1. Cancer Trials

2. Reading instructions 6.1: Introduction 6.2: General Considerations - read 6.3: Single stage phase I designs - read 6.4: Two stage phase I designs - read 6.5: Continual reassessment - read 6.6: Optimal/flexible multi stage designs - read 6.7: Randomized phase II designs - read

3. What is so special about cancer? Many cancers are life-threatening. Many cancers neither curable or controlable. Malignant disease implies limited life expectancy. Narrow therapeutic window. Many drug severely toxic even at low doses. Serious or fatal adverse drug reactions at high doses. Difficulty to get acceptance for randomization The disease The drugs

4. Ethics ?

5. Some ways to do it No healty volunteers. Terminal cancer patients with short life expectancy. Minimize exposure to experimental drug. Efficient selection of acceptable drug.

6. The cancer programme Phase I: Find the Maximum Tolerable Dose (MTD) DLT=Dose Limiting Toxicity Phase II: Investigate anti tumour actividy at MTD using e.g. tumour shrinkage as outcome. Phase III: Investigate effect on survival Sufficient anti tumour activity Acceptable probability of DLT, often between 0.1 and 0.4 Doses

7. Phase I cancer trials Objective: Find the Maximum Tolerable Dose (MTD) Use maximum likelihood to estimate and Find MTD: ; x = dose p0p0 x MTD

8. Phase I cancer trials Start with a group of 3 patients at the initial (lowest) dose level Toxicity in at least one patient Next group of 3 patients at the next higher dose level Next group of 3 patients at the same dose level Toxicity in more than one patient Next group of 3 patients at the next higher dose level Trial stops No Yes Ifis the highest dose thenis the estimated MTD Only escalation is possible. Starts at the lowest dose. Many patients on a too low dose. Design A

9. Phase I cancer designs Dose 1 Dose 2 Dose 3 Dose 4 Dose 5 Dose 6     : no DLT  : DLT Design A example Beyond first dose: Up if at most 1 red Stop if more than 1 red

10. Phase I cancer trials One patient at a time Escalation and deescaltion possible. No need to start with the lowest dose. Fit a logistic regerssion model MTD: Design B Start with a single patient at the initial dose level No Toxicity Next patient at the same dose level Next patient at the next lower dose level No Toxicity in two consequtive patients Next patient at the next higher dose level Trial stops Yes No Yes Toxicity in two consequtive patients No Next patient at the next lower dose level Yes where are the Maximum likelihood estimates.

11. Phase I cancer designs Dose 1 Dose 2 Dose 3 Dose 4 Dose 5 Dose 6   Beyond first dose: Up if 2 consecutive green Down 1 red in 2 Stop if 2 red : no DLT  : DLT Design B example 

12. Phase I cancer trials Design D Start with a group of 3 patients at the initial dose level Next group of 3 patients at the same dose level Next group of 3 patients at the next lower dose level Toxicity in one patient Next group of 3 patients at the next higher dose level Yes No Yes No Repeat the process until exhaustion of all dose levels or max sample size reached Toxicity in more than one patient Escalation and de escaltion possible. No need to start with the lowest dose. Fit a logistic regression model MTD: where are the Maximum likelihood estimates.

13. Phase I cancer designs Dose 1 Dose 2 Dose 3 Dose 4 Dose 5 Dose 6     : no DLT  : DLT Design D example  Up if no 1 DLT Constant if 1 DLT Down if more than 1 DLT Stop if no doses left or if we reached dose limit     

14. Phase I cancer trials Design BD Run design B until it stops. DLT in last patient Run design D starting at the next lower dose level. Run design D starting at same dose level.

15. Phase I cancer trials Continual reassessment designs, the Bayesian way Acceptable probability of DLT MTD Dose response model: Assumefixed. Letbe the prior distribution for the slope parameter. Since for example a gamma distribution would work

16. Phase I cancer trials Once the response, (DLT or no DLT), is available from the current patient at dose we have the data: where is the likelihood function, where on dose and response up to the i-1 patient. is the apriori for the slope parameter Estimate  as the expected value of  given the prior distribution data so far The posterior density for  and The next dose level is given by minimizing

17. Phase I cancer trials MTD is estimated as the dose x m for the hypothetical n+1 patient. The probability of DLT can be estimated as CRM is slower than designs A, B, D and BD. Estimates updated for each patient. CRM can be improved by increasing cohort size

18. Phase II cancer trials Objective: Investigate effect on tumor of MTD. Response: Sufficient tumour shrinkage. Stop developing ineffective drug quickly. Identify promising drug quickly. Two important things: Progression free survival. Non randomized single arm studies

19. Phase II cancer trials Optimal 2 stage one arm designs. First stage: n 1 patients Second stage: n 2 patients Unacceptable response rate: Acceptable response rate: Test: vs. n1n1 Stop and reject the drug if at most r 1 successes Stop and reject the drug if at most r successes n 1 + n 2

20. Phase II cancer trials How to select n 1 and n 2 ? Minimize expected sample size under H 0 : where is the probability of early termination.

