The document discusses parametric tolerance interval tests for assessing delivered dose uniformity of orally inhaled products. It provides details on: - What parametric tolerance intervals and the FDA-proposed two one-sided tolerance interval test are - How the test determines if a pre-specified proportion of doses fall within the target interval limits with a certain confidence level - Operational characteristics and acceptance criteria for the two-tiered test approach - Challenges and advantages of the parametric tolerance interval and alternative counting tests

1. Parametric Tolerance Interval Test for
Delivered Dose Uniformity (DDU)
-Siva Chaitanya Addala

2. Parametric Tolerance Intervals
• A tolerance interval is a statistical confidence interval for a specified
proportion of a population.
• The PTI test proposed by FDA involves two one-sided tolerance
intervals
• A confidence interval covers a population parameter with a stated
confidence, that is, a certain proportion of the time. There is also a
way to cover a fixed proportion of the population with a stated
confidence. Such an interval is called a tolerance interval. The
endpoints of a tolerance interval are called tolerance limits.

4. Parametric Tolerance Intervals

5. Parametric Tolerance Intervals
• The goal of a tolerance interval test is to determine whether a pre-specified
proportion (coverage) of values of an attribute (e.g., DDU) in a certain
population (e.g., a manufactured batch) falls inside a target interval [L, U]
• The intervals of interest could be specified as sets of inequalities, such as
two one-sided “observations>L” or “observations<U” or a two-sided
“L< observations<U.”
• The portions of the distribution outside the target interval are typically
called tails.

6. Coverage = Proportion of doses in the batch that
are within target interval
Emitted DoseEmitted Dose
Target Interval
Target Interval

7. PTIT as per CMC
T𝐿1 = 𝑋1 − 𝐾1 𝑠1 ≥ 80
T 𝑈1 = 𝑋1 + 𝐾1 𝑠1 ≤ 120
FDA recommends
• That applicants establish test parameters (e.g., sample
size, tolerance interval factor (k factor)) and acceptance
criteria that will ensure, to a confidence level of 95
percent, 90% coverage will meet the established upper
and lower limits (i.e., 80-120 percent of TDD).
• Two one-sided tolerance interval (TOSTI) test
• Two-tiered approach to setting acceptance criteria
• Adopt a 1:3 ratio for the change in sample size from tier
1 to tier 2 testing (i.e., if n = 10, then n+m = 30).
• Tier 1 sample size should not be smaller than 10 units.

8. 1ST tier : n units
• Pre-metered DPIs → % of TDD from n units and
calculate the mean ( 𝑿) and standard deviation (s).
• MDIs and device-metered DPIs → % of TDD from n
units and calculate 𝑿 and s. BoL and EoL for each of
the n units → of 2*n measurements.
2nd tier : +m units
• pre-metered DPIs → % of TDD from (n+m) units and
calculate the mean ( 𝑿) and standard deviation (s).
• MDIs and device-metered DPIs → % of TDD from
(n+m) units and calculate 𝑿 and s. BoL and EoL for
each of the n units → of 2*(n+m) measurements.
One-sided Tolerance Interval Factors (k1) for 95 %
Confidence Level and 90 % Coverage
Sample Size k1 Factor
10 2.911
15 2.566
20 2.396
25 2.292
30 2.22
35 2.167
40 2.125
50 2.065
60 2.022
90 1.94
120 1.899
240 1.819
480 1.766

9. Counting test : Zero tolerance
(1) The failure rate increases with sample size regardless of product quality due to the zero tolerance component;
(2) There is no explicit quality standard for the batch.
1ST tier : 10 units
For pre-metered DPIs
For MDIs and device-metered DPIs
(BoL & EoL)
85 ≥ 𝑋 ≤ 115
2nd tier : +20 units
For pre-metered DPIs
For MDIs and device-metered DPIs
(BoL & EoL)

10. Operational Characteristic Curve
Type I error (consumer risk):
batch released but is outside
specification
Type II error (Producer risk):
batch rejected but is within
specification

11. IDEAL OC Curve

13. • ≥99% Coverage : ≥98% acceptance Probability
• 87.5% Coverage : <1% acceptance Probability
• ↑ Coverage Requirement : mean is off target from LC
DDU = CQA
Batch of limiting quality

14. • OC curves for batches with the mean
ranging from on-target to 18% off-
target.
• The probability of passing the FDA
DDU test is highest when μ=100 (Δ=0)
and σ is small.
• As μ approaches 80 or 120 (Δ=20) or
as σ approaches 12, it is nearly
impossible to pass the test.

