How It Is Calculated

The Confidence Interval formula is

X  ±  Zs√(n)

Where:

• X is the mean
• Z is the Z-value from the table below
• s is the standard deviation
• n is the number of samples

Z =

80% 1.282

85% 1.440

90% 1.645

95% 1.960

99% 2.576

99.5% 2.807

99.9% 3.291

https://www.mathsisfun.com/data/confidence-interval-calculator.html

Single-Sample Confidence Interval Calculator Using the Z Statistic

http://www.socscistatistics.com/confidenceinterval/Default3.aspx

Confidence interval for a proportion

http://www.sample-size.net/confidence-interval-proportion/

Dear Hiromu-san,

What exactly are you trying to estimate? Is it the confidence interval for parameter K within your population?

If so then you need to consider θ and the distribution of η within the population.

Is 0.1 the value for η in an individual subject? If so it only tells you how that subject differs from the typical population value. Or is it the Ώ (the distribution) for η values? Ώ output is what you would be interested to estimate the distribution of K in the population, it should be expressed as variance in NONMEM.

If you have Ώ variance =0.1, η would be normally distributed, centered on 0 with a standard deviation of sqrt(0.1)= 0.32 (32% CV). The CI for K in the population would be θ x exp(±1.96x0.32), a range of 0.53 to 1.9 θ.

The standard error on η (or any parameter) usually describes the uncertainty in the parameter estimate itself. It informs on the ability of the algorithm to estimate the parameter precisely (or not), it is relevant to the confidence in the model but does not inform on the population distribution itself.

You may be interested in the following tutorial: https://support.certara.com/forums/index.php?app=core&module=attach§ion=attach&attach_id=2636

All the best

Patrice