Survival Models in SAS

Learning ObjectivesWhat 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

• 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

• Previous preterm delivery• Multiples• < 6 mos since last preg• Surgery on cervix• IVF• Uterine abnormalities• Smoking

A Long Line-Up• Chorioamnionitis• Weight Gain• UTI• BP• (G)DM• Maternal Weight• Previous Loss• Antepartum Trauma• A/P Bleeding• Polyhydramnios

This LIFE is a TESTThis life is a test-it is only a test.

If it had been an actual life, you would have received furtherinstructions 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 FailureSurvival StandardError

NumberFailed

NumberLeft LABOUR

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

More Babies Arrive Sooner - DuhTest 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

Univariate Chi-Squares for the Wilcoxon Test

Variable Test Statistic

StandardError Chi-Square Pr >

Chi-Square Label

PREV_PTD -512.1 21.2544 580.5 <.0001# Previous Preterm Deliveries

Overweight 1074.1 58.7622 334.1 <.0001

ADMITSMK -18207.7 1727.7 111.1 <.0001# Cigarettes / Day @ Admission

Rank Tests for the Association of GA_BEST with Covariates Pooled over Strata

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 ParameterEstimate

StandardError

Chi-Square 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

ADMITSMK 1 0.00368 0.0005484 45.1439 <.0001 1.004# Cigarettes / Day @ Admission

Assume makes an ass of u and meChorioamnionitis 1 -0.05611 0.12410 0.2044 0.6512 0.945

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 Hypertension

Pre_Existing_Diabete 1 -0.03388 0.11821 0.0821 0.7744 0.967 Pre-existing Diabetes

GDM 1 -0.08809 0.04698 3.5162 0.0608 0.916 Gestational Diabetes

DLABORTS 1 -0.0002450 0.01265 0.0004 0.9845 1.000# of Pregnancies, Excl. the Present, with Non-viable Foetus

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?

• SHRUG.President@gmail.com• Ron.Dewar@HowDidIGetInvolved?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

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