Applications of Gestimation using a new Stata command

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Applications of G-estimation using a new Stata
command

• Jonathan Sterne
• jonathan.sterne_at_bristol.ac.uk
• Kate Tilling
• kate.tilling_at_bristol.ac.uk
• Department of Social Medicine,University of
  Bristol UK

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Outline

• Time varying confounding and G-estimation
• G-estimation in Stata
• Applications
• Discussion and future plans

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• A covariate is a time-varying confounder for the
  effect of exposure on outcome if
• past covariate values predict current exposure
• current covariate value predicts outcome
• Example
• people with low CD4 are more likely to get HAART
• Low CD4 is a risk factor for AIDS and death

If, in addition, past exposure predicts current
covariate value then standard survival analyses
with time-updated exposure effects will give
biased exposure effect estimates For example, CD4
count predicts HAART and HAART raises CD4 counts
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G-estimation (1)

• Assume that subject i has an underlying
  counterfactual failure time Ui - the time to
  failure had they never been exposed. This is
  unobservable for subjects who were exposed at any
  time
• Assume that exposure accelerates failure time by
  a factorexp(-?) - the causal survival time
  ratio. So if ?lt0 exposure increases survival, if
  ?gt0 exposure decreases survival
• If we knew ?, then for any subject who
  experienced the outcome event at time Ti, the
  counterfactual failure time could be derived by
• Example if subject i experienced the outcome
  event at 5 years and was exposed for 3 years then
  Ui 3?exp(?)2

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G-estimation (2)

• Assume that there are no unmeasured confounders
• conditional on measured history (past and present
  confounders and past exposure) subjects present
  exposure is independent of their counterfactual
  failure time Ui
• e.g. for 2 individuals with identical histories,
  the decision to quit smoking does not depend on
  underlying survival time

Use logistic regression to search for a value of
? that satisfies this condition
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Censoring

• No competing risks
• Replace U(?) with variable indicating whether
  individual would have been observed to fail both
  if they were exposed and if they were unexposed.
• Competing risks
• Assume that conditional on known covariates
  censoring due to competing risks is independent
  of failure time
• Estimate the cumulative probability of being free
  from competing risks until end of follow up, and
  weight by the inverse of this probability.

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The stgest command

• Written for Stata
• User specifies exposure, covariates (including
  baseline and lagged covariates) and any censoring
  variables
• Data set up in Stata survival analysis format
  (i.e. start time, end time and failure indicator
  for each interval for each individual)
• Uses interval bisection method to search for
  G-estimate and 95 CI (or user can specify range
  and step for grid search)

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Caerphilly study

• 2512 men first examined 1979 to 1983, mean age at
  baseline 52 years
• Three further follow up surveys with
  ascertainment of MI and deaths to August 2000
• Data from the first examination is used to
  provide baseline exposure measures, so follow-up
  starts from the second examination
• 1756 men included in analyses
• 244 had a first MI or died from CHD between the
  second examination and the end of follow up

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Data

• Baseline
• smoking history, age, self-reported CHD, gout,
  diabetes, high blood pressure
• Every visit
• BP, BMI, smoking status, total cholesterol,
  CHD, gout, diabetes, fibrinogen

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Censoring

• Four possibilities
• Not censored 1175 (66.9)
• MI or MI death 244 (13.9)
• Death from other cause 231 (13.2)
• Lost 106 (6.0)
• Multinomial logistic regression
• estimate the probability that each id was
  censored (last two categories) as the product of
  the probability of censoring at each examination

