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MPS Research UnitCHEBS Workshop - April 20031 Anne Whitehead Medical and Pharmaceutical Statistics Research Unit The University of Reading Sample size.

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Presentation on theme: "MPS Research UnitCHEBS Workshop - April 20031 Anne Whitehead Medical and Pharmaceutical Statistics Research Unit The University of Reading Sample size."— Presentation transcript:

1 MPS Research UnitCHEBS Workshop - April Anne Whitehead Medical and Pharmaceutical Statistics Research Unit The University of Reading Sample size determination for cost-effectiveness trials

2 MPS Research UnitCHEBS Workshop - April Comparative study Parallel group design Control treatment (0) New treatment (1) n 0 subjects to receive control treatment n 1 subjects to receive new treatment

3 MPS Research UnitCHEBS Workshop - April Measure of treatment difference Let  be the measure of the advantage of new over control  > 0  new better than control  = 0  no difference  < 0  new worse than control Consider frequentist, Bayesian and decision-theoretic approaches

4 MPS Research UnitCHEBS Workshop - April Frequentist approach Focus on hypothesis testing and error rates - what might happen in repetitions of the trial e.g.Test null hypothesisH 0 :  = 0 against alternativeH 1 + :  > 0 Obtain p-value, estimate and confidence interval Conclude that new is better than control if the one-sided p-value is less than or equal to  Fix P(conclude new is better than control |  =  R ) = 1– 

5 MPS Research UnitCHEBS Workshop - April Distribution of  = 0  =  R   k Fail to Reject H 0 Reject H 0

6 MPS Research UnitCHEBS Workshop - April A general parametric approach Assume Reject H 0 if > k where  is the standard normal distribution function and P(Z > z  ) =  where Z ~ N(0, 1)

7 MPS Research UnitCHEBS Workshop - April Require

8 MPS Research UnitCHEBS Workshop - April Application to cost-effectiveness trials Briggs and Tambour (1998)  = k (  E1 –  E0 ) – (  C1 –  C0 ) is the net benefit, where  E1,  E0 are mean values for efficacy for new and control treatments  C1,  C0 are mean costs for new and control treatments kis the amount that can be paid for a unit improvement in efficacy for a single patient

9 MPS Research UnitCHEBS Workshop - April Set and solve for n 0 and n 1

10 MPS Research UnitCHEBS Workshop - April Bayesian approach Treat parameters as random variables Incorporate prior information Inference via posterior distribution for parameters Obtain estimate and credibility interval Conclude that new is better than control if P (  > 0|data) > 1 –  Fix P 0 (conclude new better than control) = 1 – 

11 MPS Research UnitCHEBS Workshop - April Likelihood function Prior h 0 (  ) is Posterior h(  |data) i.e. h(  |data) is

12 MPS Research UnitCHEBS Workshop - April P (  > 0|data) > 1 –  if i.e.

13 MPS Research UnitCHEBS Workshop - April Prior to conducting the study, so

14 MPS Research UnitCHEBS Workshop - April Require P 0 Express w in terms of n 0 and n 1, provide values for  0 and w 0 and solve for n 0 and n 1

15 MPS Research UnitCHEBS Workshop - April Application to cost-effectiveness trials O’Hagan and Stevens (2001)  = k (  E1 –  E0 ) – (  C1 –  C0 ) Use multivariate normal distribution for - separate correlations between efficacy and cost for each treatment Allow different prior distributions for the design stage (slide13) and the analysis stage (slide 11)

16 MPS Research UnitCHEBS Workshop - April Decision-theoretic approach Based on Bayesian paradigm Appropriate when outcome is a decision Explicitly model costs and benefits from possible actions Incorporate prior information Choose action which maximises expected gain

17 MPS Research UnitCHEBS Workshop - April Actions Undertake study and collect w units of information on , then one of the following actions is taken: Action 0 : Abandon new treatment Action 1 : Use new treatment thereafter

18 MPS Research UnitCHEBS Workshop - April Table of gains ( relative to continuing with control treatment)  Action 1 Action 0  0 – cw – b – cw > 0 – cw – b + r 1 – cw c = cost of collecting 1 unit of information (w) b = further development cost of new treatment r 1 = reward if new treatment is better G 0,w (  ) = – cw

19 MPS Research UnitCHEBS Workshop - April Following collection of w units of information, the expected gain from action a is G a, w (x) = E {G a,w (  )| x} Action will be taken to maximise E {G a,w (  )|x}, that is a*, w* where G a*, w* (x) = max { G a, w (x)} (Note: Action 1 will be taken if P (  > 0|data) > b/r 1 )

20 MPS Research UnitCHEBS Workshop - April At design stage consider frequentist expectation: E ( G a*, w (x)) and use this as the gain function U w (  )

21 MPS Research UnitCHEBS Workshop - April Expected gain from collecting information w is So optimal choice of w is w*, where

22 MPS Research UnitCHEBS Workshop - April This is the prior expected utility or pre-posterior gain

23 MPS Research UnitCHEBS Workshop - April Note: = E{– cw + max(r 1 P (  > 0|data) – b, 0)}

24 MPS Research UnitCHEBS Workshop - April Application to cost-effectiveness trials Could apply the general decision-theoretic approach taking q to be the net benefit The decision-theoretic approach appears to be ideal for this setting, but does require the specification of an appropriate prior and gain function

25 MPS Research UnitCHEBS Workshop - April Table of gains – ‘Simple Societal’ ( relative to continuing with control treatment)  Action 1 Action 0  0 – cw – b – cw > 0 – cw – b + r 1 – cw c = cost of collecting 1 unit of information (w) b = further development cost of new treatment r 1 = reward if new treatment is more cost-effective G 0,w (  ) = – cw

26 MPS Research UnitCHEBS Workshop - April Gains – ‘Proportional Societal’ ( relative to continuing with control treatment) c = cost of collecting 1 unit of information (w) b = further development cost of new treatment r 2 = reward if new treatment is more cost-effective G 0,w (  ) = – cw

27 MPS Research UnitCHEBS Workshop - April Gains – ‘Pharmaceutical Company’ c = cost of collecting 1 unit of information (w) b = further development cost of new treatment r 3 = reward if new treatment is more cost-effective where A is the set of outcomes which leads to Action 1, e.g. for which P (  > 0|data) > 1 – 

28 MPS Research UnitCHEBS Workshop - April References Briggs, A. and Tambour, M. (1998). The design and analysis of stochastic cost-effectiveness studies for the evaluation of health care interventions (Working Paper series in Economics and Finance No. 234). Stockholm, Sweden: Stockholm School of Economics. O’Hagan, A. and Stevens, J. W. (2001). Bayesian assessment of sample size for clinical trials of cost-effectiveness. Medical Decision Making, 21,


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