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Survival analysis

Survival analysis. Problem. Do patients survive longer after treatment A than after treatment B? Possible solutions: ANOVA on mean survival time? ANOVA on median survival time?. Progressively censored observations. Current life table Completed dataset Cohort life table

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Survival analysis

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  1. Survival analysis

  2. Problem • Do patients survive longer after treatment A than after treatment B? • Possible solutions: • ANOVA on mean survival time? • ANOVA on median survival time?

  3. Progressively censored observations • Current life table • Completed dataset • Cohort life table • Analysis “on the fly”

  4. First example of the day

  5. Person-year of observation • In total: 15.122 days ~ 41.4y • 11 patients died: 11/41.4y = 0.266 y-1 26.6 death/100y • 1000 patients in 1 y or • 100 patients in 10y

  6. Mortality rates • 11 of 25 patients died • 11/25 = 44% • When is the analysis done?

  7. 1-year survival rate • 6 patients dies the first year • 25 patients started • 24%

  8. 1-year survival rate • 3 patients less than 1 year • 6/(25-3) = 27% • Patient 7 • 24% -27%

  9. Actuarial / life table anelysis • Treatment for lung cancer

  10. Actuarial / life table anelysis • A sub-set of 13 patients undergoing the same treatment

  11. Actuarial / life table anelysis • Time interval chosen to be 3 months • ni number of patients starting a given period

  12. Actuarial / life table anelysis • di number of terminal events, in this example; progression/response • wi number of patients that have not yet been in the study long enough to finish this period

  13. Actuarial / life table anelysis • Number exposed to risk: ni – wi/2 Assuming that patients withdraw in the middle of the period on average.

  14. Actuarial / life table anelysis • qi = di/(ni – wi/2) Proportion of patients terminating in the period

  15. Actuarial / life table anelysis • pi = 1 - qi Proportion of patients surviving

  16. Actuarial / life table anelysis • Si = pi pi-1 ...pi-N Cumulative proportion of surviving Conditional probability

  17. Survival curves • How long will a lung cancer patient keep having cancer on this particular treatment?

  18. Kaplan-Meier • Simple example with only 2 ”terminal-events”.

  19. Confidence interval of the Kaplan-Meier method • Fx at first terminal event

  20. Confidence interval of the Kaplan-Meier method • Survival plot for all data on treatment 1 • Are there differences between the treatments?

  21. Comparing Two Survival Curves • One could use the confidence intervals… • But what if the confidence intervals are not overlapping only at some points? • Logrank-stats • Hazard ratio • Mantel-Haenszel methods

  22. Comparing Two Survival Curves • The logrank statistics • Aka Mantel-logrank statistics • Aka Cox-Mantel-logrank statistics

  23. Comparing Two Survival Curves • Divide the data into intervals (eg. 10 months) • Count the number of patients at risk in the groups and in total • Count the number of terminal events in the groups and in total • Calculate the expected numbers of terminal events e.g. (31-40) 44 in grp1 and 46 in grp2, 4 terminal events. expected terminal events 4x(44/90) and 4x(46/90) • Calculate the total

  24. Comparing Two Survival Curves • Smells like Chi-Square statistics

  25. Comparing Two Survival Curves • Hazard ratio

  26. Comparing Two Survival Curves • Mantel Haenszel test • Is the OR significant different from 1? • Look at cell (1,1) • Estimated value, E(ai) • Variance, V(ai)

  27. Comparing Two Survival Curves • Mantel Haenszel test • df = 1; p>0.05

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