1018Gage_Survival AnalysisB

# 1018Gage_Survival AnalysisB - October19,2004...

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Introduction to Survival Analysis October 19, 2004 Brian F. Gage, MD, MSc  with thanks to Bing Ho, MD, MPH Division of General Medical Sciences

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Presentation goals Survival analysis compared w/ other regression  techniques What is survival analysis When to use survival analysis Univariate method: Kaplan-Meier curves Multivariate methods: Cox-proportional hazards model Parametric models Assessment of adequacy of analysis Examples
Regression vs. Survival Analysis Technique Predictor Variables Outcome Variable Censoring permitted? Linear Regression Categorical or continuous Normally distributed No Logistic Regression Categorical or continuous Binary (except in polytomous log. regression) No Survival Analyses Time and categorical or continuous Binary Yes

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Regression vs. Survival Analysis Technique Mathematical model Yields Linear Regression Y=B 1 X + B o (linear) Linear changes Logistic Regression Ln(P/1-P)=B 1 X+B o (sigmoidal prob.) Odds ratios Survival Analyses h(t) = h o (t)exp( B 1 X+B o) Hazard rates
What is survival analysis? Model  time to failure  or  time to event Unlike linear regression, survival analysis has a  dichotomous (binary) outcome Unlike logistic regression, survival analysis analyzes  the time to an event  Why is that important? Able to account for censoring Can  compare survival  between 2+ groups Assess  relationship between covariates and  survival time

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Importance of censored data Why is censored data important? What is the key assumption of censoring?
Types of censoring Subject does not  experience event of  interest Incomplete follow-up Lost to follow-up Withdraws from study Dies (if not being studied) Left  or  right  censored

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When to use survival analysis Examples Time to death or clinical endpoint Time in remission after treatment of disease Recidivism rate after addiction treatment When one believes that 1+ explanatory variable(s)  explains the differences in time to an event Especially when follow-up is incomplete or  variable
Relationship between survivor function  and hazard function Survivor function, S(t) defines the probability of  surviving longer than time  t this is what the Kaplan-Meier curves show.

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