alda chap 15 time varying parameters

8/17/2019 ALDA Chap 15 Time Varying Parameters

http://slidepdf.com/reader/full/alda-chap-15-time-varying-parameters 1/6

Judith D. Singer & John B. Willett Harvard Graduate School of Education

Fitting Cox regression models

ALDA, Chapter !ourteen and !ifteen

“Time is nature’s way of keeping everything from happening at once”

Woody Allen



Chapters 14 & 15: Fitting Cox regression models

Chapters 14 & 15: Fitting Cox regression models

Including time-varying predictors !"#$"%&'t’s not always as easy as indiscrete(time) *ut it can *e done

Non-proportional hazards models !"#$+%&,ne of the ma-or advantagesof learning how to include time(varying predictors is that they allow youto test and) if necessary) relax the proportional ha.ards assumption

Including time-varying predictors !"#$"%&'t’s not always as easy as in

discrete(time) *ut it can *e done Non-proportional hazards models !"#$+%&,ne of the ma-or advantagesof learning how to include time(varying predictors is that they allow youto test and) if necessary) relax the proportional ha.ards assumption



Including time-varying predictors in a Cox regression model

Including time-varying predictors in a Cox regression model

!"#!$ %ection 151$ pp 544-545'

/odel specification is easy0 1ust add the su*script - to the time(varying predictors

#ata demands can (e high

sometimes insurmounta(le'

• )ou need to *no+ the value o, the time-

varying predictor,or everyone still at ris*

at every moment +hen someone

experiences the event

2e3uirement holds whether there are "4) "44

or ")444 uni3ue event times

5ame re3uirement as in discrete(time) *ut it

was unpro*lematic there *ecause0

6um*er of uni3ue event times wasrelatively small

7vent occurrence and predictors are

typically assessed on the same schedule

'n continuous time) you typically can’t set the

data collection schedule to coincide with

event occurrence for everyone still at risk

#ata demands can (e high

sometimes insurmounta(le'

• )ou need to *no+ the value o, the time-

varying predictor,or everyone still at ris*

at every moment +hen someone

experiences the event

2e3uirement holds whether there are "4) "44

or ")444 uni3ue event times

5ame re3uirement as in discrete(time) *ut it

was unpro*lematic there *ecause0

6um*er of uni3ue event times was

relatively small

7vent occurrence and predictors are

typically assessed on the same schedule

'n continuous time) you typically can’t set the

data collection schedule to coincide with

event occurrence for everyone still at risk

[ ]i-i -4i- 8 8 t hht 2211exp)() β β +=

.ractical implications

• 'f you’re interested in T9 predictors)

research design is crucial& :on’t wait

until the data are collected

• 6on(reversi*le dichotomies&that

themselves represent event occurrence&

are easiest eg) " st marriage) ;5 graduation%

• 2eversi*le dichotomies and continuous

predictors usually re3uire imputationdiscussed in 5ection "#$"$+ and "#$"$<%

.ractical implications

• 'f you’re interested in T9 predictors)

research design is crucial& :on’t wait

until the data are collected

• 6on(reversi*le dichotomies&that

themselves represent event occurrence&

are easiest eg) " st marriage) ;5 graduation%

• 2eversi*le dichotomies and continuous

predictors usually re3uire imputation

discussed in 5ection "#$"$+ and "#$"$<%



Including /0 non-reversi(le dichotomies in a Cox regression model: #ata example

Including /0 non-reversi(le dichotomies in a Cox regression model: #ata example

!"#!$ %ection 1511$ pp 545-551'

%ample: 1$52 men interviewed twice in "=>? and "=@#% ((32 36' started using cocaine (et+een ages 17 and 41

%ample: 1$52 men interviewed twice in "=>? and "=@#% ((32 36' started using cocaine (et+een ages 17 and 41

#ata source: urton and colleagues "==B%) 1ournal of ;ealth and 5ocial ehavior

/hree time-invariant predictors

8!9"); and 8!9")<# indicate

whether the respondent had initiatedmari-uana >$+% or other drugs <$>%

so early that he could *e characteri.ed

as a previous user at t0 age ">%

=I9/>)9 "=B"("=@#%) to account for

societal changes included as a control

predictor in every model%

Four time-varying predictors

– ?%8#; @ $ %<"#; @ ?%8#<# @ $ %<"#<# @ each

identify) at each age t- ) whether the respondenthad previously used or sold mari-uana /1% or

other drugs ,:%

– Conceptually

) think a*out a person(period data set

in which these varia*les switch from 4 to " in the

relevant year and stay at " thereafter$

– 'n reality

) we do not use a person(period data set*ut rather computer code in a person(level data set

5ection "#$") p$ #?>%

• 9ather than using contemporaneous values o, the

/0 predictors$ +e lag them (y one year Addresses

issues of rate(and state(dependence discussed in 5ection

"+$<$<) p$ ??4%



Interpreting the results o, ,itting Cox regression models +ith time-varying predictors

Interpreting the results o, ,itting Cox regression models +ith time-varying predictors

!"#!$ %ection 1511$ pp 545-551'

A0 ,nly time(

invariant predictors0 All < stat sig

0 5u*stitute

T9 use predictors

• 7ffects much larger

and still stat sig$%

• Fit much *etter use

A'C *ecause non(

nested%

C0 AddT9 sales predictors

• Creates ordinal varia*lewhen paired with use

predictors• oth use and sales are

stat sig$

• ;a.ards add up05omeone who *oth usedand sold /1 and ,: hasa ha.ard ratio ofexp#$"B4B%D147A

• est fitting model so far

:0 Add *ack time(

invariant predictors

• 7stimates are not stat

sig$

• : fits no *etter than C

• We prefer model C

6ote0 :iminishing '2T;E2 effects• ncontrolled estimateD4$+4+B

• :rops from $"##" to 4$4@?= from A to C

• 7ffects previously attri*uta*le to '2T;E2 get a*sor*ed*y T9 drug use known as su*stitution effects%



“Time flies like an arrowG

Fruit flies like a *anana”

Hroucho /arx

alda chap 15 time varying parameters

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