Serial Blood Sample Timepoints for Comparing Pharmacokinetics Profiles Between Two Different Dose Frequencies

It is very common in the drug development process that the dosing frequency needs to be studied. The dosing frequency is usually based on the pharmacokinetic profiles. In multiple-dose studies, the dose frequency decides the dosing interval: QD for once daily, BID for twice daily, and TID for three times daily. 

Usually, to compare the pharmacokinetic profiles, serial blood samples will be taken over the period of the dosing interval (between the previous dose and the next dose).  The area under the curve (AUC) will then be calculated over the dosing interval (commonly denoted as tau).

• For QD dose, Tau = 24 hours, AUCtau is AUC[0-24 hours]
• For BID dose, Tau = 12 hours, AUCtau is AUC[0-12 hours]
• For TID dose, Tau = 8 hours, AUCtau is AUC[0-8 hours]

It will be straightforward to select the Pharmacokinetics (PK) sampling time points if two drugs/formulations to be compared have the same dose interval. However, in practice, we often need to compare the PK profiles for two drugs/formulations with different dose intervals, for example, between QD versus BID, or between QD versus TID.  

For comparison of PK profiles between QD dose, BID dose, and TID dose, one will need to compare AUC[0-24 hours] with 2 x AUC[0-12 hours] for BID and with 3 x AUC[0-8 hours] for TID.

For QD dosing, serial PK samples will be collected over 24 hours. For BID dosing and TID dosing, there are two different ways to decide the serial PK samples:

For BID dosing,   

1. serial PK samples can also be collected over 24 hours, the calculated AUC[0-24 hours] can directly be compared with AUC[0-24 hours] from QD dosing even though there will be an extra dose at the middle of the 24 hours period. 
2. serial PK samples can be collected over 12 hours, then the calculated AUC[0-12 hours] needs to be multiplied by 2 in order to be compared with AUC[0-24 hours]

For TID dosing, 

1. serial PK samples can also be collected over 24 hours, the calculated AUC[0-24 hours] can directly be compared with AUC[0-24 hours] from QD dosing even though there will be two extra doses during the 24 hours period. 
2. serial PK samples can be collected over 8 hours, then the calculated AUC[0-8 hours] needs to be multiplied by 3 in order to be compared with AUC[0-24 hours]

In a study by Dawra et al, "A PK/PD study comparing twice-daily to once-daily dosing regimens of ertugliflozin in healthy subjects", the blood samples were collected for QD and BID as the followings:

For each period, blood samples for PK analysis were collected for QD dosing as follows: on days 4, 5, and 6 before administration of the morning dose, and at 0.5, 1, 2, 3, 4, 8, 12, and 24 hours after the morning dose on day 6. For BID dosing, blood samples were collected at 0.5, 1, 2, 3, 4, 8, 12 (preevening dose), 12.5, 13, 14, 15, 16, 20, and 24 hours after the morning dose on day 6.            

Notice that the blood samples for BID were collected at 0.5, 1, 2, 3, 4, 8, 12 post the morning dose and then 0.5, 1, 2, 3, 4, 8, 12 post the evening dose. 

The PK profiles for OD and BID doses are displayed in the figures below: 

This approach of the PK blood sampling schema will require an extensive number of blood draws. For the BID dose, two serial PK samples need to be drawn; for the TID dose, three serial PK samples need to be drawn. The advantage is to capture the potential impact of the circadian and diurnal cycles. 

In some situations, too many blood sample draws may not be practical, and an alternative approach needs to be taken. For example, in pediatric PK studies, the number of blood sample draws may be limited due to the restriction in the total blood volume. 

One of the alternative approaches is to draw the serial PK samples only for one dose interval, not draw additional serial PK samples after the next dose. For example, for the BID dose, the serial PK samples are drawn over 12 hours period assuming that the PK profiles after the evening dose will be the same as the PK profiles over 12 hours post the morning dose. The AUC[0-12 hours] needs to be multiplied by 2 before comparing it to the AUC[0-24 hours] for QD dose. 

In a study to compare the IVIG (every four weeks dosing schedule) and SCIG (weekly dose schedule), the serial PK samples for IVIG were drawn over 4 week period, and the serial PK samples for SCIG were drawn over 1 week period (instead of 4 week period). To compare the AUCs between IVIG and SCIG, the AUC[0-7 days] was multiplied by 4 before comparing it to the AUC[0-28 days]. With this approach, the next three weekly intervals are assumed to have the same PK profiles as the first weekly interval. We can also say that the PK profiles for the next three intervals (dotted lines) are projected or simulated.  This approach was accepted by the FDA and PK results were included in the product label. The PK profiles for IVIG and SCIG are displayed below (the dotted portion for SCIG was projected). 

Calculation of length of the study drug exposure

We have been using the following formula in calculating the length of the study drug exposure in many studies:

# of days of drug exposure = the last dose date - the first dose date + 1

However, this seems to be correct only if the subject receive daily dose of the study medication. We have many studies where the subject receive weekly infusion or every three weeks infusion of the study medication. In this situation, the above formula will underestimate the length of the study drug exposure.

The correct formula should be tied up with the dose interval.

If a subject receive weekly dose, the formula would be:
# of days of drug exposure = the last infusion date - the first infusion date + 7
or
# of weeks of drug exposure = (the last infusion date - the first infusion date + 7)/7

If a subject receive study drug every three weeks, the formula would be:
# of days of drug exposure = the last infusion date - the first infusion date + 21
or
# of weeks of drug exposure = (the last infusion date - the first infusion date + 21)/7

Sample size considering the drop out rate

Thanks for my colleagure who point out my mistake in calculating the sample size adjusting for the drop out rate. According to the sample size calculation, we estimated that 100 subjects would be needed to detect the statistical differences. Considering 20% drop out rate, what is the # of subjects to be randomized?
It is not 100 + 100*20% = 120
It should be 100 / (1-0.2) = 125
It means that with 125 randomized subjects, if 25 subjects (20% of 125) drop out, we still have 100 subjects left. This is correct way to adjust for the drop out rate.