Survival Analysis Part 2

Descriptive Summary

Below is a descriptive summary of key variables in the Data for practice_BC_lecture4_N220 dataset

## ## Gender Distribution

Gender	Count	Proportion
female	47	0.236
male	152	0.764

## 
## ## Stage Distribution

Stage	Count	Proportion
1	46	0.232
2	70	0.354
3	60	0.303
4	22	0.111

## 
## ## Summary Statistics for Continuous Variables

Variable	Min	Q1	Median	Mean	Q3	Max
age	28	53	61	61.17085	69	86
time_to_death	1	995	1943	2177.66834	3376	6220
time_to_progression	1	110	496	767.24623	1009	4052

## 
## ## Standard Deviations

Variable	SD
age	10.51939
time_to_death	1422.68805
time_to_progression	930.30350

## 
## ## Summary by Stage

Stage	Count	Mean_age	Median_time_death
1	46	58.21739	2122.5
2	70	57.82857	2035.0
3	60	66.21667	1843.0
4	22	64.72727	1146.5
NA	2	50.00000	2905.0

Kaplan-Meier Survival Analysis by Stage, Age Group, and Gender

Kaplan-Meier Survival Analysis by Stage

Kaplan-Meier Survival Analysis by age_group

Kaplan-Meier Survival Analysis by gender

Cox Proportional Hazards Models and Survival Visualization

The Cox Proportional Hazards model for time-to-death results reveal that Stage and Age are significant predictors of the risk of death. Patients in higher disease stages have a 1.84-fold increased risk of death compared to those in earlier stages (HR = 1.842, p = 0.005), indicating a strong and statistically significant association. Similarly, increasing age is associated with a higher risk of death, with each additional year increasing the risk by approximately 4.8% (HR = 1.048, p = 0.002). In contrast, other variables such as gender and the presence of mutations in Gene1 through Gene5 do not show statistically significant associations with the risk of death (p > 0.05), suggesting their limited impact in this context. These findings underscore the importance of disease stage and age in predicting survival outcomes.

The Cox Proportional Hazards model for time-to-progression shows that Stage, Gene2 and Gene3 are significant predictors of disease progression. Patients in higher disease stages have a 2.71-fold increased risk of progression compared to those in earlier stages (HR = 2.705, p < 0.001), indicating a strong and statistically significant association. Similarly, the presence of Gene2 mutation is associated with a significantly increased risk of progression, with a hazard ratio of 1.771 (p = 0.012). On the other hand, variables such as gender, age, and mutations in Gene1, Gene3, Gene4, and Gene5 do not show statistically significant associations with progression (p > 0.05). These findings highlight the critical role of disease stage and Gene2 mutation in influencing disease progression.

## ## Cox Model Results for Time-to-Death

Variable	Hazard_Ratio	CI_lower	CI_upper	P_value
Stage	1.842	1.204	2.818	0.005
gendermale	1.230	0.659	2.295	0.515
age	1.048	1.017	1.080	0.002
Gene1	0.667	0.343	1.298	0.233
Gene2	0.804	0.377	1.716	0.574
Gene3	0.774	0.355	1.690	0.521
Gene4	0.828	0.287	2.384	0.726
Gene5	1.212	0.528	2.781	0.649

## 
## ## Cox Model Results for Time-to-Progression

Variable	Hazard_Ratio	CI_lower	CI_upper	P_value
Stage	2.705	2.040	3.587	0.000
gendermale	1.033	0.661	1.615	0.885
age	0.983	0.965	1.002	0.077
Gene1	1.333	0.846	2.100	0.215
Gene2	1.771	1.133	2.768	0.012
Gene3	0.337	0.183	0.620	0.000
Gene4	1.444	0.789	2.643	0.233
Gene5	1.113	0.635	1.953	0.708