2_HW1
2025-02-03
R Markdown
DATASET 1
df <- data.frame(
ID = 1:22,
group = c(1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2),
time = c(6.8 , 7.2, 9.5, 10.4, 12.6, 16.8, 20.2, 24.6, 28.6, 30.7, 9.4, 10.6, 12.8, 14.6, 16.2, 20.7, 23.5, 24.0, 30.6, 40.2, 44.1, 46.2),
event = c(1,0,1,0,1,1,0,1,1,1,1,0,1,0,1,1,1,0,1,1,1,1)
)
View(df)Kaplan Maier estimates
## Call: survfit(formula = Surv(time, event) ~ group, data = df)
##
## group=1
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 6.8 10 1 0.900 0.0949 0.732 1.000
## 9.5 8 1 0.787 0.1340 0.564 1.000
## 12.6 6 1 0.656 0.1638 0.402 1.000
## 16.8 5 1 0.525 0.1759 0.272 1.000
## 24.6 3 1 0.350 0.1849 0.124 0.985
## 28.6 2 1 0.175 0.1545 0.031 0.987
## 30.7 1 1 0.000 NaN NA NA
##
## group=2
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 9.4 12 1 0.917 0.0798 0.7729 1.000
## 12.8 10 1 0.825 0.1128 0.6311 1.000
## 16.2 8 1 0.722 0.1380 0.4963 1.000
## 20.7 7 1 0.619 0.1520 0.3823 1.000
## 23.5 6 1 0.516 0.1578 0.2830 0.939
## 30.6 4 1 0.387 0.1627 0.1695 0.882
## 40.2 3 1 0.258 0.1511 0.0817 0.813
## 44.1 2 1 0.129 0.1184 0.0213 0.780
## 46.2 1 1 0.000 NaN NA NA
Log-Rank test
## Call:
## survdiff(formula = Surv(time, event) ~ group, data = df)
##
## N Observed Expected (O-E)^2/E (O-E)^2/V
## group=1 10 7 4.63 1.213 1.93
## group=2 12 9 11.37 0.494 1.93
##
## Chisq= 1.9 on 1 degrees of freedom, p= 0.2The Mantel-Haenszel test yields a p-value of 0.2, indicating that there is no statistically significant difference between the two survival distributions. The chi-square value of 1.9 differs from the manually calculated result, suggesting a possible calculation error in the manual approach. However, the overall conclusion remains consistent—there is no significant difference in survival distributions.
DATASET 2
Kaplan Maier estimates
## Call: survfit(formula = Surv(Time, Status) ~ Group, data = s_data)
##
## Group=1
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 1 21 4 0.8095 0.0857 0.65785 0.996
## 2 17 1 0.7619 0.0929 0.59988 0.968
## 3 16 1 0.7143 0.0986 0.54500 0.936
## 4 15 2 0.6190 0.1060 0.44260 0.866
## 5 13 1 0.5714 0.1080 0.39455 0.828
## 8 12 4 0.3810 0.1060 0.22085 0.657
## 11 8 2 0.2857 0.0986 0.14529 0.562
## 12 6 2 0.1905 0.0857 0.07887 0.460
## 15 4 1 0.1429 0.0764 0.05011 0.407
## 17 3 1 0.0952 0.0641 0.02549 0.356
## 22 2 1 0.0476 0.0465 0.00703 0.322
## 23 1 1 0.0000 NaN NA NA
##
## Group=2
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 6 21 3 0.857 0.0764 0.720 1.000
## 7 17 1 0.807 0.0869 0.653 0.996
## 10 15 1 0.753 0.0963 0.586 0.968
## 13 12 1 0.690 0.1068 0.510 0.935
## 16 11 1 0.627 0.1141 0.439 0.896
## 22 7 1 0.538 0.1282 0.337 0.858
## 23 6 1 0.448 0.1346 0.249 0.807
## strata median lower upper
## 1 Group=1 8 4 12
## 2 Group=2 23 16 NAThe median survival time is 8 months for Group 1 and 23 months for Group 2, indicating a longer survival duration in Group 2.
Log-Rank test
## Call:
## survdiff(formula = Surv(Time, Status) ~ Group, data = s_data)
##
## N Observed Expected (O-E)^2/E (O-E)^2/V
## Group=1 21 21 10.8 9.68 16.8
## Group=2 21 9 19.2 5.43 16.8
##
## Chisq= 16.8 on 1 degrees of freedom, p= 4e-05The log-rank test yielded a very small p-value, which allows us to reject the null hypothesis. This indicates that the survival distributions between the treatment group and placebo group differ statistically.