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list id visit examdat exitdate mi examdat2
cursmok if touse id visit examdat
exitdate mi examdat2 cursmok 16. 1021
1 10sep1979 31jul1984 0 31jul1984
0 17. 1021 2 31jul1984 17mar1992
0 31jul1984 0 18. 1021 3
17mar1992 18jun1996 1 31jul1984 0
19. 1022 1 10sep1979 19sep1984 0
19sep1984 1 20. 1022 2 19sep1984
20nov1989 0 19sep1984 1 21. 1022
3 20nov1989 28oct1993 0 19sep1984
1 22. 1022 4 28oct1993 31dec1998
0 19sep1984 0 23. 1023 1
10sep1979 03oct1984 0 03oct1984 1
24. 1023 2 03oct1984 20nov1989 0
03oct1984 1 25. 1023 3 20nov1989
08nov1993 0 03oct1984 1 26. 1023
4 08nov1993 31dec1998 0 03oct1984
1
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. stset exitdate, id(id) failure(mi) origin(time
examdat2) scale(365.25) id id
failure event mi 0 mi . obs. time
interval (exitdate_n-1, exitdate exit on or
before failure t for analysis
(time-origin)/365.25 origin time
examdat2 ----------------------------------------
------------------------------- 6377 total
obs. 1756 obs. end on or before
enter() ------------------------------------------
----------------------------- 4621 obs.
remaining, representing 1756 subjects
244 failures in single failure-per-subject data
18547.87 total analysis time at risk, at risk
from t 0
earliest observed entry t 0
last observed exit t
14.47502
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. list id visit examdat exitdate mi _t0 _t _d
_st if touse, noobs nodisp id visit
examdat exitdate mi _t0 _t _d
_st 1021 1 10sep1979 31jul1984 0
. . . 0 1021 2 31jul1984
17mar1992 0 0.00 7.63 0 1 1021
3 17mar1992 18jun1996 1 7.63 11.88
1 1 1022 1 10sep1979 19sep1984
0 . . . 0 1022 2
19sep1984 20nov1989 0 0.00 5.17 0
1 1022 3 20nov1989 28oct1993 0
5.17 9.11 0 1 1022 4 28oct1993
31dec1998 0 9.11 14.28 0 1 1023
1 10sep1979 03oct1984 0 . .
. 0 1023 2 03oct1984 20nov1989
0 0.00 5.13 0 1 1023 3
20nov1989 08nov1993 0 5.13 9.10 0
1 1023 4 08nov1993 31dec1998 0
9.10 14.24 0 1
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. makebase cursmok hearta gout highbp diabet
fibrin chol cholsq / gt / bpsyst bpdias obese
thin, firstvis(1) visit(visit) Baseline
confounders storage display
value variable name type format label
variable label ---------------------------------
------------------------------------ Bcursmok
byte 9.0g Bhearta
byte 9.0g Bgout
byte 9.0g Bhighbp
byte 9.0g Bdiabet
byte 9.0g Bfibrin
float 9.0g Bchol
float 9.0g Bcholsq
float 9.0g Bbpsyst
int 9.0g Bbpdias
int 9.0g Bobese
byte 9.0g Bthin
byte 9.0g
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. makelag cursmok hearta gout highbp diabet
fibrin chol cholsq / gt / bpsyst bpdias obese
thin, firstvis(1) visit(visit) Lagged
confounders storage display
value variable name type format label
variable label ---------------------------------
------------------------------------- Lcursmok
byte 9.0g Lhearta
byte 9.0g Lgout
byte 9.0g Lhighbp
byte 9.0g Ldiabet
byte 9.0g Lfibrin
float 9.0g Lchol
float 9.0g Lcholsq
float 9.0g Lbpsyst
int 9.0g Lbpdias
int 9.0g Lobese
byte 9.0g Lthin
byte 9.0g
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. stcox cursmok Agegrp hearta gout highbp diabet
fibrin chol cholsq bpsyst bpdias obese thin
B L failure _d mi analysis time
_t (exitdate-origin)/365.25
origin time examdat2 id
id No. of subjects 1756
Number of obs 4621 No. of failures
244 Time at risk 18547.87132
LR chi2(41)
178.92 Log likelihood -1662.3478
Prob gt chi2 0.0000 ----------------
--------------------------------------------------
---- _t _d Haz. Ratio Std. Err.
z Pgtz 95 Conf. Interval ------------
--------------------------------------------------
------- cursmok 1.014992 .2085446 0.07
0.942 .6785331 1.518288 (remaining output
omitted)
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. stgest cursmok Agegrp fibrin hearta gout
highbp diabet chol cholsq bpsyst bpdias obese
thin, visit(visit) firstvis(2)
lagconf(cursmok fibrin hearta gout highbp diabet
chol cholsq bpsyst bpdias obese thin)
baseconf(fibrin hearta gout highbp cursmok chol
cholsq diabet bpsyst bpdias obese thin)
lasttime(mienddat) range(-2 2) saveres(caergestsmo
knocens) replace causvar cursmok visit
visit Range -2 2, rnum 2 Search method
interval bisection -2.00 2.00 0.00 1.00 0.50
0.25 0.13 0.19 0.22 0.23 0.24 0.24 0.24 0.24 0.38
0.31 0.34 0.36 0.37 0.37 0.37 0.37 -1.00 -0.50
-0.25 -0.13 -0.06 -0.03 -0.02 -0.01 -0.00 -0.00
-0.00 savres caergestsmoknocens G estimate of
psi for cursmok 0.239 (95 CI -0.001 to
0.368) Causal survival time ratio for cursmok
0.787 (95 CI 0.692 to 1.001)
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. weibull _t cursmok Agegrp hearta gout highbp
diabet fibrin chol cholsq bpsyst bpdias obese
thin B L if visitgt2, dead(_d) t0(_t0) hr
_t Haz. Ratio Std Err z Pgtz 95
Conf. Interval --------------------------------
--------------------------------- cursmok
1.01690 .2083929 0.08 0.935 .6805221
1.519549 (rest of output omitted) . gesttowb
g-estimated hazard ratio 1.28 ( 1.00 to 1.47)
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. allowing for censoring due to competing
risks . stgest cursmok Agegrp fibrin hearta
gout highbp diabet chol cholsq bpsyst bpdias
obese thin, visit(visit) firstvis(2)
lagconf(fibrin hearta gout highbp diabet cursmok
chol cholsq bpsyst bpdias obese thin)
baseconf(fibrin hearta gout highbp cursmok chol
cholsq diabet bpsyst bpdias obese thin)
lasttime(mienddat) saveres(caergestsmok) replace
idcens(idcrcens) range(-2 2) pnotcens(pnotcens)
G estimate of psi for cursmok 0.290 (95 CI
-0.190 to 0.773) Causal survival time ratio for
cursmok 0.748 (95 CI 0.462 to 1.210) .
gesttowb g-estimated hazard ratio 1.34 ( 0.82 to
2.19)
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Atherosclerosis Risk in Communities (ARIC) study

