1. Harvard T.H. Chan School of Public Health
Considerations for the choice of statistical methods for PCOR questions
Sara Lodi
Harvard T.H. Chan School of Public Health
February 25th 2016

2. Recap from earlier today…
We conduct observational studies when a question cannot be answered with a RCT
Target trial: hypothetical RCT that we would have preferred to conduct…
Design and analyse the observational study to emulate the target trial

3. Emulating the target trial
Formulation of the question and study design
Eg eligibility criteria, intervention, outcome definition, ect
Identification of data requirements
Do we have data on all possible confounders?
Statistical analyses of the observational study
Tailored to the specific question and the data

4. In this talk…
Focus on the choice of the statistical methods to emulate a target trial using observational data
Identify some situations where standard methods fail
time-varying confounding and informative censoring
Introduce inverse probability weighting

5. Statistical methods for observational studies
Needed to adjust for confounding and selection bias
Assume sufficient data to emulate the target trial
Standard methods
Stratification, propensity score, logistic regression, Cox models, etc
G-methods
Inverse probability weighting of marginal structural models, g-formula and g-estimation of structural nested models

6. Standard methods
G-methods OR

7. Good news: work well most of the times!
Standard methods
G-methods OR
Good news: work well most of the times!
Often needed when things evolve/change over time

8. Questions in PCOR are often about time-varying treatments
Often about long-term outcomes in chronic diseases (HIV disease, cardiovascular disease, diabetes, chronic liver disease, etc):
Treatment optimization over the long-term
Time-varying treatments and prognostic measures

9. Observational data
Large populations followed-up prospectively for long periods
Capture history of treatment, confounders and outcome
Variety of settings and diversity of patients

10. Examples of observational data
Claims data (Medicare or Medicaid)
Clinical records (HIV-CAUSAL Collaboration, UK CPRD data)
Longitudinal cohorts (Nurses’ Health Study, Framingham Heart Study)

11. Example of HIV data Administrative censoring 1 June 2015 L
HIV diagnosis
CD4 400
HIV-RNA 1000
Start antiretroviral treatment
Drug resistance detected
Treatment change
Stroke
21Jan 2012
1 Feb 2013
3 March 2014
1 June 2015
HIV diagnosis
CD4 200
HIV-RNA 10000
TB diagnosis
TB death
1Jun 2012
3 Aug 2012
15 Jun 2014
HIV diagnosis
CD4 600
HIV-RNA 1000
Pregnancy
Start antiretroviral treatment
Last visit L
1 Apr 2012
1 Apr 2013
1 Dec 2013

12. Time-varying confounding and treatment confounder feedback

13. Effect of Antiretroviral Treatment (ART) on the risk of death
Antiretroviral treatment (ART) is effective in reducing the risk of AIDS morbidity and mortality
Observational studies at the beginning of the ART era failed to replicate results of RCTs

14. Effect of Antiretroviral Treatment (ART) on the risk of death
(HIV-CAUSAL Collaboration. AIDS 2009)
TARGET TRIAL
Eligibility criteria
HIV-1-infected and ART-naïve
Treatment arms
Always treated (ART) versus never treated (no ART)
Outcome
Death
Start/End follow-up
From randomization to death, loss f-u, 5 years
Analysis plan
Hazard ratios of death for ART vs no ART treatment arm

15. In the observational data…
Administrative censoring 1 June 2015
HIV diagnosis
CD4 400
HIV-RNA 1000
ART started
Treatment change
Last visit
HIV diagnosis
CD4 200
HIV-RNA 10000
TB diagnosis
Death
HIV diagnosis
CD4 600
HIV-RNA 1000
ART started
Last visit L

16. In the observational data…
No baseline randomization
ART status is time-varying
ART initiation depends on prognostic factors that vary over time (time-varying confounders)

17. Treatment-confounder feedback
At: Antiretroviral therapy
Y: Death
Lt: CD4 cell count
U: Immunologic status A0 L1 A1 Y U

18. Treatment-confounder feedback
At: Antiretroviral therapy
Y: Death
Lt: CD4 cell count
U: Immunologic status A0 L1 A1 Y U
The time-varying confounders are affected by previous treatment

