For quantitative biological or chemical studies, it is important to assess the reproducibility of your method. This slideshow takes you step by step from data collection to assessment of reproducibility, following FDA Bioanalytical Method Validation standards. From linear regressions to limits-of-quantitation, this brief but detailed document will get you started. Prepared by: Dr. Kelsey Boes (Orcid ID:0000-0002-4163-5075)

1. Stats for Quant:
Statistical Assessment of Reproducibility in
Quantitative Studies
Dr. Kelsey Boes | Vinueza Labs
April 12, 2018

2. three main
measures of
reproducibility
1. accuracy
2. precision
3. limit of quantitation (LLOQ)
percent error*
coefficient of variation* (CV%)
lower limit of quantitation
1
corresponding
statistical measures
*should be calculated for
intraday (across the course of one day) and
interday (across the course of several days)
Reference: U.S. Food and Drug Administration: Guidance for Industry Bioanalytical Method Validation. (2001)

3. FDA standards for validation of
quantitation method
2
validation parameter measure FDA target
linearity R2 good
precision coefficient of variation 0±15%
(±20% at limit-of-quantitation)
accuracy percent error 100±15%
(±20% at limit-of-quantitation)
sensitivity lower limit-of-quantitation
good enough for
application
Reference: U.S. Food and Drug Administration: Guidance for Industry Bioanalytical Method Validation. (2001)

4. General Workflow
• Data Collection
• run your quantitation curve samples
• in triplicate on three different days
• Regression
• plot each run of data (concentration vs. response)
• fit each plot with a linear regression
• Statistics
• assess accuracy with coefficient of variation
• assess precision with percent error
• assess lower limit of quantitation
3

5. Linear Regressions
creating your quantitation curves
4

6. Building the Quantitation Curve
5
• plot concentration (x) vs. analyte response (y)
• if internal standard was used, divide analyte
response by internal standard response
• generate a linear regression
• check that R2 value is close to 1.0
• note the slope (m) and y-intercept (b)
• repeat for every run
• 3+ plots and linear regressions per day
• 9+ plots and linear regressions total

7. Accuracy
measured through percent error
6

8. accuracy | intraday
7
analyte peak height (or area)
divided by
internal standard peak height
(or area)
arithmetic mean
= 100 +
𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑 𝑐𝑜𝑛𝑐 − 𝑡ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙 𝑐𝑜𝑛𝑐
𝑡ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛
∗ 100%
= (𝑎𝑣𝑔 𝑜𝑓 𝑟𝑎𝑡𝑖𝑜𝑠 – 𝒃) 𝒎
where b and m are taken from
the average of the day’s linear
regressions of the quantitation
curves, y=mx+b (average of m
values and average of b values)

9. accuracy | interday
8
arithmetic mean of the
avg ratios from each day
= 100 +
𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑 𝑐𝑜𝑛𝑐 − 𝑡ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙 𝑐𝑜𝑛𝑐
𝑡ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛
∗ 100%
= (𝑎𝑣𝑔 𝑜𝑓 𝑟𝑎𝑡𝑖𝑜𝑠 – 𝒃) 𝒎
where b and m are taken from
the average of all the linear
regressions of the quantitation
curves from every day run,
y=mx+b (average of all m values
and average of all b values)

10. Precision
measured through coefficient of variation (CV%)
9

11. precision | intraday
10
analyte peak height (or area)
divided by
internal standard peak height (or area)
arithmetic mean
= (𝑟𝑎𝑡𝑖𝑜 – 𝒃) 𝒎 where b and m are taken from
that specific run’s linear
regression of the quantitation
curve, y=mx+b
= 𝑆𝑇𝐷𝐸𝑉. 𝑆(𝑎𝑙𝑙 𝑐𝑎𝑙𝑐 𝑐𝑜𝑛𝑐)
=
𝑠𝑡𝑑 𝑑𝑒𝑣
𝑎𝑣𝑔 𝑜𝑓 𝑐𝑎𝑙𝑐 𝑐𝑜𝑛𝑐
∗ 100

12. precision | interday
11
= 𝑆𝑇𝐷𝐸𝑉. 𝑆(“𝑎𝑣𝑔 𝑜𝑓 𝑐𝑎𝑙𝑐 𝑐𝑜𝑛𝑐” 𝑓𝑟𝑜𝑚 𝑒𝑎𝑐ℎ 𝑑𝑎𝑦)
=
𝑠𝑡𝑑 𝑑𝑒𝑣
𝑎𝑣𝑔 𝑜𝑓 𝑐𝑎𝑙𝑐 𝑐𝑜𝑛𝑐
∗ 100
arithmetic mean of the
“avg of calc conc” from each day

13. Lower Limit-of-Quantitation
based on variability in slope and y-intercept of quantitation curve
12

14. lower limit of quantitation
13
arithmetic mean of each day’s avg
where b and m are taken from that
specific run’s linear regression of the
quantitation curve, y=mx+b
= 𝑆𝑇𝐷𝐸𝑉. 𝑆(𝑒𝑎𝑐ℎ 𝑑𝑎𝑦′
𝑠 “𝑎𝑣𝑔”)
=
𝑠𝑡𝑑 𝑑𝑒𝑣
# 𝑜𝑓 𝑑𝑎𝑦𝑠
= 10 ∗
𝑠𝑡𝑑 𝑒𝑟𝑟𝑜𝑟 𝑜𝑓 𝒃
𝑎𝑣𝑔 𝒎
Reference: Shrivastava, A., Gupta, V.B.: Methods for the
determination of limit of detection and limit of quantitation of
the analytical methods. Chronicles Young Sci. 2, 21–25
(2011). doi:10.4103/2229-5186.79345

15. 14