lecture 3 survival analysis. the slang current life table –what is the life time now? cohort life...
TRANSCRIPT
The slang
• Current life table– What is the life time now?
• Cohort life table– What is the life time of this group?
Problem• Do patients survive longer after treatment
A than after treatment B?
• Possible solutions:– ANOVA on mean survival time?– ANOVA on median survival time?
• Survival analysis– Aka. Actuarial / life table analysis
Person-year of observation• In total: 15122 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
Actuarial / life table anelysis• Wi number of patients
that have not yet been in the study long enough to finish this period
Actuarial / life table anelysis• Number exposed to risk:
• ni – wi/2
• Assuming that patients withdraw in the middle of the period on average.
Actuarial / life table anelysis• qi = di/(ni – wi/2)
• Proportion of patients terminating in the period
Actuarial / life table anelysis• Si = pi pi-1 ...pi-N
• Cumulative proportion of surviving
• Conditional probability
A few concerns • Withdrawals are assumed to happen at
time midpoints– Kaplan Meiers method will fix this
• The probability of surviving a period is treated as if it is independent of survival of other periods.
Kaplan-Meier product limit method
• Changes in the survival curve are calculated when an event occurs
• Withdrawals are ignored as events
Confidence of survival curves• Standard Error (SE)
• Assumed to be normally distributed
• 95% confidence is 1.96*SE
( ) ii i
i i i
dSE S S
n n d
Comparing survival curves• Two principle methods
– Logrank statistics– Mantel Haenszel chi-square statistics
Mantel Haenszel chi-square statistics
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a d nOR
b c n
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_i
Row total Col totalE a
Grand total
2
( )( )( )( )( )
( 1)i
a b b d a b c dV a
n n
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i i
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a E aMantel Haenszel
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