SASSTAT Copyright 2013 SAS Institute Inc All rights

АНАЛИЗ ВЫЖИВАЕМОСТИ SAS/STAT Copyright © 2013, SAS Institute Inc. All rights reserved.

ФУНКЦИЯ ВЫЖИВАЕМОСТИ Copyright © 2013, SAS Institute Inc. All rights reserved.

EXPLORATORY DATA ANALYSIS USING SURVIVAL CURVES Copyright © 2013, SAS Institute Inc. All rights reserved.

KAPLAN-MEIER MODEL Количество выбывших в интервал времени T (number at death) Количество под угрозой выбывания (number at risk) Copyright © 2013, SAS Institute Inc. All rights reserved.

KAPLAN-MEIER MODEL : COMPARING SURVIVAL CURVES Confidence Limits Different Statistical Tests - Copyright © 2013, SAS Institute Inc. All rights reserved. Log Rank Wilcoxon Likelihood-Ratio

KAPLAN-MEIER MODEL : DIFFERENT STATISTICAL TESTS Log Rank Wilcoxon Likelihood-Ratio (parametric) Copyright © 2013, SAS Institute Inc. All rights reserved. Distribution of Event times Exponential

PROC LIFETEST Copyright © 2013, SAS Institute Inc. All rights reserved.

PROC LIFETEST: COMPARING SURVIVAL CURVES Copyright © 2013, SAS Institute Inc. All rights reserved.

PROC LIFETEST: COMPARING SURVIVAL CURVES Are Hazard Functions proportional? YES Copyright © 2013, SAS Institute Inc. All rights reserved. Does Likelihood-Ratio test applicable? NO

PROC LIFETEST: COMPARING MULTIPLE SURVIVAL CURVES proc lifetest data=sasuser. methadone plots=(survival(cb=hw)) notable; time*status(0); strata dose(50 70) / test=logrank adjust=schef fe nodetail; run; Copyright © 2013, SAS Institute Inc. All rights reserved.

PROC LIFETEST: COMPARING MULTIPLE SURVIVAL CURVES proc lifetest data=sasuser. methadone plots=(survival(cb=hw)) notable; time*status(0); strata dose(50 70) / test=logrank adjust=schef fe nodetail; run; Dose < 50 and Dose =60 differ? NO Dose > 70 and Dose =60 differ? YES Dose > 70 and Dose <50 differ? YES Copyright © 2013, SAS Institute Inc. All rights reserved.

ALTERNATIVE TO KAPLAN-MEIER: LIFE TABLE METHODS LIFE TABLE the same as Kaplan. Meier Estimate, but … LARGE SAMPLES Copyright © 2013, SAS Institute Inc. All rights reserved. GROUP OBSERVATIONS INTO BINS CENSORED OBS ARE CENSORED IN THE MIDDLE OF INTERVAL

ALTERNATIVE TO KAPLAN-MEIER: LIFE TABLE METHODS proc lifetest data=sasuser. methadone plots=(survival(failure) hazard) method=life intervals=183 365 548; time*status(0); strata clinic / test=(all) nodetail; run; Copyright © 2013, SAS Institute Inc. All rights reserved.

COX’S PROPORTIONAL HAZARDS MODEL Copyright © 2013, SAS Institute Inc. All rights reserved.

SURVIVAL MODELS Ø Models in Survival Analysis are written in terms of Hazard Functions Ø They assess the relationship of covariates to survival times Ø Models can be parametric or semi-parametric PARAMETRIC PROC LIFEREG 1. Distribution of Event Times is specified 2. Hazard function is completely specified (except for params) Exp Hazards Weibull Hazards Usually a poor choice! Copyright © 2013, SAS Institute Inc. All rights reserved. SEMI-PARAMETRIC PROC PHREG 1. Distribution of Event Times is unknown 2. Hazard function is unspecified Cox Proportional Hazards Model OK for !

COX PROPORTIONAL HAZARDS MODEL 1. The model provides the primary information desired from a survival analysis 2. Minimum of assumptions 3. Robust regression estimates of the influence of covariates 4. Thus, the model is extremely popular Copyright © 2013, SAS Institute Inc. All rights reserved.

PROPORTIONAL HAZARDS ASSUMPTION Copyright © 2013, SAS Institute Inc. All rights reserved.

DERIVING COEFFICIENTS: PARTIAL LIKELIHOOD MAXIMIZATION ILLUSTRATION Copyright © 2013, SAS Institute Inc. All rights reserved.

