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Multiple Outcome Survival Models

Terry Therneau

May 2013

Liver Transplant in 1999

I

Region

I

Status

I

1: acute failure

I2A: chronic, near death

I2B: chronic, severe

I3: other

I Score I

0, 5, or 10 points for compatable blood type

I0{10 points for waiting time

w w w w w w w w w w w w

889092949698

Year

Number (1000s)

t t t t t t t t t t t t d d d d d d d d d d d d 0 2 4 6 8 10 12 14

Transplants

Waiting

Died on list

Impact of Waiting Time

I All Mayo patients listed from Feb 1990 to Aug 1999 I

815 subjects: 636 OLT, 66 death, 37 withdraw, 76 censored

I age, sex, MELD, blood typeI Primary question: Did increased waiting time harm survival?

For whom?

I Simple (wrong) analysis: Kaplan-Meier curves of death by epoch, censoring at OLT or withdrawal

Impact of Waiting Time

I All Mayo patients listed from Feb 1990 to Aug 1999 I

815 subjects: 636 OLT, 66 death, 37 withdraw, 76 censored

I age, sex, MELD, blood typeI Primary question: Did increased waiting time harm survival?

For whom?

I Simple (wrong) analysis: Kaplan-Meier curves of death by epoch, censoring at OLT or withdrawal

012345

0.0 0.2 0.4 0.6 0.8 1.0

Years from listing

Death

A KM is the wrong curve

I

Answers the wrong question

I \What do we think that death rates would be, if the other outcomes ceased to exist?"I

Who cares?I

Treats transplant aslost to follow-up

I \Uninformative censoring" assumption I

KM censoring other causes

I

Answers a question we rarely want

IThe answer is almost certainly wrong

A KM is the wrong curve

I

Answers the wrong question

I \What do we think that death rates would be, if the other outcomes ceased to exist?"I

Who cares?I

Treats transplant aslost to follow-up

I \Uninformative censoring" assumption I

KM censoring other causes

I

Answers a question we rarely want

IThe answer is almost certainly wrong

A KM is the wrong curve

I

Answers the wrong question

I \What do we think that death rates would be, if the other outcomes ceased to exist?"I

Who cares?I

Treats transplant aslost to follow-up

I \Uninformative censoring" assumption I

KM censoring other causes

I

Answers a question we rarely want

IThe answer is almost certainly wrong

Prevalence curves

I

Pj(t) = Pr(in statejat timet)

I

Pij(t) = Pr(in statejatt, starting in statei)I

ij(t) = hazard function rate of change from stateitoj, given you are in statei hazard functions don't care about the past I ij(t) =Rt

0ij(s) = cumulative hazard

I

P=exp() in a 2-state modelI

incidence = synonym for hazard (epidemiology) I \Cumulative Incidence Function" = synonym for prevalence.

One of the worst labels in our literature

I confusing

Imisleading

Iextremely well established

Prevalence curves

I

Pj(t) = Pr(in statejat timet)

I

Pij(t) = Pr(in statejatt, starting in statei)I

ij(t) = hazard function rate of change from stateitoj, given you are in statei hazard functions don't care about the past I ij(t) =Rt

0ij(s) = cumulative hazard

I

P=exp() in a 2-state modelI

incidence = synonym for hazard (epidemiology) I \Cumulative Incidence Function" = synonym for prevalence.

One of the worst labels in our literature

I confusing

Imisleading

Iextremely well established

Prevalence curves

I

Pj(t) = Pr(in statejat timet)

I

Pij(t) = Pr(in statejatt, starting in statei)I

ij(t) = hazard function rate of change from stateitoj, given you are in statei hazard functions don't care about the past I ij(t) =Rt

0ij(s) = cumulative hazard

I

P=exp() in a 2-state modelI

incidence = synonym for hazard (epidemiology) I \Cumulative Incidence Function" = synonym for prevalence.

One of the worst labels in our literature

I confusing

Imisleading

Iextremely well established

0 20 40
60
80
Years

Prevalence

0123

Transplant

Died

Withdrew

0 20 40
60
80
Years

Prevalence

0123

Transplant

Died

Withdrew

"KM" of death

Drawing the curves

I Built into the R survival package since survival 2.37-1 I (Available in other R packages prior to this) I Leteventbe a factor variable (class variable) with \censoring" as it's rst level. I Use this as the status variable in thesurvfitfunction I Standard print, plot, etc of usual survival curves the default for plots is uphill rather than downhill. > table(cdata$event) censored death ltx withdraw

76 66 636 37

> cfit1 <- survfit(Surv(years, event)1, cdata) > plot(cfit1, mark.time=F, lwd=2, col=c(1,2,4), xlab='Years', ylab='Prevalence') > legend(1.5, .5, c("Transplant", "Died", "Withdrew"), col=c(1,2,4), lty=1, bty='n', cex=1.2, lwd=2) > abline(v=1, lty=2)

R and SAS

I

No, I don't know how to do this in SAS.I

Two sets of wrenches. Use them both.