21. Phase II cancer trials To get  and  we need the probabtility to reject a drug

22. Phase II cancer trials 1: Assume specific values of p 0, p 1,  and  2: For each value of the total sample size n, n 1  [1,n-1] and r 1  [0,n 1 ] 3: Find the largest value of r that gives the correct 4: Check if the combination: n 1, n 2, r 1 and r satisfies 5: If it does, compare E[N] for this design with previous feasible designs. Start the search at !: not unimodal Given p 0, p 1,  and , select n 1, n 2, r 1 and r such that is minimized. Nice discrete problem.

23. Phase II cancer trials Optimal 2 stage designs with: Corresponding designs with minimal maximal* sample size *) Minimize total sample size (n) first, then select n 0 to minimize E[N] under p 0

24. Phase II cancer trials Optimal flexible 2 stage designs. In practise it might be difficult to get the sample sizes n 1 and n 2 exactly at their prespecified values. Solution: let N 1  {n 1, …n 1 +k} with P(N 1 =n 1j )=1/k, j=1,…k and N 2  {n 2, …n 2 +k} with P(N 2 =n 2j )=1/k, j=1,…k. P(N 1 =n 1 +i,N 2 =n 2 +j)=1/k 2, i=1,…,k; j=1,…,k. N 1 and N 2 independent, n 1 +k< n 2. Total sample size N=N 1 +N 2 First stage: n 1 to n 1 +k patients Second stage: n 2 to n 2 +k patients n 1 to n 1 +k Stop and reject the drug if at most r i successes, i=1,…,k Stop and reject the drug if at most R i successes, j=1,…,k n 1 +n 2 to n 1 +n 2 +2k

25. Phase II cancer trials For a given combination of n i =n 1 +i and N j =n 2 +j: where Minimize the average E[N] (Average over all possisble stopping points )

26. Phase II cancer trials Flexible designs with 8 consecutive values of n 1 and n 2.

27. Phase II cancer trials Optimal three stage designs The optimal 2 stage design does not stop it there is a ”long” initial sequence of consecutive failures. First stage: n 1 patients: Second stage: n 2 patients: Stop and reject the drug if no successes Stop and reject the drug if at most r 2 successes Third stage: n 3 patients:Stop and reject the drug if at most r 3 successes For each n 1 such that: Determine n 2, r 2, n 3, r 3 that minimizes the expected sample size. More? The probability of no responses in the first n 1 observations is less than  given an acceptane response rate p 1.

28. Phase II cancer trials Optimal 3 stage design with n 1 at least 5 and Example:

29. Phase II cancer trials Randomized multiple-arm phase II designs Say that we have 2 treatments with P(tumour response)=p 1 and p 2 Select treatment 1 for further development if Ambiguous if Select p 2 Select p 1 Ambiguous Assume p 2 >p 1. The probability of correct selection is

30. Phase II cancer trials The probability of ambiguity is Assume p 2 >p 1. The probability of correct selection is

31. Phase II cancer trials Probability of outcomes for different sample sizes (  =0.05) Select n such that: nP1P1 P2P2 P Corr P Amb P Corr +0.5P Amb 500.250.350.710.240.83 750.250.350.760.210.87 1000.250.350.760.230.87 nP1P1 P2P2 P Corr P Amb P Corr +0.5P Amb 500.200.350.870.120.93 750.200.350.920.070.96 1000.200.350.940.060.97

32. Phase II cancer trials Sample size can be calculated approximately by using Where The power of the test of is given by is the upper  /2 quantile of the standard normal distribution

33. Phase II cancer trials Letting it can be showed that: Sample size can be calulated for a given value of.

34. Phase II cancer trials Many phase II cancer trials not randomized Treatment effect can not be estimated due to variations in: Patient selection Response criteria Inter observer variability Protocol complience Reporting procedure Sample size (?)

35. Phase III cancer trial It’s all about survival! Diagnosis Treatment Progression Death from the cancer Death from other causes Progression free survival Cause specific survival All cause survival

36. The competing risks model Diagnosed with D Death from other cause Death caused by D The aim is to estimate the cause specific survival function for death caused by D.