Standard Deviation Upper Confidence Interval for Variance Component Analysis

[Michelle_Ricci]

Please consider adding an upper confidence interval for the standard deviation to the variance component analysis output in the Fit Model platform.  Guidance in ICH Q14 contains acceptance criteria related to the Upper 95% confidence interval of the intermediate precision of during assay validation. 

Currently, the variance, 95% CI of the variance and the standard deviation (point estimate) are calculated.  The variance from the VCA is used outside of JMP to manually calculate the intermediate precision value (upper CI of the standard deviation).   

[Sarah-Sylvestre]

@Michelle_Ricci - Thank you for your suggestion! We have captured your request and will take it under consideration.

[SamGardner]

@Michelle_Ricci thanks for this idea.  I was involved with writing USP <1220> which incorporates the same ideas as ICH Q14, so I think I understand the need.  This is type of problem  that I think we should try to address, and this is an example:

An experiment is performed by varying the following parameters

• Instrument:  Instrument 1, Instrument 2, Instrument 3
• Analyst: Analyst 1, Analyst 2, Analyst 3
• Sample Prep: Prep 1, Prep 2, Prep 3
• Replicate Measurement: Rep 1, Rep 2, Rep 3

Instrument and Analyst would be crossed, and Sample Prep would be nested in the (Instrument x Analyst) level, and Replicate would be nested within Sample Prep.  

The estimated total variation would be

(s_total)^2 = (s_analyst)^2 + (s_instrument)^2 + (s_instrumentXanalyst)^2 + (s_sampleprep)^2 / n_preps + (s_replicate)^2 / n_reps

Note that n_preps and n_reps would need to be specified, and ideally this data could be used to determine the appropriate number of preps and reps to get a desired total variability.  

The above estimate would also need to have an associated confidence interval to make this feature complete.  

Let me know if you think that is on-target with the type of problem we should be looking at.  

[Michelle_Ricci]

Yes! Thank you @SamGardner  that experiment is what I was describing.  Currently, a fractional factorial design is being used then in the Fit Model platform (from your example) Instrument, Analyst and Sample prep would be set as random factors to complete the VCA.  Moving forward it would be ideal to determine the appropriate number of preps and reps to obtain a desired total variability  

[YangStellaSong]

Hello Michelle, @Michelle_Ricci, how did you calculate the 95% CI of the standard deviation from the 95% CI of the variance given by the VCA in JMP? Thank you!

[Michelle_Ricci]

@YangStellaSong I use the formula given in Statistical Intervals: A Guide for Practitioners and Researchers page 50. 

the formula is also given on this NIST site (screen shot provided)