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# glm

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## Chao Zhou

on 3 May 2010

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#### Transcript of glm

Survival analysis Derivation Primary purpose: model and analyse time-to-
event data. Data that have a principal endpoint at the time when an event occurs. (failures)
Time until an electrical component fails, or time to first recurence of a tumor after initial treatment. Hazard function h(t) Censored observation
Exponential regression model Weibull regression model Cox proportional hazards model Compare with GLM Type 1: experiment stop at a particular time Type 2:experiment stop after r out of n failed Random censoring Left censored and doubly censored Interval censoring: event happend between two time points Truncation Nonparametric Methods Kaplan-Meier (K-M) estimate Empirical survivor function (esf): Treat censored data as if there were no censored observations. 12,13,13+,14,14,17+ 12,13,13,14,14,17 S(t) 6/6 5/6 3/6 1/6 0 t <12 12 13 14 17 t S(t)
<12 1
12 1*5/6 =5/6
13 5/6*3/5 =3/6
14 3/6*1/3 =1/6
17 1/6*0 =0 K-M adjusts the esf to reflect the presence of right-censored observations. t S(t)
<12 1
12 1*5/6=5/6
13 5/6*4/5=4/6
13+ 4/6*4/4=4/6
14 4/6*1/3=4/18
17+ 4/18*1/1=4/18 Tests related to nonparametric methods Compare two groups Fisher’s exact test: Mantel-Haenszel/log-rank test: Parametric Methods Weibull R code Work cited:
Survival Analysis Using S , by Mara Tableman and Jong Sung Kim;
Survival Analysis in R , by David Diez Thanks!
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