Survival Models, John Fahey, Reproductive Care Program

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Survival Models in SAS
Learning Objectives
What type of data merits these?
What tools does SAS have?
How do I do descriptive analysis?
How do I do modelling?
Is the model appropriate?
A.Pope - Essay on Criticism Part ii Line 15
My Data Stops in the Middle
• Outcome is typically a time duration until an
event
• Outcome is not observed for some proportion
of the population
• Often the outcome is death of a patient
– Other examples
• Failure of an electronic component
• Divorce
• Change cell phone provider
SAS to the rescue
• Exploratory
– FREQ
– UNIVARIATE
– MEANS/SUMMARY
– GPLOT
• Time-to-event most commonly analysed using
– LIFETEST
– PHREG
Baby’s First Dataset
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NSAPD: Mum’s and babes since 1980
All NS births since 1988
Comprehensive clinical and demographic data
Includes gestational age at birth/delivery
Spontaneous / Induced / No Labour
Question: What factors associated with
premature birth?
How is this ‘time-to-event’?
• Birth is the event
• When birth would have happened is censored
– Induced labour
– Straight to Caesarean Section
• Measured in weeks since LMP
• A (large) set of known risk factors
• Many captured in Atlee
The Usual Suspects
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Previous preterm delivery
Multiples
< 6 mos since last preg
Surgery on cervix
IVF
Uterine abnormalities
Smoking
A Long Line-Up
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Chorioamnionitis
Weight Gain
UTI
BP
(G)DM
Maternal Weight
Previous Loss
Antepartum Trauma
A/P Bleeding
Polyhydramnios
This LIFE is a TEST
This life is a test-it is only a test.
If it had been an actual life, you would have received further
instructions on where to go and what to do.
Remember, this life is only a test.
• proc lifetest
• data = Work.ForSHRUG
• plots = (s,ls,lls)
• maxtime = 45;
• time GA_Best * Spontaneous_Labour ( 0 );
• id Labour /* censoring = Induced / None */;
• strata DLNumFet;
• test Prev_PTD Overweight AdmitSmk;
• /* latter two most interesting from population health perspective */
• run;
The LIFETEST Procedure
Stratum 4: # of Foetuses = Twins
Product-Limit Survival Estimates
GA_BEST
Survival Failure
Survival
Standard
Error
32.0000
0.9075
0.0925
0.00324
743
7111
S
33.0000
0.8837
0.1163
0.00359
927
6819
S
34.0000
0.8465
0.1535
0.00407
1210
6383
S
35.0000
0.7884
0.2116
0.00466
1638
5761
S
36.0000
0.7119
0.2881
0.00525
2176
4918
S
37.0000
0.6154
0.3846
0.00582
2784
3717
S
38.0000
0.4864
0.5136
0.00651
3417
2145
S
39.0000
0.3550
0.6450
0.00745
3821
861
S
40.0000
0.2125
0.7875
0.00837
4076
325
S
41.0000
0.0999
0.9001
0.00868
4186
76
S
42.0000
0.0543
0.9457
0.00859
4210
22
S
43.1430
0.0339
0.9661
0.00979
4214
6
S
Number Number
LABOUR
Failed
Left
More Babies Arrive Sooner - Duh
Test of Equality over Strata
Test
Chi-Square
DF
Pr >
Chi-Square
Log-Rank
12814.4469
3
<.0001
Wilcoxon
17518.2974
3
<.0001
-2Log(LR)
184.4172
3
<.0001
Lots of Data = Tiny p-values
Rank Tests for the Association of GA_BEST with Covariates Pooled over Strata
Univariate Chi-Squares for the Wilcoxon Test
Variable
Test
Statistic
Standard
Error
Chi-Square
Pr >
Chi-Square
Label
# Previous
Preterm
Deliveries
PREV_PTD
-512.1
21.2544
580.5
<.0001
Overweight
1074.1
58.7622
334.1
<.0001
ADMITSMK
-18207.7
1727.7
111.1
<.0001
# Cigarettes /
Day @
Admission
Apply the “C” test
Make the punishment fit the crime
Smoking and weight matter … how
much?
