha: diff > 0
Pr(T < t) = 0.0000 Pr(|T| > |t|) = 0.0000 Pr(T > t) = 1.0000
. ttest wheeze, by(crisis) unequal
Two-sample t test with unequal variances
------------------------------------------------------------------------------
Group | Obs Mean Std. Err. Std. Dev. [95% Conf. Interval]
---------+--------------------------------------------------------------------
absent | 873 36.16151 2.299032 67.92851 31.64923 40.67379
present | 155 43.63871 6.940243 86.40533 29.92834 57.34908
---------+--------------------------------------------------------------------
combined | 1028 37.28891 2.21521 71.02504 32.94206 41.63577
---------+--------------------------------------------------------------------
diff | -7.477198 7.311123 -21.89896 6.944566
------------------------------------------------------------------------------
diff = mean(absent) - mean(present) t = -1.0227
Ho: diff = 0 Satterthwaite's degrees of freedom = 189.25
Ha: diff < 0 Ha: diff != 0 Ha: diff > 0
Pr(T < t) = 0.1539 Pr(|T| > |t|) = 0.3077 Pr(T > t) = 0.8461
. ttest admiss, by(crisis) unequal
Two-sample t test with unequal variances
------------------------------------------------------------------------------
Group | Obs Mean Std. Err. Std. Dev. [95% Conf. Interval]
---------+--------------------------------------------------------------------
absent | 876 2.003425 .1936601 5.731815 1.623332 2.383517
present | 154 6.727273 .5150541 6.391654 5.709737 7.744809
---------+--------------------------------------------------------------------
combined | 1030 2.709709 .1891512 6.070544 2.338543 3.080875
---------+--------------------------------------------------------------------
diff | -4.723848 .550259 -5.808947 -3.638749
------------------------------------------------------------------------------
diff = mean(absent) - mean(present) t = -8.5848
Ho: diff = 0 Satterthwaite's degrees of freedom = 198.625
Ha: diff < 0 Ha: diff != 0 Ha: diff > 0
Pr(T < t) = 0.0000 Pr(|T| > |t|) = 0.0000 Pr(T > t) = 1.0000
. ttest pulse, by(crisis) unequal
Two-sample t test with unequal variances
------------------------------------------------------------------------------
Group | Obs Mean Std. Err. Std. Dev. [95% Conf. Interval]
---------+--------------------------------------------------------------------
absent | 869 136.5201 .7079134 20.86844 135.1307 137.9096
present | 154 133.2532 1.890531 23.46087 129.5183 136.9882
---------+--------------------------------------------------------------------
combined | 1023 136.0283 .6659108 21.29874 134.7216 137.3351
---------+--------------------------------------------------------------------
diff | 3.266891 2.018725 -.7140408 7.247824
------------------------------------------------------------------------------
diff = mean(absent) - mean(present) t = 1.6183
Ho: diff = 0 Satterthwaite's degrees of freedom = 198.227
Ha: diff < 0 Ha: diff != 0 Ha: diff > 0
Pr(T < t) = 0.9464 Pr(|T| > |t|) = 0.1072 Pr(T > t) = 0.0536
. ttest resp, by(crisis) unequal
Two-sample t test with unequal variances
------------------------------------------------------------------------------
Group | Obs Mean Std. Err. Std. Dev. [95% Conf. Interval]
---------+--------------------------------------------------------------------
absent | 871 44.88749 .4467426 13.18459 44.01067 45.7643
present | 149 41.2349 1.025318 12.51561 39.20874 43.26105
---------+--------------------------------------------------------------------
combined | 1020 44.35392 .411634 13.14654 43.54617 45.16167
---------+--------------------------------------------------------------------
diff | 3.652586 1.118417 1.447716 5.857457
------------------------------------------------------------------------------
diff = mean(absent) - mean(present) t = 3.2659
Ho: diff = 0 Satterthwaite's degrees of freedom = 208.251
Ha: diff < 0 Ha: diff != 0 Ha: diff > 0
Pr(T < t) = 0.9994 Pr(|T| > |t|) = 0.0013 Pr(T > t) = 0.0006
Age, previous admissions, and respiration are significantly related to the crisis plan.
Children given a crisis plan were more likely to be girls than were other children, and tended to be older, to have had more previous admissions, and to have slower respiration.
Back to Exercise: Readmission to hospital for asthmatic children.
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Last updated: 6 February, 2008.