Lab 9

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Lab 9 Survival Analysis Henian Chen, M.D.,
Ph.D.
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Description of Data   SURVIVAL65.TXT is data
from a study on multiple myeloma in which
researchers treated 65 patients with alkylating
agents. Of those patients, 48 died during the
study and 17 survived. The goal of this study is
to identify important prognostic factors.
  TIME survival time in months from
diagnosis STATUS 1 dead, 0 alive
(censored) LOGBUN log blood urea nitrogen (BUN)
at diagnosis HGB hemoglobin at
diagnosis PLATELET platelets at diagnosis 0
abnormal, 1 normal AGE age at diagnosis in
years LOGWBC log WBC at diagnosis FRACTURE
fractures at diagnosis 0 none, 1
present LOGPBM log percentage of plasma cells in
bone marrow PROTEIN proteinuria at
diagnosis SALCIUM serum calcium at diagnosis
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• LIFETEST procedure
• Estimation of the distribution of the
• survival times by nonparametric
• methods
• Kaplan-Meier method
• (also called product-limit method)
• 2. life table method

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Kaplan-Meier Estimates for Total Sample proc
import datafile'asurvival65.txt' outsurvival65
dbmstab replace run proc lifetest
datasurvival65 methodkm plots(s,lls) title
'Distribution of Survival Times for 65 Myeloma
Patients by Kaplan-Meier Method' time
timestatus(0) run MethodKM or PL
Kaplan-Meier (KM) or
product-limit (PL) estimates MethodLT or
LIFE life table estimates By default,
MethodPL. PlotsS plot the survival curve
(estimated survival distribution
function (SDF) against time)
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Plots LLS plot the log-log(estimated SDF)
against log(time) to show the distribution of the
survival time. Exponential Distribution the
hazard function is constant and does not depend
on time, the graph is approximately a straight
line, the slope is 1. Weibull Distribution
the hazard function changes with time, the
graph is approximately a straight line, but the
slope is not 1.
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Life Table Estimates for Total
Sample proc lifetest datasurvival65 methodlt
plots(s,lls) width10 title 'Distribution of
Survival Times for 65 Myeloma Patients by Life
Table Method' time timestatus(0) run
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Comparison of Two Survival Curves for Normal
Platelet and Abnormal Platelet by
Kaplan-Meier proc lifetest datasurvival65
methodkm plots(s,lls) time timestatus(0) stra
ta platelet run Log-Rank test for Weibull
distribution or proportional hazards assumption,
using weight1 so that each failure time has
equal weighting.
Wilcoxon test For lognormal distribution, using
weightthe total number at risk at that time so
that earlier times receive greater weight than
later times, placing less emphasis on the later
failure times. -2Log(LR) Likelihood Ratio
test for exponential distribution survival data.

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PHREG procedure Procedure PHREG performs
regression analysis of survival data based on the
Cox proportional hazards model. Procedure PHREG
also performs conditional logistic regression
analysis for matched case-control studies
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SAS Program for Cox Model proc import
datafile'asurvival65.txt' outsurvival65
dbmstab replace run proc phreg
datasurvival65 model timestatus(0) logbun hgb
platelet age logwbc fracture logpbm protein
calcium /selectionstepwise details rl run
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• TIME survival time in months from
  diagnosis
• STATUS 1 dead, 0 alive (censored)
• Cox Regression Model
• model timestatus(0) nine independent variables
• Linear Regression Model
• model time nine independent variables
• Can we fit a linear regression model for this
  data?
• NO !!
• We dont know the distribution of the survival
  times.
• Linear regression model treats the censored data
  as non-censored data.

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Logistic Regression Model model status nine
independent variables Can we fit a logistic
regression model for this data? NO !! It
is not right to use logistic regression to fit
the survival data because it treats different
strata (different time points) as one stratum
(the last time point). It is not right if you
dont use the information of time when you have
it. You have to use logistic regression if you
dont have the information of survival time.
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Patient A time10 months, status1 (dead) id
time status sex age A 0 0
F 30.00 A 1 0
F 30.08 A 2 0
F 30.17 A 3 0
F 30.25 A 4 0
F 30.33 A 5 0
F 30.42 A 6 0 F
30.50 A 7 0 F
30.58 A 8 0 F
30.67 A 9 0 F
30.75 A 10 1 F
30.83 Logistic
regression (one stratum)
Survival Analysis (11 strata)
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LIFEREG procedure Procedure LIFEREG fits
parametric models for survival data by using
maximum likelihood. If you has clear idea about
the distribution of survival times, you should
use parametric models
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SAS Program for 7 Parametric Models (using the
SURVIVAL65.TXT DATA) proc lifereg
datasurvival65 class platelet fracture model
timestatus(0)logbun hgb platelet age logwbc
fracture logpbm protein calcium /distribution
weibull run WEIBULL Weibull
distribution EXPONENTIAL exponential
distribution GAMMA generalized gamma
distribution LLOGISTIC loglogistic
distribution LNORMAL lognormal
distribution LOGISTIC logistic
distribution NORMAL normal distribution
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Results of the Weibull Regression Model  
Standard 95 Confidence
Chi- Parameter DF Estimate Error
Limits Square Pr gt ChiSq Intercept
1 7.0556 2.7719 1.6228 12.4883 6.48
0.0109 LOGBUN 1 -1.5325 0.5412
-2.5932 -0.4718 8.02 0.0046 HGB
1 0.0970 0.0621 -0.0248 0.2187 2.44
0.1185 PLATELET 1 -0.2655 0.4557
-1.1585 0.6276 0.34 0.5602 AGE
1 0.0103 0.0169 -0.0228 0.0434 0.37
0.5411 LOGWBC 1 -0.4008 0.5989
-1.5746 0.7729 0.45 0.5033 FRACTURE
1 0.3324 0.3526 -0.3587 1.0234 0.89
0.3459 LOGPBM 1 -0.3871
0.4290 -1.2280 0.4538 0.81
0.3670 PROTEIN 1 -0.0092 0.0228
-0.0540 0.0356 0.16 0.6862 CALCIUM
1 -0.0998 0.0898 -0.2758 0.0761 1.24
0.2661 Scale 1 0.8671 0.0927
0.7032 1.0694 Weibull Shape 1 1.1532
0.1233 0.9351 1.4222 -- An increase in one
unit of the LOGBUN increases the log of the
hazard of dying by 1.5325, controlling for other
variables -- An increase in one unit of the
LOGBUN increases the hazard of dying by 363
exp(1.5325)4.63-1 The coefficients are
expected to have opposite signs for parametric
models