Anyone who refuses to use anything but SAS is running a race with leg irons. I

Neither is easy to learn in toto

I

Well crafted, sensible, readable languages.

(SAS macro excepted)

IThe problem is that they are so very BIG.

IFind a good book and use only what you need.

I Most of what I will show in the course can be done in either. I

I will usually show R output

Iit is more compact and easier to t onto the slide

R and SAS

I

No, I don't know how to do this in SAS.I

Two sets of wrenches. Use them both.

Anyone who refuses to use anything but SAS is running a race with leg irons. I

Neither is easy to learn in toto

I

Well crafted, sensible, readable languages.

(SAS macro excepted)

IThe problem is that they are so very BIG.

IFind a good book and use only what you need.

I Most of what I will show in the course can be done in either. I

I will usually show R output

Iit is more compact and easier to t onto the slide

Transplants (death in red)0

20 40
60
80
Years

Prevalence

0123

1990-92

1993-95

1996-97

1998-99

Death0

2 4 6 8 Years Death 0123
90-92
93-95
96-97
98-99
cfit2 <- survfit(Surv(years, event)period, cdata) plot(cfit2[, 1:2], mark.time=F, col=c(2,1,2,3,2,4,2,6), lwd=1:2, xmax=3, xaxt='n', xlab="Years", ylab="Prevalence", yscale=100) axis(1, 0:3, 0:3) text(c(.1, 1.4, 1, 2), c(.9, .88, .7, .6), levels(period), col=c(1,3,4,6), cex=1.2) cfit2[,1:2] records n.max n.start events median 0.95LCL 0.95UCL death, period=1990-92 170 170 170 170 NA NA NA ltx, period=1990-92 170 170 170 170 0.123 0.151 0.101 death, period=1993-95 244 244 244 243 NA NA NA ltx, period=1993-95 244 244 244 243 0.381 0.435 0.337 death, period=1996-97 210 210 210 194 NA NA NA ltx, period=1996-97 210 210 210 194 0.542 0.805 0.460 death, period=1998-99 191 191 191 132 NA NA NA ltx, period=1998-99 191 191 191 132 1.221 1.525 0.997 I

Classic Survival

I

Time to death

Time to failure

IWell understoodI

Multiple Endpoints

I

Recurrent events

I repeat infections in cystic brosis I

Concurrent events

I

Parallel endpoints in primary biliary cirrhois

I

Mulit-state outcomes

I treatment/response/recurrence/death I

Classic Survival

I

Time to death

Time to failure

IWell understoodI

Multiple Endpoints

I

Recurrent events

I repeat infections in cystic brosis I

Concurrent events

I

Parallel endpoints in primary biliary cirrhois

I

Mulit-state outcomes

I treatment/response/recurrence/death

Focus on examples

I When I How I

Usefulness

Multiple events

1.

Flo wdiagra ms

2.

Data setup

3.

Examples

I

Chronic Granulomous Disease (mulitple recurrence)

IExubera (100 recurrences per subject)

ICystic Fibrosis

IPrimary Biliary Cirrhosis

IIdiopathic Bence Jones (illness-death)

4.

T ests,curves, sample size, time scales

5.

P erilsof Time Dep endentCova riates

6.

Mixed Eect sMo dels

Competing risks

Sequential

Andersen-Gill

Multi-StateEach box is a prevalence, each arrow is a hazard.

Data set up

I

Look at the picture

I every arrow is a strata (a hazard function) Ievery strata is a separate set of observations in the data set i.e., all those at risk of making that transition

Iboxes contain subjects

Ieach subject in a box will have an observation in all strata eminating from the box

Istatus =1 for the arrow they actually travel

I

Time scale

I time from start of disease, start of study, entry to state, ... Iwhich time is the most important driver of risk?I

Building the data is dull, tedious, essential

Data set up

I

Look at the picture

I every arrow is a strata (a hazard function) Ievery strata is a separate set of observations in the data set i.e., all those at risk of making that transition

Iboxes contain subjects

Ieach subject in a box will have an observation in all strata eminating from the box

Istatus =1 for the arrow they actually travel

I

Time scale

I time from start of disease, start of study, entry to state, ... Iwhich time is the most important driver of risk?I

Building the data is dull, tedious, essential

Covariates

I

Which covariates aect which transitions

I

Which covariates have common eect

I

DecideI

Biological truth: nothing is exactly the same

I

Practical truth: only so many df to spend

Covariates

I

Which covariates aect which transitions

I

Which covariates have common eect

I

DecideI

Biological truth: nothing is exactly the same

I

Practical truth: only so many df to spend

CGD data

A clinical trial of gamma interferon versus placebo in children with CGD, a genetic defect that leads to multiple recurrent infections.

The data set is found in Fleming and Harrington.

From practical experience, clinical scientists conducting the rIFN-g trial suggested that the risk of recurrent infection remained constant regardless of the number of previous infections. This suggests use of a simple repeated events or A-G model.quotesdbs_dbs6.pdfusesText_12