Biostatistics Case

Q1,

Age: Continuous

Urgency of operation ordinal

Length of hospital stay continuous

Type of surgery nominal

Ejection fraction estimate ordinal

Preoperative dialysis nominal

Q2,

Patients' ages in each mortality groups

Group Statistics

Mortality Status N Mean Std. Deviation Std. Error Mean

Age No 973 65.1778 13.07279 .41909

Yes 26 72.4766 6.58434 1.29130

Independent Samples Test result

Levene's Test for Equality of Variances t-test for Equality of Means

F Sig. t df Sig. (2-tailed) Mean Difference Std. Error Difference 95% Confidence Interval of the Difference

Lower Upper

Age Equal variances assumed 10.804 .001 -2.836 997 .005 -7.29885 2.57339 -12.34873 -2.24896

Equal variances not assumed -5.376 30.535 .000 -7.29885 1.35760 -10.06940 -4.52829

As age is a continuous data and mortality status is nominal data, it can be solved by using independent samples t-test

Hypotheses:

* Null hypothesis: there is no difference of the mean ages between the 30-day mortality statuses.

* Alternative hypothesis: two groups have different mean ages

Assumptions:

* Ages in each group follows normal distribution.

* Groups are independent.

* Patients within each group are independent.

As equality of variances is 13.072792/ 6.584342 =3.9 > 2, the equal variances is not assumed.

T-score = difference in sample means/ se= -5.376

P- value:

By using SPSS data package, the p-value for t=-5.376 is less than 0.000 < 0.005, since the p-value is very small smaller than 0.005, we reject the null hypothesis and the difference in the mean of ages for alive and death is significant.

Conclusion: the mean age for cardiac disease death is 72 which is higher than those of the alive group (65), as within the 95% CI (-10.069, -4.528), it does not include "0", and the p-value is much smaller than 0.005, thus the result suggests that the difference in ages can lead to significantly different mortality rate. The study results support that patients with higher age are more like to contribute to the 30-day mortality rate.

Q3,

Using SPSS data package,

Length of hospital stay compared to the health status

As they are asymmetrical data, we must use Kruskal-wallis test on SPSS,

LOS as compared by different cardiac illness status

Status N Mean Rank

Length of hospital stay Elective 616 392.02

Urgent 331 676.63

Emergency 47 634.45

Salvage 4 809.13

Total 998

Descriptives

Status Statistic Std. Error

Length of hospital stay Elective Mean 9.8117 .64413

95% Confidence Interval for Mean Lower Bound 8.5467

Upper Bound 11.0767

5% Trimmed Mean 8.3481

Median 7.0000

Variance 255.584

Std. Deviation 15.98699

Minimum .00

Maximum 374.00

Range 374.00

Interquartile Range 4.00

Skewness 19.503 .098

Kurtosis 439.726 .197

Urgent Mean 17.5015 .87272

95% Confidence Interval for Mean Lower Bound 15.7847

Upper Bound 19.2183

5% Trimmed Mean 15.3013

Median 13.0000

Variance 252.105

Std. Deviation 15.87782

Minimum 1.00

Maximum 154.00

Range 153.00

Interquartile Range 10.00

Skewness 4.594 .134

Kurtosis 29.535 .267

Emergency Mean 24.1277 4.57375

95% Confidence Interval for Mean Lower Bound 14.9212

Upper Bound 33.3341

5% Trimmed Mean 19.1761

Median 14.0000

Variance 983.201

Std. Deviation 31.35603

Minimum .00

Maximum 160.00

Range 160.00

Interquartile Range 18.00

Skewness 2.933 .347

Kurtosis 9.399 .681

Salvage Mean 44.0000 29.05455

95% Confidence Interval for Mean Lower Bound -48.4645

Upper Bound 136.4645

5% Trimmed Mean 41.0556

Median 17.5000