A Pharmacokinetic Drug Interaction Study of Drug-72 and Drug-12 Department of Mathematic & Statistics York University Yufeng Lin Xiaofeng Zhou

Problem Two drugs: –drug-72 with half-life time of 72 hours, taken once daily –drug-12 with half-life time of 12 hours with potential interaction, taken twice daily Maximum concentration: –drug-72 alone is expected to be at 6 hours –drug-72 and drug-12 together (interaction) is expected to be at 4 hours Question: Is there an interaction between these two drugs?

Assumption High tolerability Moderate effect sizes Different pharmacological profiles Potentially different effects on outcomes. Using α= 0.05 & β=80%

METHODS Subjects –twenty-four normal, healthy adult male and female paid volunteers Method –multiple dose within subjects, 2-way crossover design with double blind of drug- 72 and drug-12 –all subjects will receive two treatment conditions during 180 days period. – washout period = 5 * 72 =360 hours Study Procedures –randomized assign 24 health adults into two groups A and B by a computer- generated code –Medication combination: Drug-72 + placebo Drug-72 + drug-12 –all subjects will be dosed with each medication combination start from Feb 1st midnight –period1: Feb.1 st ---May.1 st (90 days) washout period: May.2 nd ---May.16 th (15 days=360 hours) period2: May.17th---Aug.14 th (90 days)

Continue…. Study Procedures –randomized assigned each group to one of the drug combinations –every 24 hours are a small time interval for a 180 days treatment condition –in every 24 hours period, Treatment conditions were: Group A, take drug-72 and placebo (1 capsulate for each) and group B, take drug-72 and drug-12 (1 capsulate) on midnight Every 12 hours, group 1, take placebo (1 capsulate) and group 2, take drug-12 (1 capsulate). Repeated until 180 days period reached.

| Period 1 | Washout | Period 2 | placebo > > 72 +placebo

In period 1, group A take drug-72+ placebo at time 0 and placebo only at time 12 hours in every 24 hours period, group B take drug-72+drug-12 at time 0 and drug-12 at time 12 hours in every 24 hours period. 12h 24h 0h Group A: drug-72+placebo Group A: drug-72+placebo Group B: drug-72+drug-12 Group B: drug-12 Group B: drug-72+drug-12 Group A: placebo only In the period 2, reverse the treatment conditions

In every 24 hours period, for each group we do blood draw two times, and record c(4) and c(6). c(4): blood concentration at 4 hours c(6): blood concentration at 6 hours 0h 4h6h 24h Blood draw 1 Blood draw 2 Total blood draws needed is 360 for each group

Statistical Analyses primary endpoint in the study is Cmax (maximum blood concentration). during first period, for each group, do hypotheses test: H0: C(6) – C(4) >= 0 vs H1: C(6) – C(4) < 0 then for the group, if H0 is true, we can tell that the group patients have taken the drug-72 and placebo, while if H0 is reject, then that group patients have taken the drug-72 and drug-12 because the maximum concentration is at 4 hours when interaction occurs. If in period 1 we get H0 is true and in period 2 H1 is true for the same group, then it approximately shows the evidence that the interaction effect has occur.

Some explanation The washout period Using minimum duration of 5 times the half-life of the treatment i.e. 72 * 5 = 360 hours =15 days. We need 360 blood draws during the 180 days trial. (Since during every 24 hours, we need do two blood draws on 4 hours and 6 hours, and total we have 180 days, so we need 2 * 180 = 360) We use double-blind to keep both subjects and investigators are unware of treatment assignment  If patients drop out during the study, we still keep their records and do analysis, but additional analysis will be perform only using the data collected from the patients who complete the trial.