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? 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) The dose with probability of dose limiting toxicity less than p 0 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 often between 0.1 and 0.4Doses

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

8. Phase I cancer trials Design A 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 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 Trial stops Yes No Ifis the highest dose thenis the estimated MTD Only escalation possible. Start at the lowest dose. Many patients on too low dose.

9. Phase I cancer trials Escalation and deescaltion possible. No need to start with the lowest dose. 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 Toxicity in two consequtive patients Yes No Next patient at the next lower dose level Yes

10. 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 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: Assumefixed. Letbe the prior distribution for the slope parameter.

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

14. Phase I cancer trials The next dose level is given by minimizing 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

15. 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.

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

17. Phase II cancer trials How to select n 1 and n 2 ? Minimize expected sample size under H 0 : whereis the probability of early termination. Given p 0, p 1,  and , select n 1, n 2, r 1 and r such that is minimized.Nice discrete problem.

18. Phase II cancer trials Assume specific values of p 0, p 1,  and  For each value of the total sample size n, n 1  [1,n-1] and r 1  [0,n 1 ] Find the largest value of r that gives the correct Check if the combination: n 1, n 2, r 1 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 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 1j,N 2 =n 2j )=1/k 2, j=1,…k. N 1 and N 2 independent, n 1 +k< n 2. Total samplesize N=N 1 +N 2

21. Phase II cancer trials For a given combination of n 1 +i and n 2 +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 n 1 and n 2.

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: 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?

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

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

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

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

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 Letting it can be showed that: 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. 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

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

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: : the “expected” survival given age, sex and calender year 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.

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

39. Solution: Let only individuals at risk contribute to the expected survival. where is then number of individuals at risk at time t. andis 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 estimateusing where =event times = # events at time Now the continuous time relative survival is given by:

44. Illustrated t

45. t

46. Example

48. 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 IntervensionIncidenceDeath IncidenceIntervensionDeath Often observational studies i.e. no randomization.