## Larger difference between upper and lower limit of 90% CI [Power / Sample Size]

Dear mirza baig,

» I am new comer on this forum

Welcome !

» If we got larger difference between 90% CI limit for any primary factor like AUC0-t, AUC 0-infinity or Cmax e.g. lower limit is 90% and upper limit is 120% so what could be the predictions about the factors that widen the limit (both factor in vitro or in vivo).

First, I would clarify that getting a result of 90-120 % is not something abnormal. I would actually be more uneasy to see something like 99-103 %.

Basically, the main factor will be the number of subjects in your study and how good your assumptions on intra-subject variability were when you calculated the number of subjects required...

I will try and explain simply, but I would suggest you to take a look at Helmut's lectures on BE, and more specifically on sample size calculations.

So first, the width of the 90 % confidence interval depends on the intra-subject variability of the PK parameters (Cmax and AUC). This variability is a characteristic of the molecule that you study (some molecules have a low variability, some have a large variability). It can be increased by external factors: first the formulation you are studying (a bad formulation can increase the variability - and sometimes the reference product is the one that has a poor formulation, not the generic !), food (fasted vs. fed), and how well your study was standardised. The higher the intra-subject CV, the wider the 90 % CI.

The other factor that directly influences the width of the 90 % CI is the number of subjects in your study. You will get a narrower 90 % CI with 48 subjects than with 24.

When you write the protocol of the study, you have to calculate the number of subjects you will enrol. The calculation takes the following into consideration:

The intra-CV is the tricky part. You don't always have reliable information in literature. If you have already done studies on the same molecule you can use this information. If not, you have to run a pilot study first. But there is some uncertainty in the data from pilots: the less subjects you have in the pilot, the more the intra-CV you get from it may be far from reality. Helmut would tell you that you need to calculate the confidence interval of your estimate of the intra-CV and then to be conservative. Even if you use data from a previous full-scale study, there will be some experimental uncertainty around this value: don't consider it as carved in stone.

When they are missing data on the intra-CV, some people will just play it quick and dirty: they will write some value and a number of subjects in the protocol, depending on how much the sponsor is ready to pay. That's clearly unethical. If the variability is higher, your study will be under-powered and will fail, and you will have exposed the subjects to the drug unnecessarily. If the variability is lower, your study will be overpowered and you will have exposed too many subjects.

Keep in mind also that Cmax and AUC have a different variability. You have to use the largest of the two to calculate the number of subjects needed.

So now back to your question regarding the width of the 90 % CI at the end of your study. If you get a very narrow 90 % CI, it may be because:

Again, have a look at Helmut's lectures. You'll see some data and figures that will make all this much clearer.

» I am new comer on this forum

Welcome !

» If we got larger difference between 90% CI limit for any primary factor like AUC0-t, AUC 0-infinity or Cmax e.g. lower limit is 90% and upper limit is 120% so what could be the predictions about the factors that widen the limit (both factor in vitro or in vivo).

First, I would clarify that getting a result of 90-120 % is not something abnormal. I would actually be more uneasy to see something like 99-103 %.

Basically, the main factor will be the number of subjects in your study and how good your assumptions on intra-subject variability were when you calculated the number of subjects required...

I will try and explain simply, but I would suggest you to take a look at Helmut's lectures on BE, and more specifically on sample size calculations.

So first, the width of the 90 % confidence interval depends on the intra-subject variability of the PK parameters (Cmax and AUC). This variability is a characteristic of the molecule that you study (some molecules have a low variability, some have a large variability). It can be increased by external factors: first the formulation you are studying (a bad formulation can increase the variability - and sometimes the reference product is the one that has a poor formulation, not the generic !), food (fasted vs. fed), and how well your study was standardised. The higher the intra-subject CV, the wider the 90 % CI.

The other factor that directly influences the width of the 90 % CI is the number of subjects in your study. You will get a narrower 90 % CI with 48 subjects than with 24.

When you write the protocol of the study, you have to calculate the number of subjects you will enrol. The calculation takes the following into consideration:

- the difference between the two formulations that you expect you may get. This is generally set at 5 %,

- the intra-CV that you
*assume*you will get, based on whatever information is available to you,

- the desired power of your study, generally set at 80 or 90 %. This means, that if your generic is really bioequivalent to the originator, you will have 80 or 90 % chances that the 90 % CI will fall fully within the acceptance limits of 80.00 - 125.00 %.

The intra-CV is the tricky part. You don't always have reliable information in literature. If you have already done studies on the same molecule you can use this information. If not, you have to run a pilot study first. But there is some uncertainty in the data from pilots: the less subjects you have in the pilot, the more the intra-CV you get from it may be far from reality. Helmut would tell you that you need to calculate the confidence interval of your estimate of the intra-CV and then to be conservative. Even if you use data from a previous full-scale study, there will be some experimental uncertainty around this value: don't consider it as carved in stone.

When they are missing data on the intra-CV, some people will just play it quick and dirty: they will write some value and a number of subjects in the protocol, depending on how much the sponsor is ready to pay. That's clearly unethical. If the variability is higher, your study will be under-powered and will fail, and you will have exposed the subjects to the drug unnecessarily. If the variability is lower, your study will be overpowered and you will have exposed too many subjects.

Keep in mind also that Cmax and AUC have a different variability. You have to use the largest of the two to calculate the number of subjects needed.

So now back to your question regarding the width of the 90 % CI at the end of your study. If you get a very narrow 90 % CI, it may be because:

- the molecule has a very, very low variability, and even the minimum number of subjects set in guidelines (12 subjects) is more than enough to show BE. Actually I don't think anybody is doing studies with less than 18 or even 24 subjects nowadays,

- the intra-CV used to calculate the number of subjects was over-estimated for whatever reason, so the number of subjects enrolled is higher than really needed,

- AUC and Cmax have rather different intra-CV, and you're looking at the 90 % CI of the parameter with the lowest variability,

- the sponsor got ripped off by a dishonest CRO which deliberately overestimated the number of subjects needed in order to make more money.

Again, have a look at Helmut's lectures. You'll see some data and figures that will make all this much clearer.

—

Regards

Ohlbe

Regards

Ohlbe

### Complete thread:

- Larger difference between upper and lower limit of 90% CI - mirza baig, 2018-11-28 16:14
- Larger difference between upper and lower limit of 90% CI - Ohlbe, 2018-11-28 23:49