• Hazards – not just for golf any more
• Proportional Hazards REGression
• Doesn’t assume functional form for baseline
hazard
• Does assume that effect of covariate
proportional over time
• Manifests itself as, e.g., parallel lines on plot
Deciphering the code
• proc phreg
• data = Work.ForSHRUG
• plots ( overlay timerange = 24, 44 )=
•
( cumhaz survival ) /* interesting weeks */
• simple/* compare healthy/unhealthy */;
• where Weighted_Ran > 0.9;
• /* 10% of 'healthy' + 55% w/ 1 risk factor + */
Modelling – not just for the young and
beautiful !
• model GA_Best * Spontaneous_Labour ( 0 ) =
•
Prev_PTD DLNumFet AdmitSmk
Chorioamnionitis Gest_HT PrexHT
Pre_Existing_Diabetes GDM DLAborts Overweight
Underweight ;
• assess var = ( Prev_PTD DLNumFet AdmitSmk
Chorioamnionitis Gest_HT PrexHT GDM DLAborts
Pre_Existing_Diabetes Overweight Underweight )
•
ph;
/* / resample seed = 19 */
/* takes 8 hours to run! */
Odious? NO – ODS – Yes!
• ODS GRAPHICS ON; ODS GRAPHICS OFF;
What about plurality?
Transformational Experience
On the other hand …
But what about the question?
Analysis of Maximum Likelihood Estimates
Parameter
DF
Parameter Standard
Estimate
Error
ChiSquare
Pr > ChiSq
Hazard
Ratio
Label
PREV_PTD
1
0.47499
0.03067
239.8634 <.0001
1.608
# Previous
Preterm
Deliveries
DLNUMFET
1
1.43623
0.05435
698.4233 <.0001
4.205
# of Foetuses
1.004
# Cigarettes /
Day @
Admission
ADMITSMK
1
0.00368
0.0005484 45.1439
<.0001
Assume makes an ass of u and me
Chorioamnionitis
1
-0.05611
0.12410
0.2044
Gest_HT
1
-0.88739
0.13010
46.5222 <.0001 0.412 Gestational Hypertension
PrexHT
1
-0.34641
0.10133
11.6869 0.0006 0.707
Pre_Existing_Diabete 1
-0.03388
0.11821
0.0821
0.7744 0.967 Pre-existing Diabetes
GDM
-0.08809
0.04698
3.5162
0.0608 0.916 Gestational Diabetes
0.0004
# of Pregnancies, Excl.
0.9845 1.000 the Present, with Nonviable Foetus
DLABORTS
1
1
-0.0002450 0.01265
0.6512 0.945
Pre-existing
Hypertension
Criticism
A little learning is a dangerous thing;
Drink deep, or taste not the Pierian spring:
There shallow draughts intoxicate the brain,
And drinking largely sobers us again.
Two of 372 rhyming couplets
Competing Risks
• Censoring must be non-informative
• Here some covariates are associated with
– Induction
– No Labour
– Need different models
• Look at cumulative probability of 3 outcomes
One last tidbit
• %CIF macro
•
http://support.sas.com/kb/45/addl/fusion_45997_13_fusion_45997_12_cif.txt
• Crude cumulative incidence function
• No covariates
• Endpoints (time to spontaneous labour, e.g.) subject to
competing risks
– Induction for reason associated with length of
pregnancy
– No Labour for …
• Comes with confidence limits
• Needs Base & IML ( in 9.2 also GRAPH )
• No recommendation
Questions?
• [email protected][email protected]?ca
• http://www.ats.ucla.edu/stat/examples/asa/test_proportionality.htm
•
http://www4.stat.ncsu.edu/~lu/ST790/homework/Biometrika-1993-LIN-557-72.pdf
• http://escarela.com/archivo/anahuac/03o/residuals.pdf
• SAS is a registered trademark or trademark of SAS Institute
Inc. in Canada, the USA and other countries with
dysfunctional political institutions.

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