Complier Average Causal Effect analysis

1. Complier Average Causal Effect analysis Jon Nicholl ScHARR, Sheffield

2. Pragmatic evaluations allow patients and clinicians to comply with treatment regimes as they would in practice • This often means not completing (adhering to) or following (complying with) the allocated treatment, eg X-overs in surgical trials • ITT analysis of everyone gives a true estimate of the real world population treatment effect, but not of the effect in an individual who is treated (because ITT is diluted by non-compliers)

3. Dealing with non-compliance in TAU or TAU+placebo controlled trials:Complier Average Causal Effect analysis ITT analysis: all A vs all B = 0.233 / 0.266 = 0.875. This estimate is diluted (biased towards 1.0) by the non-compliers

4. Sometimes the average effect in individuals who comply is estimated by a per protocol analysis

5. Dealing with non-compliance in TAU or TAU+placebo controlled trials:Complier Average Causal Effect analysis ITT analysis: all A vs all B = 0.233 / 0.266 = 0.875. This estimate is diluted (biased towards 1.0) by the non-compliers Per protocol analysis: Complied A vs all B = 0.2 / 0.266 = 0.75

6. Per protocol analysis • Pointless. It certainly doesn’t work in pragmatic, open trials • And may not in double blind placebo controlled trials

7. Five-year mortality in CHD patients given clofibrate, according to cumulative adherence to protocol prescription. NEJM 1980; 303: 1038-

8. Five-year mortality in CHD patients given clofibrate, according to cumulative adherence to protocol prescription.

9. Selection by patient preference:Five-year mortality in CHD patients given clofibrate, according to cumulative adherence to protocol prescription. The problem is different types of patients have different adherence/compliance rates Can we estimate the control treatment effect in patients who would have complied with A?

10. Dealing with non-compliance in TAU or TAU+placebo controlled trials:Complier Average Causal Effect analysis CACE analysis: Complied A vs ER in controls who would have complied with A = 0.2 / ?

11. Why is this important for cmRCT ? • How does it work?

12. Why is it important? • cmRCT designs randomly select some eligible patients from the cohort to be offered a treatment • For an unbiased analysis all eligible patients offered the treatment are compared with all eligible patients not selected • If the take up of the offer is low, cmRCT designs may seriously underestimate the treatment effect • CACE is a method for adjusting for this

13. How does CACE analysis work? CACE analysis: Complied A vs ER in controls who would have complied with A = 0.2 / ?

14. How does CACE analysis work? First, we imagine that there are two types of patient – ‘compliers with A’ and ‘non-compliers with A’. since the trial is randomised, we know (estimate) what % of controls are ‘non-compliers with A’ = 100/300

15. How does CACE analysis work? Next, we assume that controls had the same treatment as intervention group A patients who didn’t comply. So the event rate in controls who are ‘non-compliers with A’ would be the same as non-compliers with A given treatment A = 0.3 Is this assumption reasonable?

16. Is this assumption reasonable? • Design: TAU + A vs TAU • Assumption is right • Design: A vs TAU. • Then the question is whether non-compliers with A have TAU or nothing • When non-compliance = X-over the assumption is right • When A = offer of A, and TAU = no offer, then the assumption is also likely to be right unless the offer of A affects outcome • Design: TAU + A vs TAU + placebo. • Then the question is whether there is a placebo effect

17. How does CACE analysis work? Given the event rate, we can now estimate the number of events in the control group who are ‘non-compliers with A’ = 100 x 0.3 = 30

18. How does CACE analysis work? And, by subtraction, the number of events in the control group who are ‘compliers with A’

19. How does CACE analysis work? And hence we can estimate the event rate in the control group who are ‘compliers with A’

20. How does CACE analysis work? CACE analysis: Complied A vs ER in controls who would have complied with A = 0.2 / 0.25 = 0.8

21. How does CACE analysis work? ITT analysis: All A vs all B = 0.233 / 0.266 = 0.875 Per protocol analysis: Complied A vs all B = 0.2 / 0.266 = 0.75 CACE analysis: Complied A vs ER in controls who would have complied with A = 0.2 / 0.25 = 0.8

22. The analysis works in the same way for continuous outcomes (200 x ?) + (100 x 50.0) = 52.0 ITT analysis: All A vs all B = 56.7 – 52.0 = 4.7 Per protocol analysis: Complied A vs all B = 60.0 – 52.0 = 8.0 CACE analysis: Complied A vs ER in controls who would have complied with A = 60.0 – 53.0 = 7.0

23. CACE was made for cmRCT trials • CACE analysis can be used for A vs TAU trials as in cmRCT designs • It is very helpful for dealing with compliance rather than adherence (ie when patients randomised to treatment don’t take it up at all). This is the case in trials of the offer of treatment - as in cmRCT designs • Some sort of CACE analysis (as opposed to ITT) is essential when compliance is low – as may be the case in cmRCT studies because there is no pre-selection of patients

24. Thank you • Compliance/adherence and CACE analysis: • Hewitt CE, et al. Can Med Assoc J 2006;175:347 (for a simple explanation). • Dunn G, et al. Statistical methods in medical research 2005; 14: 369-395 (for a statistical exploration)