## Regulatory acceptance pre-mature discontinuation of study [Study Per­for­mance]

Hi Vaibhav,

which assumptions (CV, T/R-ratio) and target power lead to the sample size?

» We have been doing patient PK study for USFDA submission and […] 36 should complete both periods.
» So far we have enrolled 37 subjects since pre-valence of diseases covered in study is rare and limitations of site selection. […] only 31 subjects will be considered for stat. analysis.
» Now, situation is Reference product got expired and if we want to procure another lot of reference product for remaining 03 subjects then the cost would be 10 million.

Apart from the cost, using different batches in a study is not acceptable. See below why there are no problems expected with 31 subjects. Send me a check for \$ 500,000 (peanuts) for delivering the soothing news.

» 1. Can we stop the study with 37 subjects and perform stat. analysis with 31 subjects?

Yes.

» 2. Does FDA accept this type of study if we perform analysis with 31 subjects and file pre-plan deviation.

Why not? Your sample size was based on an assumed recruitment rate and an anticipated dropout-rate. You can’t be blamed if assumptions are not realized in a study. Happens all the time. A smaller sample size does not affect the patient’s risk $$\small{\alpha}$$ (the only thing regulators are interested in) – it increases only $$\small{\beta}$$, the producer’s risk of failure.

Say, you assumed a CV of 24%, a T/R-ratio of 0.95, and targeted at least 90% power $$\small{(\pi=1-\beta)}$$.

library(PowerTOST) # change the values below to yours CV     <- 0.24 theta0 <- 0.95 target <- 0.90 design <- "2x2" plan   <- sampleN.TOST(CV = CV, theta0 = theta0, targetpower = target, design = design)

You get:
+++++++++++ Equivalence test - TOST +++++++++++             Sample size estimation ----------------------------------------------- Study design: 2x2 crossover log-transformed data (multiplicative model) alpha = 0.05, target power = 0.9 BE margins = 0.8 ... 1.25 True ratio = 0.95,  CV = 0.24 Sample size (total)  n     power 36   0.914510

What will happen if you have just 31 eligible subjects?
elig  <- 31 power <- suppressMessages(power.TOST(CV = CV, theta0 = theta0, design = design, n = elig)) fmt1  <- "%5.2f%%" fmt2  <- "(n = %.0f)" cat("Planned power:", sprintf(fmt1, 100 * plan[["Achieved power"]]),     sprintf(fmt2, plan[["Sample size"]]),     "\nActual power :", sprintf(fmt1, 100 * power), sprintf(fmt2, elig),     "\nRelative loss:",     sprintf(fmt1, 100 * (1 - power / plan[["Achieved power"]])), "\n")

You get:
Planned power: 91.45% (n = 36) Actual power : 87.14% (n = 31) Relative loss:  4.71%

Would such a relative loss in power really hurt?
Recall that the CV and the T/-ratio were assumptions as well. Power is much more sensitive to deviations of these parameters than the sample size. See also this article.

» 3. If we procure another lot of reference product then should we keep retention samples 30 capsules?

Forget it (see above).

» 4. What will be the anticipated challenges w.r.t. stat. analysis or regulatory acceptance?

None.

Dif-tor heh smusma 🖖
Helmut Schütz

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