15. • Figure illustrates how each one-sided
test performs individually with respect
to the tail areas (top panel) and with
respect to coverage (bottom panel).
• The acceptance rate is 5% when the
tail area is 6.25%, when the batch
mean on target.
• The coverage requirement for the one-
sided test changes with the batch
mean.
• A batch with 4% off-target mean must
have 92.7% coverage to pass the single
“one-tail” test with 5% probability.

16. • The top panel shows the OC curves as a function of the
tail area
• When two single-tail tests are combined, the OC
curves are not overlapping, and the probability of
acceptance for batches with tail areas that do not
exceed 6.25% is far below the 5% observed for each
single-tail test.
• For a batch on target, each of the tails must be no
more than 4.25% in order to have 5% acceptance
probability (i.e., 91.5% coverage is required).
• This effect is due to multiplicity as the testing of each
tail independently increases the probability of failure.
• The bottom panel presents the OC curves as a function
of the batch coverage. The coverage required for a 5%
acceptance is 91.5% and increases for off target
batches. For example, for a batch 4% off target, 92.7%
coverage is needed to pass with 5% rate.

17. The practical implication is that this test
provides an incentive to have batches on
target with very low variability, most
of the time

18. Simulated Case Study of PTI-TOST Application
• Simulated batches were created with varying average doses but always with a within batch standard deviation of 6% LC,
• Generating one million doses for a batch assuming a normal distribution, doses were tallied in the 80–120% LC range,
below 80% LC, and above 120% LC
• Samples were taken to apply the counting test and PTI test 10,000 times; 10 in the first tier, followed by additional 20 in
the second tier if necessary.

20. Conclusion
Advantages of PTI-TOST:
• PTI test can more effectively deal with non-
repeating extreme values (“flyers”).
• There are fewer random failures during extended
testing (e.g., process validation).
• Unlike counting test, PTI test rewards rather than
penalizes more testing and hence more
information about the product. This may be
important for validation and stability studies or for
post-approval changes.
Disadvantages of a PTI-TOST:
• The test is less used/less familiar to industry and
regulators of OIPs.
• Implementation requires thorough knowledge of
the product and process variability (hence,
upfront investment in extensive testing).
• It is more complex: the effect of changing a
parameter (e.g., test coefficients K’s) is less
obvious than changing a criterion in the counting
test.
Advantages of counting test:
• More familiar to industry and regulators, therefore may
be more amenable to adapting the requirements to
develop more appropriate product specific
specifications..
Disadvantages of a counting test:
• The failure rate increases with sample size regardless of
product quality due to the zero tolerance component;
• There is no explicit quality standard for the batch.
Nevertheless, there is no indication that current
commercial products controlled by counting tests are in
any way deficient in safety or efficacy

21. References
1. Novick S, Christopher D, Dey M, Lyapustina S, Golden M, Leiner S, et al. A Two One-Sided
Parametric Tolerance Interval Test For Control of Delivered Dose Uniformity—Part 1-
Characterization of FDA Proposed Test. AAPS PharmSciTech. 2009;10(3):820–8.
doi:10.1208/s12249-009-9270-x.
2. Novick S, Christopher D, Dey M, Lyapustina S, Golden M, Leiner S, et al. A Two One-Sided
Parametric Tolerance Interval Test For Control of Delivered Dose Uniformity—Part 2
EffectofChanging Parameters. AAPS PharmSciTech. 2009;10(3):841–9. doi:10.1208/s12249-009-
9269-3.
3. Novick S, Christopher D, Dey M, Lyapustina S, Golden M, Leiner S, et al. A Two One-Sided
Parametric Tolerance Interval Test For Control of Delivered Dose Uniformity—Part 3-
Investigation of Robustness to Deviations from Normality. AAPS PharmSciTech. 2009;10(3):829–4
0. doi:10.1208/s12249-009-9271-9.
4. Challenges and Opportunities in Implementing the FDA Default Parametric Tolerance Interval
Two One-Sided Test for Delivered Dose Uniformity of Orally Inhaled Products DOI:
10.1208/s12249-011-9683-1
5. Using Tolerance Intervals for Assessment of Pharmaceutical Quality Xiaoyu Dong, Yi Tsong, Meiyu
Shen & Jinglin Zhong DOI: 10.1080/10543406.2014.972512
6. FDA/CDER (2018) Draft guidance for industry “Metered dose inhaler (MDI) and dry powder inhaler
(DPI) drug products-Quality Considerations chemistry, manufacturing, and controls
documentation”, April 2018.