19. Treatment-confounder feedback
At: Antiretroviral therapy
Y: Death
Lt: CD4 cell count
U: Immunologic status A0 L1 A1 Y U
Standard methods don’t work
Need to use g-methods

20. IPW Inverse probability weighting of marginal structural models
Pseudo-population with no confounding by L1
Any outcome model can be used (marginal structural model)

21. Inverse probability weighting of marginal structural models
STEP 1
Model for treatment
Covariates: time-varying confounders
Example:
Logistic regression model for ART initiation CD4 count and other time-varying confounders as covariates

22. Inverse probability weighting of marginal structural models
STEP 2
Use models from STEP 1 to estimate IP weights as the inverse of the predicted probability of receiving their treatment

23. Inverse probability weighting of marginal structural models
STEP 3
A model for outcome with weights
Covariates: time-varying treatment and (optional) baseline confounders, no time-varying confounders
Example:
Weighted Cox model for death with time-varying ART initiation status and baseline confounders as covariates

24. Effect of Antiretroviral Treatment (ART) on the risk of death
(HIV-CAUSAL Collaboration. AIDS 2009)
Standard method
IPW

25. Inverse probability weighting of marginal structural models
Assumptions
No unmeasured or residual baseline or time-varying confounding
Models for treatment and outcome should be correctly specified
Positivity – the probability of having every value of the treatment is greater than zero

26. Informative censoring

27. Informative censoring
Administrative censoring 1 June 2015
HIV diagnosis
CD4 400
HIV-RNA 1000
ART started
Treatment change
HIV diagnosis
CD4 200
HIV-RNA 10000
TB diagnosis
Death
HIV diagnosis
CD4 600
HIV-RNA 1000
ART started
Last visit L

28. Informative censoring
Standard methods assume non informative censoring
Individuals who are lost to follow-up have similar survival prospects compared to those who continue to be followed
Censoring due to loss to follow up can be informative
Time-varying selection bias

29. Inverse probability weighting of censoring
A model for censoring
Covariates: time-varying confounders
Used to estimate IP weights as the inverse of the predicted probability of not being censored
A model for outcome (with weights)
Covariates: time-varying treatment and (optional) baseline confounders, no time-varying confounders

30. Examples from literature using IPW
Comparison of immediate vs. deferred initiation of androgen deprivation therapy in prostate cancer patients with PSA-only relapse. Garcia-Albeniz X al 2015
Relationship between Epoetin Alfa Dose and Mortality. Wang O et al 2010

31. Examples where g-methods are not needed
Comparative effectiveness of two first line ART combinations (lopinavir versus atazanavir) on clinical outcomes. Cain el al. 2015
Treatment: lopinavir or atazanavir at ART initiation
Effect of warfarin following AMI in patients with atrial fibrillation. Carrero J et al 2015
Treatment: warfarin or no warfarin at hospital discharge

32. Summary
Standard methods work well when treatment is not time-varying (assume we have enough good data to adjust for confounding)
G-methods are needed in the presence of:
Treatment confounding feedback and informative censoring
IPW can be used to correct for these issues

33. References Applications of IPW
HIV-CAUSAL Coll. The effect of combined antiretroviral therapy on the overall mortality of HIV-infected individuals. AIDS Jan 2;24(1):
Garcia de Albaniz X el al. Immediate vs. deferred initiation of androgen deprivation therapy in prostate cancer patients with PSA-only relapse. European Journal of Cancer May;51(7):817-24
Wang O el al. Relationship between epoetin alfa dose and mortality: findings from a marginal structural model. Clin J Am Soc Nephrol Feb;5(2):182-8
Applications where g-methods are not needed
Carrero J at al. Warfarin, kidney dysfunction, and outcomes following acute myocardial infarction in patients with atrial fibrillation. JAMA Mar 5;311(9):
Cain L et al. Boosted lopinavir- versus boosted atazanavir-containing regimens and immunologic, virologic, and clinical outcomes. Clin Infect Dis Apr 15;60(8):1262-8