• 15, 792 members of 4 communities in the USA
• baseline exam between 1987 and 1989
• 3 follow-up exams at 3 year intervals
• followed up for death, CHD and stroke

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ARIC data

• Baseline
• smoking history, education level, age, sex,
  ethnicity, self-reported stroke/CHD
• Every visit
• BP, BMI, smoking status, total, HDL and LDL
  cholesterol, diabetes status, use of
  anti-hypertensive medication

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ARIC data

• 13898 persons with data on visits 1 and 2
• 7699 (55) female
• Mean age 54 (min45, max65).
• CHD present in 625 (5)
• 9754 (70) not on anti-hypertensive medication at
  visits 1 or 2.

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Methods

• Weibull analysis and G-estimation
• Outcomes - death, incident CHD.
• CHD as outcome - exclude those with CHD at
  baseline/1st visit, censor if die of other causes
• Exposures - BP, smoking, BMI, HDL,LDL
• BP - exclude those on anti-hypertensives at
  baseline, censor at anti hypertensive use.

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Results

• Published in the American Journal of
  Epidemiology, April 15th 2002.
• Tilling K, Sterne JAC, Szklo M. G-estimation of
  the effects of cardiovascular risk factors on
  all-cause mortality and CHD the ARIC study. AJE
  2004 155 710-718
• Summary effects tended to be under-estimated by
  Weibull compared to g-estimation.

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Discussion - model specification

• Model specified that exposure at a given visit
  multiplies survival from that moment by a given
  amount.
• Alternatives
• effect on survival only lasts for a given period
  (e.g. use of anti-hypertensives)
• effect on survival starts after a given period
  (e.g. possible lagged effect of smoking)

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Future work and (we hope) collaboration

• Implement MSMs in Stata
• Effect of cardiovascular risk factors (e.g.
  smoking, fibrinogen) and anti-hypertensives in
  Caerphilly study
• Effect of treatments (e.g. anti-hypertensives,
  anti-platelet agents) on stroke recurrence using
  South London Stroke Register

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Future work and (we hope) collaboration

• Causal effect of HAART
• When to start
• Effect of different drug combinations
• Will require large collaborations between cohorts
• Aim to build on an existing collaboration between
  13 cohorts involving 12500 patients starting
  HAART

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