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Lab 11 Survival Analysis Exercises

Evan Woods 2024-01-11

Applied

Question 10:

This exercise focuses on the brain tumor data, which is included in the ISLR2 R library.

  • Question 10-a: Plot the Kaplan-Meier survival curve with ±1 standard error bands, using the survfit() function in the survival package.
    • Answer (Python):

  • Question 10-b: Draw a bootstrap sample of size n = 88 from the pairs (y, δ), and compute the resulting Kaplan-Meier survival curve. Repeat this process B = 200 times. Use the results to obtain an estimate of the standard error of the Kaplan-Meier survival curve at each timepoint. Compare this to the standard errors obtained in (a).
    • Answer (R):
A bootstrapped sample of size 88:

  • Question 10-c: Fit a Cox proportional hazards model that uses all of the predictors to predict survival. Summarize the main findings.
    • Answer:
Call:
coxph(formula = Surv(time, status) ~ ., data = BrainCancer)

  n= 87, number of events= 35 
   (1 observation deleted due to missingness)

                       coef exp(coef) se(coef)      z Pr(>|z|)    
sexMale             0.18375   1.20171  0.36036  0.510  0.61012    
diagnosisLG glioma  0.91502   2.49683  0.63816  1.434  0.15161    
diagnosisHG glioma  2.15457   8.62414  0.45052  4.782 1.73e-06 ***
diagnosisOther      0.88570   2.42467  0.65787  1.346  0.17821    
locSupratentorial   0.44119   1.55456  0.70367  0.627  0.53066    
ki                 -0.05496   0.94653  0.01831 -3.001  0.00269 ** 
gtv                 0.03429   1.03489  0.02233  1.536  0.12466    
stereoSRT           0.17778   1.19456  0.60158  0.296  0.76760    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

                   exp(coef) exp(-coef) lower .95 upper .95
sexMale               1.2017     0.8321    0.5930    2.4352
diagnosisLG glioma    2.4968     0.4005    0.7148    8.7215
diagnosisHG glioma    8.6241     0.1160    3.5664   20.8546
diagnosisOther        2.4247     0.4124    0.6678    8.8031
locSupratentorial     1.5546     0.6433    0.3914    6.1741
ki                    0.9465     1.0565    0.9132    0.9811
gtv                   1.0349     0.9663    0.9906    1.0812
stereoSRT             1.1946     0.8371    0.3674    3.8839

Concordance= 0.794  (se = 0.04 )
Likelihood ratio test= 41.37  on 8 df,   p=2e-06
Wald test            = 38.7  on 8 df,   p=6e-06
Score (logrank) test = 46.59  on 8 df,   p=2e-07

The risk of death associated with HG glioma is more than 8 times the risk
of death associated with meningioma. This is a statistically significant
difference. Because the Karnofsky index is negative, there a lower risk of death
and greater chance of life expectancy with an increased Karnofsky score.
  • Question 10-d: Stratify the data by the value of ki.
    • Answer:
Call: survfit(formula = Surv(time, status) ~ ki, data = BrainCancer)

        n events median 0.95LCL 0.95UCL
ki=40   1      1   3.38      NA      NA
ki=60   5      3  31.25    11.6      NA
ki=70  14      6  33.41    10.8      NA
ki=80  36     18  35.93    22.0      NA
ki=90  27      6     NA      NA      NA
ki=100  5      1  51.02    51.0      NA