Residual Risk and Waste in Donated Blood with Pooled Nucleic Acid

Testing

Hrayer Aprahamian, Dr. Ebru Bish, Dr. Douglas Bish

Virginia Polytechnic Institute and State University, Dept. of Industrial and Systems Engineering, Blacksburg, VA

Research supported by the National Science Foundation

October 8, 2015

Motivation• Blood products are vital healthcare commodities.• Transfusion-transmitted infections (TTI) include:• HIV, HBV, HCV, WNV and Babesiosis (among others).

• Even with advances in testing technology, the risk of transmitting an infection through blood transfusion remains.• Effectively managing the limited resources to improve the

safety of blood is crucial.• Accurately measuring this risk is of utmost importance to

aid with strategic decision-making. 2

The Challenges• Screening tests are not perfectly reliable.• FDA requires or recommends a set of infections for which

the blood needs to be tested in the US, but does not specify a testing strategy.• Nucleic Acid Tests (NAT) are more sensitive but are

considerably more expensive and time-consuming:• Individually testing using NAT might not be a feasible

option.

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The Challenges• Pooled testing is often used to reduce testing costs:• Dilution effect.

• Increases waste figures.

• In practice, failed samples are re-tested.• Numerous re-testing schemes are available.

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The Challenges• Residual risk alone does not provide the complete picture.

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Resid

ual r

isk

Testing cost

Expected waste

Testing strategy

The Challenges• Individual variability in viral growth.• In sample test variability (i.e., testing the same sample

multiple times may yield different outcomes).• Infectivity of the blood sample: Low viral loads in blood

may not cause infection.

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Research Objective• Develop realistic and accurate expressions for the

performance metrics.

• Determine the best testing strategy:• Pooling size ()

• Re-test strategy

• Number of re-tests ()

• Screening test

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Viral Model

• Doubling time viral load model:

• To incorporate individual variability, we model as a random variable.

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• Infectivity of the viral load is modelled as a binomial with each viral particle having a probability of to cause infection.

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Infectivity

Testing Error• Test sensitivity follows a probit model if unit is infected and in

the window period.

• Test specificity is assumed to be a constant and independent of the pooling size.

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Re-test Schemes• We examine four types of re-test schemes:

1) No re-test.

2) Pooled re-testing:The initial master pool is re-tested times.

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m

Re-test Schemes3) Dorfman-type (individual) re-testing:

Each individual sample in the master pool is re-tested times.

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1

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1

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1

11⋯

1

m

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Re-test Schemes4) Array-based re-testing:

The samples are placed in a matrix. pools, each of size , are constructed from samples in each row and column and tested. The process is repeated times.

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Re-test Schemes• Decision rule is crucial for determining the outcome of the

re-test:• We adopt the Believe the positive decision rule for all re-test

schemes (except array based).

• In the array re-test scheme a sample is rejected if at least one of the columns AND one of the rows fail corresponding to that node fails.

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Re-test Schemes

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Re-test #1 Re-test #2

Events• : Sample is infected.• W: Infected sample is in the window period.• Let be the event that the overall test outcome is negative:

• Let be the event that blood sample is infectious.

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Residual Risk (RR)• Residual Risk = Probability of an infected and infectious blood unit being released into the blood pool.

• Waste= Number of infection-free blood units that are falsely discarded.18

Expected Waste

Expected Number of Tests

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• Expected number of tests only depends on the outcome of the initial pool.

Analysis – Residual Risk

Lemma 1.

Analysis – Expected Tests

Lemma 2.

Analysis – Expected WasteLemma 3.

Case Study• We perform a case study using data available on South

Africa.• Some major findings are:• Performing re-tests increases both the risk and the expected number

of test.

• The benefits of re-tests is to reduce the expected waste.

• Adding a single re-test drastically reduces the waste figures.

• Array-based re-testing schemes outperforms other schemes when:• Testing costs are high.

• Prevalence rates are high23

Cost-effectiveness

240 2 4 6 8 10 12 14 16

$19.00

$19.50

$20.00

$20.50

$21.00

$21.50

$22.00 Individual Re-test

m=0m=1m=2m=4m=8

Pool Size (Sp)

Cost

per

don

atio

n

Best solution

Current practice

Cost-effectiveness

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• Switching to the best solution reduces cost by 3.5%.

• In 2013 16.1 million units collected and tested which translates to a saving of:

Conclusions• Determining the “best” testing strategy is not a trivial

matter.

• The expressions derived provides an accurate approach to weight in the trade-offs being incurred to determine a suitable testing strategy.

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Reference and Contact Info.

Aprahamian, H., Bish, D., and Bish, E. “Residual Risk and Waste in Donated Blood with Pooled Nucleic Acid Testing ”, submitted for publication.

Email: ahrayer@vt.edu

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Thank you

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