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1、1,Survival Analysis,Luonan Chen Chinese Academy of Sciences,2,Overview,What is survival analysis? Terminology and data structure. Survival/hazard functions. Parametric survival method Semi-parametric method Non-parametric method,What is survival analysis?,Model time to failure or time to event Unlik
2、e linear regression, survival analysis has a dichotomous (binary) outcome Unlike logistic regression, survival analysis analyzes the time to an event Why is that important? Can account for censoring Can compare survival between 2+ groups Assess relationship between covariates and survival time,4,Ear
3、ly example of survival analysis,Roughly, what shape is this function?,What was a persons chance of surviving past 20? Past 36?,This is survival analysis! We estimate this curveonly the outcome can be any binary event, not just death.,percentage,5,Survival analysis,Statistical methods: analyze longit
4、udinal data on the occurrence of events. Events: include death, injury, onset of illness, recovery from illness (binary variables) or transition above or below the clinical threshold of a meaningful continuous variable (e.g. CD4 counts). Data: include randomized clinical trial or cohort study design
5、.,6,Estimate time-to-event for a group of individuals, such as time until second heart-attack for a group of MI patients. To compare time-to-event between two or more groups, such as treated vs. placebo MI patients in a randomized controlled trial. To assess the relationship of co-variables to time-
6、to-event, such as: does weight, insulin resistance, or cholesterol influence survival time of MI patients? Note: expected time-to-event = 1/incidence rate,Objectives of survival analysis,7,Why use survival analysis?,1. Why not compare mean time-to-event between your groups using a t-test or linear r
7、egression? - ignores censoring 2. Why not compare proportion of events in your groups using risk/odds ratios or logistic regression? -ignores time,Types of censoring 截尾,Subject does not experience event of interest Incomplete follow-up Lost to follow-up Withdraws from study Dies (if not being studie
8、d) Left or right censored,Regression vs. Survival Analysis,Regression vs. Survival Analysis,Basic methods for survival analysis 1非参数法 Non-Parametric survival analysis ：不考虑数据的分布类型；有Kaplan-Meier法和寿命表法。 2参数法 Parametric survival analysis ：要知道数据的分布类型。有指数分布法， Weibull分布法，对数正态回归分布法等。 3半参数法 Semi-Parametric s
9、urvival analysis ：具有参数和非参数的特点。如Cox模型法。,12,Survival Analysis(生存分析) Terms,Time-to-event生存时间: The time from entry into a study until a subject has a particular outcome Censoring截尾: Subjects are said to be censored if they are lost to follow up or drop out of the study, or if the study ends before they
10、die or have an outcome of interest. They are counted as alive or disease-free for the time they were enrolled in the study. If dropout is related to both outcome and treatment, dropouts may bias the results,13,Data Structure: survival analysis,Two-variable outcome : Time variable: ti = time at last
11、disease-free observation or time at event Censoring variable: ci =1 if had the event; ci =0 no event by time ti,14,Right Censoring (Tt),Common examples Termination of the study Death due to a cause that is not the event of interest Loss to follow-up We know that subject survived at least to time t.,
12、15,1. Choice of time of origin. Note varying start times.,不同时进入观察,16,同时进入观察,2. Count every subjects time since their baseline data collection., ,17,Introduction to survival distributions,Ti the event time for an individual, is a random variable having a probability distribution. Different models for
13、 survival data are distinguished by different choice of distribution for Ti.,18,Describing Survival Distributions,Parametric survival analysis is based on so-called “Waiting Time” distributions (ex: exponential probability distribution). The idea: Assume that times-to-event for individuals in your d
14、ataset follow a continuous probability distribution (which we may or may not be able to pin down mathematically). For all possible times Ti after baseline, there is a certain probability that an individual will have an event at exactly time Ti. For example, human beings have a certain probability of
15、 dying at ages 3, 25, 80, and 140: P(T=3), P(T=25), P(T=80), P(T=140). These probabilities are obviously vastly different.,19,Probability density function: f(t),In the case of human longevity, Ti is unlikely to follow a normal distribution, because the probability of death is not highest in the midd
16、le ages, but at the beginning and end of life. Hypothetical data:,20,Probability density function: f(t),The probability of the failure time occurring at exactly time t (out of the whole range of possible ts).,21,Survival function: 1-F(t),The goal of survival analysis is to estimate and compare survival experiences of different groups. Survival experience is described by the cumulative survival function:,Example: If t=100 years, S(t=100) = probability of surviving beyond
