ABSTRACT

Threshold Treatment Lag . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 8.4.2 Increasing the Sample Size When There Is a Treatment

Lag . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258 8.4.3 Interaction between Weighted Statistics and

Non-proportional Hazards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258 8.4.4 Estimating the Treatment Effect in a Trial with a

Threshold Treatment Anti-lag . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 8.4.5 Sample Size Re-estimation in the Presence of Treatment

Lag or Anti-lag: Concluding Remark . . . . . . . . . . . . . . . . . . . . 260 8.4.6 Conditional Power, Current Trends, and

Non-proportional Hazards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260 8.5 How the Markov Model Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261

8.5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 8.5.2 The Exponential Model for Calculating Cumulative

Survival Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261

Trials: Issues in Design and

8.5.3 The Life-table Approach to Calculating Cumulative Survival Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261

8.5.4 The Markov Model Approach to Calculating Cumulative Survival Probabilities . . . . . . . . . . . . . . . . . . . . . . . 264 8.5.4.1 2-State Markov Model: At Risk, Failure . . . . . 265 8.5.4.2 3-State Markov Model: At Risk, Failure, Loss 267 8.5.4.3 4-State Markov Model: At Risk, Failure,

Loss, ODIS (Non-compliance) . . . . . . . . . . . . . . . . 269 8.5.5 Using the Markov Model to Calculate Sample Sizes for

the Log-rank Statistic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274 8.5.6 Speed and Accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275

8.6 Discussion and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277

There are copious formulas for sample size calculation designed for dealing with what is a vast variety of possible experimentation. This chapter will focus on one small corner of that methodology: sample size calculations for oncology survival clinical trials. Such trials present many challenges. These emanate largely from the difficulties in controlling the experiment. Unlike experiments on plots of land or laboratory animals, the treatment of patients is much more complex. In oncology trials, patients may experience adverse reactions severe enough that treatment must be suspended or abandoned on a patient by patient basis. And patients may discontinue trial participation entirely. In preventive oncology trials, patients may be given a bottle of pills, to be taken, say, twice a day. Perhaps they will take those pills as prescribed, or most of them, or perhaps very few. Maybe they will return to the clinic for their next scheduled exams to pick up another bottle of pills. Maybe not. Recruitment of patients into a trial is one of the more difficult aspects of trial management. Recruitment patterns usually involve a slow start up. Often clinical sites must be added to attempt to meet recruitment goals. As will be discussed below, slow recruitment may compromise power.