RANDOMIZED CLINICAL TRIAL

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• RANDOMIZED CLINICAL TRIAL
• TEN INDIVIDUALS RANDOMLY ALLOCATED TO TWO DRUG
  GROUPS AND FOLLOWED OVER TWO MONTHS FROM JANUARY
  1 TO FEBRUARY 28
• THREE INDIVIDUALS DIED

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• ID G CEN D1 M1 Y1 D2 M2 Y2
• 1 1 0 5 2 2006 28 2 2006
• 2 0 0 3 2 2006 28 2 2006
• 3 1 0 25 1 2006 28 2 2006
• 4 0 0 21 1 2006 28 2 2006
• 5 1 0 20 1 2006 28 2 2006
• 6 0 1 18 1 2006 24 2 2006
• 7 0 0 17 1 2006 28 2 2006
• 8 1 1 16 1 2006 25 2 2006
• 9 0 0 14 1 2006 28 2 2006
• 10 1 1 5 1 2006 23 1 2006

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• DATA STUDY
• INPUT ID GROUP CENSOR
• DAY1 MON1 YEAR1 DAY2 MON YEAR2
• TIME1 MDY(MON1, DAY1, YEAR1)
• TIME2 MDY(MON2, DAY2, YEAR2)
• START MDY( 1 , 1 , 2006 )
• DIFF1 TIME1 - START
• DIFF2 TIME2 - START
• DD TIME2 - TIME1
• DATALINES

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• DATASET STUDY
• ID TIME1 TIME2 CENSOR FOLLOWUP
• 1 16837 16860 1
  23
• 2 16835 16860 0
  25
• 3 16826 16860 0
  34
• 4 16822 16860 0
  38
• 5 16821 16860 1
  39
• 6 16819 16856 0
  37
• 7 16818 16860 0
  42
• 8 16817 16857 1
  40
• 9 16815 16860 0
  45
• 10 16806 16824 0
  18

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• PROC LIFEREG DATA STUDY
• MODEL FOLLOWUP
• / DIST EXPONENTIAL
• OUTPUT OUT OUTSURV
• CDF CDFEXP
• DATA CDFSURV SET OUTSURV
• SURVEXP 1 - CDFEXP

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• LIFEREG Procedure
• Data Set WORK.STUDY
• Dependent Variable Log(FOLLOWUP)
• Number of Observations 10
• Noncensored Values 10
• Right Censored Values 0
• Left Censored Values 0
• Interval Censored Values 0
• Name of Distribution Exponential
• Log Likelihood -10.3766
• Parameter DF Beta StdErr 95 CI X2 P
• Intercept 1 3.53 0.316 2.9 4.2 125 lt0.0001
  
• Scale 0 1.00 0.000 1.0 1.0
• Weib Scale 1 34.10 10.783 18.4 63.4
• Weib Shape 0 1.00 0.000 1.0 1.0

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WEIBULL SURVIVAL FUNCTION
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• INTERCEPT ONLY MODEL

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• PROC MEANS DATA STUDY N SUM
• VAR FOLLOWUP
• The MEANS Procedure
• Analysis Variable FOLLOWUP
• N Sum
• 10 341
• RATE 10 / 341 0.0293
  

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• DATA STUDY
• MODEL FOLLOWUP CENSOR(0)
• / DIST EXPONENTIAL
• OUTPUT OUT OUTSURV
• CDF CDFEXP

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• The LIFEREG Procedure
  (Correct Analysis)
• Censoring Variable CENSOR
• Censoring Value(s) 0
• Number of Observations 10
• Noncensored Values 3
• Right Censored Values 7
• Name of Distribution
  Exponential
• Log Likelihood
  -7.00964
• Parameter DF Beta StdErr 95
  CI X2 P
• Intercept 1 4.73 0.577 3.60
  5.86 67.2 lt0.0001
• Scale 0 1.0 0.0
  1.00 1.00
• Weib Scale 1 113.7 65.6 36.66
  352.43
• Weib Shape 0 1.0 0.0 1.00
  1.00
• RATE 3 / 341 0.0088
  exp(-4.73) 0.0088

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• KAPLAN MEIER SURVIVAL FUNCTION
• ID CENSOR TIME
• 10 1
  18
• 1 0
  23
• 2 0
  25
• 3 0
  34
• 6 1
  37
• 4 0
  38
• 5 0
  39
• 8 1
  40
• 7 0
  42
• 9 0
  45

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• PROPORTIONAL
• HAZARDS
• MODEL

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• COMPARING SURVIVAL TIMES IN
• TWO GROUPS
• USING THE SAS PROCEDURE PHREG
• TO PERFORM A
• PROPORTIONAL HAZARDS ANALYSIS

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• REVIEW LIKELIHOOD AND LOG LIKELIHOOD
• INTERCEPT ONLY MODEL

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• HOMEMADE LIKELIHOOD PROGRAM
• DATA PH DO BETA -6 TO 6 BY 0.001
• K EXP(BETA)
• L1 K / ( 5 K 5 ) L2 1 / (2
  K 4 )
• L3 K / ( K 2 )
• L L1 L2 L3 LOGL LOG(L)
  
