1. Total Analytical Error Evaluation in Quantitative and Qualitative Assays
May F. Mo
FDA/Industry Statistics Workshop
Washington, DC - September 29, 2006

2. Background Total Analytical Error (TAE) NOT a new concept
Assay errors from all sources of the data collection experiment – including systematic and random error
CLSI Proposed Guideline January 2002
CLSI Approved Guideline April 2003
FDA/Industry collaboration in developing the guideline
TAE concepts have been seen in publications since 1960s.
TAE does not include pre-analytical and post-analytical errors.

3. Cause and Effect Diagram for Total Analytical Error (from EP21-A)

4. Importance of TAE For Clinicians For Laboratories For Manufacturers
TAE provides a metric of assay quality that can directly equate to medical errors
For Laboratories
TAE provides a simple, cost effective method for comparing assay products
For Manufacturers
TAE guides manufacturers to set appropriate design goals and evaluate the product directly to user needs
From a clinician’s standpoint, TAE is more important metric, because an incorrect laboratory result, regardless of which error source causes it, is harmful.
It is difficult to otherwise two assays that one has a higher precision and the other has a higher bias.
For regulator, this can be a quick, one-step acceptance of substantial equivalence of two assays.

5. TAE Evaluation Methods
TAE is evaluated by assessing if the combination of errors from all sources is within some acceptance limit. The common evaluation methods are (Krouwer, 2002):
Direct Estimation
Indirect Estimation
Simulated Estimation
Note: All methods are based on the quantitative assays.

6. Direct Estimation
Direct Estimation (Distribution of Differences Method)
EP21 Recommendation
Calculate differences of study assay vs. reference assay
TAE limit estimated as the CLI of the differences
- No need to estimate and combine individual source errors
Visual tools - Bland & Altman and “Mountain Plot”
Mountain Plot – a folded empirical cumulative distribution plot
CLI – Confidence Limits for Individual Observations

7. Direct Estimation (Continued)
Is distribution of differences normal?
Parametric? Nonparametric? or Data Transformation?
Tolerance Interval: A range that contains a specified proportion of a sampled population with a specified confidence. (EP21)
Parametric or nonparametric methods to report tolerance intervals are covered in Statistical Intervals by Hahn and Meeker (1991).
TAE limit can be considered as the 2.5th/97.5th percentile (nonparametric) or CLI, which have uncertainty as well.
The interval is an one time measure of the range that contains a specified proportion of sampled population.
Tolerance Interval: Statistical inference – a range with confidence.
A two-sided nonparametric 100(1-)% tolerance interval to contain at least 100p% of the sampled differences from a sample of size n is [x(l), x(u)].

8. Tolerance Interval (TI) Calculation
A two-sided 100(1-)% TI to contain at least 100p% of the sampled differences from a sample of size n:
Parametric:
where k depends on , p and n, and can be obtained from published tables, or derived using noncentral t-distribution (Odeh and Owen, 1980)
Nonparametric
TI based on rank statistics is [x(l), x(u)].
The value of l and u depend on , p and n, and can be derived using published tables, or using equation provided in Hahn and Meeker (1991)
Both calculations are now available in SAS:
PROC UNIVARIACIPCTDF for nonparamatric (distribution-free)
CIPCTNORMAL for parametric
The only problem is SAS currently only provides TL for percentiles 1, 5, 10, , 90, 95, 99. The most needed 2.5th and 97.5th are not currently provided. This concern has been raised to SAS.

9. Indirect Estimation Indirect Estimation (Simple Combination Model)
TAE = Bias + k * Imprecision
Simple to apply
Fits well with the Six-Sigma quality concepts
Not recommended by EP21 - Underestimate TAE
Simulation Method (Research Use)
Cost-efficient
Model the impact of an individual error component to TAE
Can underestimate TAE
K is the number of SD. It is mostly assigned as 2 or 1.65.
This model underestimate TAE for the following reasons:
Not using real patient samples
Neglecting random interference bias
Not including all sources of potential systematic error
Can simulation method be used to support TAE claim?

10. Industry Practices Quantitative Assays
Set Product Requirement
Set allowable TAE (aTAE) limit based on medical opinion and marketing needs
Break aTAE down to precision and bias design requirements using simple combination model.
Example: TAE = Bias + 2*SD (for 2 sigma performance)
Design Verification and Validation
Verify design requirements individually
A direct assessment of total error should be conducted to ensure aTAE is met.
This is also called ‘error budgeting’
Each error components meeting the design requirement can not guarantee aTAE is met.

11. Industry Practices Quantitative Assays
TAE Claims in Package Inserts
Not Yet Common
Concerns?
Indirect method – Is it sufficient to establish a TAE claim?
Direct method - When the reference assay is not a “gold standard”, TAE has measurement error from both assays … How to interpret?
User environment – Are our customers ready to use TAE claims in the package inserts?

