Cancer Trials

1. Cancer Trials

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

3. What is so special about cancer? The disease • Many cancers are life-threatening. • Many cancers neither curable or controlable. • Malignant disease implies limited life expectancy. The drugs • 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

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. Doses The cancer programme Phase I: Find the Maximum Tolerable Dose (MTD) The dose with probability of dose limiting toxicity less than p0 DLT=Dose Limiting Toxicity often between 0.1 and 0.4 Investigate anti tumour actividy at MTD using e.g. tumour shrinkage as outcome. Phase II: Sufficient anti tumour activity Investigate effect on survival Phase III:

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

8. Start with a group of 3 patients at the initial dose level No toxicity Next group of 3 patients at the next higher dose level Yes No Next group of 3 patients at the same dose level Toxicity in at most one patient Next group of 3 patients at the next higher dose level Yes No Trial stops Phase I cancer trials Design A If is the highest dose then is the estimated MTD • Only escalation possible. • Start at the lowest dose. • Many patients on too low dose.

9. Start with a single patient at the initial dose level No toxicity Yes Next patient at the same dose level No Next patient at the next lower dose level No Toxicity in two consequtive patients Yes Next patient at the next higher dose level No Toxicity in two consequtive patients Yes Next patient at the next lower dose level No Trial stops Phase I cancer trials Design B • Escalation and deescaltion possible. • No need to start with the lowest dose. MTD:

10. Start with a group of 3 patients at the initial dose level Toxicity in more than one patient Yes Next group of 3 patients at the next lower dose level No Toxicity in one patient Yes Next group of 3 patients at the same dose level No Next group of 3 patients at the next higher dose level Repeat the process until exhaustion of all dose levels or max sample size reached Phase I cancer trials Design D • Escalation and deescaltion possible. • No need to start with the lowest dose. MTD:

11. 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.

12. Phase I cancer trials Continual reassessment designs Acceptable probability of DLT MTD Dose response model: Assume fixed. Let be the prior distribution for the slope parameter.

13. is the likelihood function, and Once the response, DLT or no DLT, is available from the current patient at dose is the cumulative data up to the i-1 patient. the estimated slope is update as: Phase I cancer trials where where

14. Phase I cancer trials The next dose level is given by minimizing MTD is estimated as the dose xm 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

15. Phase II cancer trials Objective: Investigate effect on tumor of MTD. Response: Sufficient tumour shrinkage. Progression free survival. Two important things: • Stop developing ineffective drug quickly. • Identify promising drug quickly.

16. Unacceptable response rate: Acceptable response rate: vs. Test: Phase II cancer trials Optimal 2 stage designs. First stage: n1 patients: Stop and reject the drug if at most r1 successes Second stage: n2 patients: Stop and reject the drug if at most r successes

17. is minimized. Phase II cancer trials How to select n1 and n2 ? Minimize expected sample size under H0: where is the probability of early termination. Given p0, p1,  and , select n1, n2, r1 and r such that Nice discrete problem.

18. Phase II cancer trials Assume specific values of p0, p1,  and  For each value of the total sample size n, n1[1,n-1] and r1[0,n1] Find the largest value of r that gives the correct Check if the combination:n1, n2, r1 and r satisfies If it does, compare E[N] for this design with previous feasible designs. Start the search at !: not unimodal

19. Phase II cancer trials Optimal 2 stage designs with: Corresponding designs with minimal maximal sample size

20. Phase II cancer trials Optimal flexible 2 stage designs. In practise it might be difficult to get the sample sizes n1 and n2 exactly at their prespecified values. Solution: let N1{n1, …n1+k} with P(N1=n1j)=1/k, j=1,…k and N2{n2, …n2+k} with P(N2=n2j)=1/k , j=1,…k. N1 and N2 independent, n1+k< n2. P(N1=n1j ,N2=n2j)=1/k2 , j=1,…k. Total samplesize N=N1+N2

21. Phase II cancer trials For a given combination of n1 +i and n2 +j: where Minimize the average E[N] (Average over all possisble stopping points)

22. Phase II cancer trials Flexible designs with 8 consucutive values of n1 and n2.

23. 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: n1 patients: Stop and reject the drug if no successes Second stage: n2 patients: Stop and reject the drug if at most r2 successes Third stage: n3 patients: Stop and reject the drug if at most r3 successes For each n1 such that: Determine n2, r2, n3, r3 that minimizes the expected sample size. More?

24. Phase II cancer trials Example: Optimal 3 stage design with n1 at least 5 and

25. Phase II cancer trials Multiple-arm phase II designs Say that we have 2 treatments with P(tumour response)=p1 and p2 Select treatment i for further development if Ambiguous if Assume p2>p1. The probability of correct secection is

26. Ambiguous if Phase II cancer trials The probability of ambiguity is

27. Phase II cancer trials Select n such that: Probability of outcomes for different sample sizes (=0.05)

28. 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

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

30. 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 (?)

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

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

33. The usual way The cause specific survival, , is usually estimated using the cause of death information and standard methods such as Kaplan-Meier or life tables, censoring for causes of death other than D. Problem: The actual cause of death is not always equal to the registered cause of death.

34. The model : can be formulated using the corresponding survival functions as: using Estimate:

35. Estimation can be estimated directly from data. relating to deaths from causes other than D can be estimated using data from a population registry if: D is a ‘rare’ cause of death in the population. The study population has the same risk of dying from other causes as the background population. : the “expected” survival given age, sex and calender year

36. The intuitive way (no formulas) • We have the annual survival probability given age, sex and calender year. • Multiply to get the probability of surviving k years for each individual • Average to get the expected survival.

37. Converting intuition into formulas Individuals i=1 …n, time intervals j=1 to k For each individual we have the “expected” probability of surviving time interval j. Now is called the Ederer I estimate of the expected survial

38. Problemo age 91 95 88 82 85 at risk at tj 77 74 72 72 73 70 66 63 t tj tj+1 All inividuals contributes to Only individuals at risk at tj contributes to

39. Solution: Let only individuals at risk contribute to the expected survival. where is then number of individuals at risk at time t. and is the index set of individuals at risk at time t The Ederer II estimate

40. Expected survival for a group pf patients diagnosed with prostate cancer 1992

41. Estimated cause specific survival of patients diagnosed with prostate cancer 1992

42. Continuous time, expected hazard : ‘expected’ morality (hazard) from the population for individual i. : at risk indicator for individual i at time t. : number of individuals at risk The expected integrated hazard is now given by

43. Cont. time relative survival Rewriting the model: using integrated hazards we can estimate using =event times where = # events at time Now the continuous time relative survival is given by:

44. Illustrated t

45. Illustrated t

46. Example

47. Example

48. Intervension Incidence Death Incidence Intervension Death Population based trials In many countries there are cancer registers where data on all cases of cancer diagnoses are collected. Many countries also have a cause of death registry Often observational studies i.e. no randomization.