• OUTPUT
  END
• PROC SORT BY DESCENDING LOGL
• PROC PRINT DATA PH(OBS 3 ) RUN

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• HOMEMADE LIKELIHOOD PROGRAM
• BETA K L1 L2 L3
  PROD LOGL
• 1.174 3.235 0.153 0.096 0.618
  .009017 -4.7086
• 1.175 3.238 0.153 0.095 0.618
  .009017 -4.7086
• 1.173 3.232 0.153 0.096 0.618
  .009017 -4.7086
• NOTE Dataset WORK.PH has 10001 observations.

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• PROC PHREG DATA STUDY
• MODEL
• FOLLOWUP CENSOR(0) GROUP

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• Model Fit Statistics
• Without
  With
• Criterion Covariates
  Covariates
• -2 LOG L 10.386
  9.417
• Testing Global Null Hypothesis BETA0
• Test ChiSquare
  DF P
• Likelihood Ratio 0.969 1
  0.325
• Wald 0.900
  1 0.343
• Parameter
  Hazard
• Variable Estimate StdErr X2
  P Ratio
• GROUP 1.174 1.238 0.900
  0.34 3.24

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• TIME DEPENDENT
• COVARIATES

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• FOUR POSSIBLE SCENARIOS
• __________________
• 
  
• _____________________
• 
  
• _________DIE
• 
  
• ____________DIE
  
• START
  END
• DATE
  DATE

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• The CONTENTS Procedure
• Alphabetic List of Variables and Attributes
• Variable Type Len Format Label
• 5 AGEGROUP Num 3 Age group at
  enrollment
• 2 AIDSDATE Num 4 Date of AIDS
  diagnosis
• 10 ASYMDATE Num 8 Date last
  asymptomatic
• 12 CD200 Num 8 CD4lt200 ever?
• 13 CD200D Num 8 Date first CD4lt200
• 14 CD200V Num 8 Value first CD4lt200
• 8 CENSDATE Num 8 Date censored
• 6 DEATH Num 3 Deceased
• 7 DTH_DATE Num 8 Date of death
• 15 ID Num 8
• 4 MALE Num 3 Male gender?
• 1 PCP Num 3 PCP?
• 11 PCP_DATE Num 8 Date of first PCP

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• PROC PRINT DATA LOVE.HIVCLASS NOOBS
• VAR ID RX_START AIDSDATE
• DTH_DATE CENSDATE
  
• ID RX_START AIDSDATE DTH_DATE CENSDATE
• 375 88-02-01 10927 11413
  .
• 303 88-03-01 10713 11474
  .
• 418 88-03-01 .
  . 12692
• 429 88-03-01 10774 10958
  .

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• PROC PRINT DATA TEMP NOOBS
• VAR ID RX_START DEATH
  DTH_DATE
• FORMAT RX_START DTH_DATE DATE9.
  
• ID RX_START DEATH
  DTH_DATE
• 375 01FEB1988 1
  01APR1991
• 303 01MAR1988 1
  01JUN1991
• 418 01MAR1988 0
  .
• 429 01MAR1988 1
  01JAN1990

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• CREATING THE TIME DEPENDENT
• VARIABLE XCD200 BY PROGRAMMING
• WITHIN THE SAS PROCEDURE PHREG
• USING THE VARIABLE CDTIME

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• DATA TTT SET TO.HIVCLASS
• IF DEATH 1 THEN LASTTIME DTH_DATE
• IF DEATH 0 THEN LASTTIME CENSDATE
• FOLLOWUP LASTTIME - RX_START
• CDTIME CD200D - RX_START
  

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• PROC PHREG
• MODEL FOLLOWUP DECEASED(0) XCD200
• IF (CDTIME . OR CDTIME GT FOLLOWUP )
• THEN DO XCD200 0
  END
• ELSE XCD200 1
  RUN

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• TIME DEPENDENT VARIABLES
• SCENARIO
• 
  CD4(X) 1
• 1 CD4(0) 0 ______X_____________DIE
  
  
• 
  
• 2 CD4(0) 0 ___________________________
  _DIE
  
• 
  CD4(X) 1
• 3 CD4(0) 1 _______________X__________D
  IE
• 
  
  
  
• 4 CD4(0) 1 ____________DIE
• 
  CD4(X)1
• 5 CD4(0) 0 ______________X________CENS
  OR
• 6 CD4(0) 0 ____________________CENSOR
• 
  CD4(X)1
• 7 CD4(0) 1 ________X________________CEN
  SOR
  
  
• 8 CD4(0) 1 ________________CENSOR

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• SUPPOSE RESPONSE VARIABLE
• IS AIDS AND NOT DEATH
• _______________DEATH
• ____________AIDS____CENSOR
• __________AIDS_________DEATH