12. Generalize TAE to Qualitative Assays
Motivation
TAE provides rationale to establish product requirements
TAE provides a final metric to evaluate if a product meets medical needs
Challenge
TAE is a quantitative concept
TAE does not apply to low negative and high positive samples

13. TAE in Qualitative Assays
The performance of a qualitative assay relies on its precision and bias near the medical decision point (cutoff) …
TAE evaluation applicable and desirable for the cutoff zone
Direct estimation not realistic due to limited patient samples around cutoff
Indirect modeled approach may be more practical

14. aTAE in Qualitative Assays
How to define aTAE for the near cutoff zone?
EP12-A Guidance:
The 95% interval - the values above and below the cutoff point at which repeated results are 95% positive or 95% negative, respectively
Grayzone - the zone of uncertainty between the 95% interval limits
It seems that the focus of EP12-A in measurement error around cutoff is random error (precision) rather than systematic error (bias) …

15. aTAE in Qualitative Assays
Grayzone 5% 5%
Upper 95%
Interval
Lower 95%
Interval
Cutoff

16. aTAE in Qualitative Assays
Set aTAE for the near cutoff zone
Incorporating measurement errors from both precision and bias, aTAE can be set as ½ of the grayzone. That is, the test result at 1.2 S/CO should read as positive (>1.0 S/CO) while test results at 0.8 S/CO should read as negative (<1.0 S/CO).
Assuming that grayzone is S/CO for an assay, aTAE will be 0.2 S/CO or 20% (assuming cutoff=1.0 S/CO)
When the above aTAE is met, there should be <  (i.e., 0.05) probability that a test results will deviate >20% from the true value, and cause a change in the final interpretation.

17. aTAE in Qualitative Assays
Set aTAE for the near cutoff zone
For an assay that reports an indeterminate result, aTAE can be extended as the size the grayzone.
The test result at 1.2 S/CO should not read as negative (<0.8 S/CO) while test results at 0.8 S/CO should not read as positive (>1.2 S/CO).
In this case aTAE can be set at 0.4 S/CO or 50% for results around 0.8 S/CO and 33% for results around 1.2 S/CO.

18. TAE Evaluation for Qualitative assay
Direct Evaluation – Not realistic
Indirect Evaluation
TAE = Bias +  * Precision
Challenge: How to define and measure Bias?
How to include ALL bias sources?
Alternative: TAE =  * Reproducibility
Reproducibility includes variations contributed from instrument, lot, calibration, operator, etc …
Underestimate TAE is still then main concern
The instrument to instrument, lot to lot, calibration to calibration variation are typically considered as bias, rather than imprecision.
If TAE estimate<aTAE, a claim cannot be established; however, if TAE>aTAE, then the conclusion can be made that the product failed the aTAE goal.

19. TAE in Qualitative Assays
How do different types of bias impact TAE?
Bias impacts both S and CO
As a proportional bias
The will be no bias in S/CO
As a fixed bias
The bias in S/CO is unknown and depends on the value of S relative to CO (=1.0) and size of the bias
CO=1.0
Bias S
-0.2
-0.1
0.1
0.2
0.8
0.75
0.78
0.82
0.83
0.9
0.88
0.89
0.91
0.92
1.0
1.00
1.1
1.13
1.11
1.09
1.08
1.2
1.25
1.22
1.18
1.17

20. TAE in Qualitative Assays
How does different type of biases impact TAE?
Fixed bias for both S and CO: The impact on S/CO is relatively small for the near cutoff range ( S/CO)
Biases that impact S and CO differently:
Interferences
Tube Type
Storage
Sample Carry Over
Crossreactivity …

21. Conclusion
TAE is an useful evaluation method for both quantitative and qualitative assays. For qualitative assays, TAE should be evaluated for the near cutoff zone using indirect estimation. Since indirect method underestimates TAE, it may not be sufficient to support a claim.

22. References
NCCLS. Estimation of Total Analytical Error for Clinical Laboratory Methods; Approved Guideline. NCCLS Document EP21-A [ISBN X]. NCCLS, 940 West Valley Road, Suite 1400, Wayne, Pennsylvania USA, 2003.
NCCLS. User Protocol for Evaluation of Qualitative Test Performance; Approved Guideline. NCCLS Document EP12-A [ISBN ]. NCCLS, 940 West Valley Road, Suite 1400, Wayne, Pennsylvania USA, 2002.
Hahn GJ, Meeker WQ. Statistical Intervals: A Guide for Practitioners. New York: John Wiley and Sons, 1991.
Krouwer JS, Monti KL. A simple graphical method to evaluate laboratory assays. Eur J Clin Chem Biochem 1995; 33:525–7.
Odeh, RE, Owen, DB. Tables for Normal Tolerance Limits, Sampling Plans, and Screening. New York Marcel Dekker, 1980.