DERIVING COEFFICIENTS: PARTIAL LIKELIHOOD MAXIMIZATION Copyright © 2013, SAS Institute Inc. All rights reserved.

TIED OBSERVATIONS Tied observations They must be taken into account in Partial Likelihood calculation! SAS/STAT PROC PHREG does it automatically! (Breslow approximation) Copyright © 2013, SAS Institute Inc. All rights reserved.

PROC PHREG Copyright © 2013, SAS Institute Inc. All rights reserved.

PROC PHREG: FIT COX REGRESSION MODEL TO METHADONE DATA COEFFICIENT ESTIMATE COEFFICIENT not equal to 0? Copyright © 2013, SAS Institute Inc. All rights reserved.

PROC PHREG: ADJUST SURVIVAL CURVES Copyright © 2013, SAS Institute Inc. All rights reserved.

COX PH MODEL ASSESSMENT COX MODEL ASSUMPTIONS 1. Proportional Hazards The effect of the predictor is the same over all values of time 2. Linearity Log Hazard linearly depends on predictors 3. Additivity The joint effect of predictors equals the sum of their separate effects Copyright © 2013, SAS Institute Inc. All rights reserved. TIME-VARIABLE DEPENDENCE CUMULATIVE RESIDUALS PLOT

ASSESS PH USING TIME-VARIABLE DEPENDENCE Copyright © 2013, SAS Institute Inc. All rights reserved.

ASSESS PH USING CUMULATIVE RESIDUALS PLOT RESIDUAL Simulated Observed SIMULATE IT! Copyright © 2013, SAS Institute Inc. All rights reserved.

MODELS WITH NON-PROPORTIONAL HAZARDS Copyright © 2013, SAS Institute Inc. All rights reserved.

MODELING NON-PROPORTIONAL HAZARDS WAYS to HANDLE NONPROPORTIONAL HAZARDS 1. Stratified Cox PH Vary Baseline hazard 2. Cox PH with time-dependent vars Model non-proportionality using interactions with functions of time 3. Piecewise Cox PH The effect of variable is assessed separately for different times Copyright © 2013, SAS Institute Inc. All rights reserved.

STRATIFIED COX MODEL Copyright © 2013, SAS Institute Inc. All rights reserved.

STRATIFIED COX MODEL 1. Dose*Clinic & Clinic*Prison DROP Dose*Clinic 2. Clinic*Prison DROP Clinic*Prison Copyright © 2013, SAS Institute Inc. All rights reserved.

STRATIFIED COX MODEL 3. No interactions STAY at this model complexity 4. Try to adjust Baseline Hazard by Clinic Copyright © 2013, SAS Institute Inc. All rights reserved.

MODELS WITH INTERACTIONS WITH TIME 2 WAYS of INTRODUCING TIME INTO PARAMETER ESTIMATES Change the effect β of the variable Change the variable itself Copyright © 2013, SAS Institute Inc. All rights reserved.

MODELS WITH INTERACTIONS WITH TIME KEEP Copyright © 2013, SAS Institute Inc. All rights reserved.

PIECEWISE COX MODEL CREATE INTERACTION with HEAVISIDE FUNCTION! Copyright © 2013, SAS Institute Inc. All rights reserved.

PIECEWISE COX MODEL Copyright © 2013, SAS Institute Inc. All rights reserved.

ADVANCED TOPICS Copyright © 2013, SAS Institute Inc. All rights reserved.

TIME-DEPENDENT COVARIATES New time-dependent covariates must be specified inside PROC PHREG proc phreg data=sasuser. methadone; class Clinic (param=ref ref='2'); model Time*Status(0)=Clinic Dose Prison Drink / ties=exact rl=pl; Drink=(0 <= Drink. Start < Time); run; Copyright © 2013, SAS Institute Inc. All rights reserved.

MODELING THE EFFECT OF TIME-DEPENDENT PREDICTORS Coefficients are the same for the whole survey period Copyright © 2013, SAS Institute Inc. All rights reserved. «Drink» is time dependent and it’s important!

REPEATED EVENTS Some events are intrinsically repeatable: pregnancy, infection One should account for this in survival analysis Copyright © 2013, SAS Institute Inc. All rights reserved.

REPEATED EVENTS: DIFFERENT MODELS FOR SUCC EVENTS Model men’s muscle soreness in 4 intervals depending on age and treatment 1. 2. Build different survival models for successive events Copyright © 2013, SAS Institute Inc. All rights reserved. 3. Drop 4. Drop