生统课件2016SurvivalAnalysisLecture.pptVIP

* The model: Cox regression Components: A baseline hazard function that is left unspecified but must be positive (=the hazard when all covariates are 0) A linear function of a set of k fixed covariates that is exponentiated. (=the relative risk) Can take on any form * The model The point is to compare the hazard rates of individuals who have different covariates: Hence, called Proportional hazards: Hazard functions should be strictly parallel. * Introduction to Kaplan-Meier No math assumptions! (either about the underlying hazard function or about proportional hazards). Simply, the empirical probability of surviving past certain times in the sample (taking into account censoring). 3. Non-parametric method: * Introduction to Kaplan-Meier Non-parametric estimate of the survival function. Commonly used to describe survivorship of study populations. Commonly used to compare two study populations. Intuitive graphical presentation. Beginning of study End of study ? Time in months ? Subject B Subject A Subject C Subject D Subject E Survival Data (right-censored) 1. subject E dies at 4 months X 100% ? Time in months ? Corresponding Kaplan-Meier Curve Probability of surviving to 4 months is 100% = 5/5 Fraction surviving this death = 4/5 Subject E dies at 4 months Beginning of study End of study ? Time in months ? Subject B Subject A Subject C Subject D Subject E Survival Data 2. subject A drops out after 6 months 1. subject E dies at 4 months X 3. subject C dies at 7 months X 100% ? Time in months ? Corresponding Kaplan-Meier Curve subject C dies at 7 months Fraction surviving this death = 2/3 Beginning of study End of study ? Time in months ? Subject B Subject A Subject C Subject D Subject E Survival Data 2. subject A drops out after 6 months 4. Subjects B and D survive for the whole year-long study period 1. subject E dies at 4 months X 3. subject C dies at 7 months X * 100% ? Time in months ? Corresponding Kaplan-Meier