APHL Vaccine Strain Selection (VSS) Calculators: User

Upon opening the standard calulator, select among the desired Modes 1 to 3. Each of these modes performs a specific task, described below with step-by-step instuctions provided in the following pages.

• Mode 1 (Growth of known drift variant): Upon selecting a drift variant (DV) corresponding to a particular type/subtype/lineage (TSL), the calculator computes the minimum sample size of the type/subtype/lineage required to achieve a desired number of successful growth events in tissue and eggs.

• Mode 2 (Baseline surveillance): Having chosen a type/subtype/lineage and a threshold at which to detect unknown, novel drift variants (NDVs), this calculator determines the minimum sample size necessary to achieve baseline surveilance.

• Mode 3 (Hybrid calculator): This mode combines the functionality of Modes 1 and 2 to compute the minimum additional number of samples needed to achieve baseline surveillance for novel drift variants of a type/subtype/lineage in which the user already seeks growth of a known drift variant in tissue and eggs.

APHL Vaccine Strain Selection (VSS) Calculators: User GuideJune 2014

The Vaccine Strain Selection (VSS) calculators are designed for the purposes of sample size calculation, evaluation of data confidence, and automated allocation of sample requests. These calculators were created in Microsoft Excel for internal use by the Centers for Disease Control and Prevention (CDC) and Association of Public Health Labs (APHL) and consist of two parts: (1) a standard calculator [VSS.Calculator.xls] containing three modes, and (2) an advanced calculator [VSS.Advanced.xlsm]. This user's guide reviews the functionality of each of these calculators in detail.

Standard calculator [VSS.Calculator.xls]

1

select desired mode

Value25

13001.9%

78%18%

14.0%

1

280

Inverse z-value Confidence Sample size Ave./cycle Ave./(cycle*lab)

-2.326 99% 2355 1177.5 14.7-1.645 95% 1345 672.5 8.4-1.282 90% 941 470.5 5.9-1.036 85% 720 360.0 4.5-0.842 80% 573 286.5 3.6-0.674 75% 465 232.5 2.9-0.524 70% 383 191.5 2.4-0.385 65% 318 159.0 2.0-0.253 60% 265 132.5 1.7-0.126 55% 222 111.0 1.40.000 50% 186 93.0 1.2

Value500

74.1%1.351.16

APHL: Vaccine Strain Selection (VSS) Calculator [Mode 1: Growth of known drift variant]

Parameters (enter ONLY in blue boxes)Current number of selected DV (not cumulative)

Current number of TSL corresponding to DV (not cumulative)

Current estimated prevalence of DV among TSL

Probability of successful growth of DV in tissue culture

Probability of successful growth of DV in eggs

Probability of successful growth of DV in both tissue and eggs

Desired additional successful growth events of DV

Submission cycles remaining

Growth of known drift variant (DV) (using input from rows 13-19)

Probability of achieving desired number of growth events

Expected total number of successful growth events

Standard deviation of number of successful growth events

Number of labs participating

Data confidence/yield calculator (enter ONLY in blue boxes)Total TSL sample size

2355!

1345!

941!720!

573! 465! 383! 318! 265! 222! 186!

0!

500!

1000!

1500!

2000!

2500!

99%! 95%! 90%! 85%! 80%! 75%! 70%! 65%! 60%! 55%! 50%!

Required total number of TSL samples!

14.7!

8.4!

5.9!4.5!

3.6! 2.9! 2.4! 2.0! 1.7! 1.4! 1.2!

0.0!

2.0!

4.0!

6.0!

8.0!

10.0!

12.0!

14.0!

16.0!

99%! 95%! 90%! 85%! 80%! 75%! 70%! 65%! 60%! 55%! 50%!

Required average number of TSL samples per cycle per lab!

For a known drift variant (DV), this calculator computes the minimum sample size of its type/subtype/lineage (TSL) required to achieve a given number of successful growth events in tissue and eggs. Results are presented as the number of TSL samples necessary to obtain the required number of growth events at a chosen confidence level.!!For example, suppose we would like to be 75% confident of obtaining at least 1 more successful growth events of DV at the current estimated prevalence of 1.9% (25/1300) among its TSL, with 78% probability that an individual DV sample grows in tissue culture and 18% probability it grows in eggs. APHL must then obtain 465 TSL samples across all labs and submission cycles. With 2 submission cycles remaining and 80 labs participating, the average number of TSL samples each PHL must submit per cycle is 2.9.!

Given the total number of TSL samples (across all labs and submission cycles) to be submitted, the yield calculator outputs the probability of obtaining the number of successful growth events chosen above. This provides an estimate of data confidence. The expected yield and its standard deviation are also provided.!

1) To begin, determine the drift variant (DV) desired for growth in tissue and eggs. In Box 1, input the number of samples of this DV obtained in the latest cycle and the corresponding number of samples of the type/subtype/lineage (TSL) to which it belongs. This provides the calculator an estimate of the current prevalence of the DV among its TSL, shown just below Box 1.

2) In Box 2, input the estimated probability of growth of a DV sample in tissue culture, and the probability of growth of a DV sample in eggs (knowing it has already grown in tissue culture). The product of these probabilities is an estimate for the probability of growth in both tissue and eggs, shown just below Box 2.

3) In Box 3, provide the desired number of DV samples to be successfully grown in tissue and eggs.

4) In Box 4, input the number of remaining submission cycles and the number of labs providing samples.

5) Given these inputs, the calculator determines the minimum number of TSL samples (Box 6) necessary to achieve the desired number of sucessfully grown DV samples from Box 3 at a chosen confidence level (Box 5). This is plotted in Box 8. Furthermore, a minimum sample size per submission cycle per participating lab (Box 7) is determined using the values in Box 4 and is plotted in Box 9.

6) A data confidence calculator is also provided for the user's convenience. Given a total TSL sample size in Box 10, the calculator computes the probability that the desired number of DV samples will be grown succesfully in tissue and eggs using the inputs from Boxes 1-4. The expected number and standard deviation of DV samples grown is shown below Box 10.

Note: The mathematical model and formulas used for Mode 1 are derived in Appendix A of the User Guide.

Mode 1 (Growth of known drift variant): Step-by-step instructions

Box 1

Box 2

Box 3

Box 4

Box 5 Box 6 Box 7

Box 8

Box 9

Box 10

2

0 1/700 1/500 1/333 1/250 1/200 1/150 1/100 1/50 1/2599% 4603 3222 2301 1532 1149 919 689 459 228 11395% 2995 2096 1497 997 748 598 448 299 149 7490% 2302 1611 1151 766 575 460 345 230 114 5785% 1897 1328 948 631 474 379 284 189 94 4780% 1609 1126 804 536 402 322 241 161 80 4075% 1386 970 693 461 346 277 208 138 69 3470% 1204 843 602 401 301 241 180 120 60 3065% 1050 735 525 350 262 210 157 105 52 2660% 916 641 458 305 229 183 137 92 46 2355% 799 559 399 266 200 160 120 80 40 2050% 693 485 347 231 173 139 104 69 35 17

Value1/200

280

Confidence Sample size Ave./cycle Ave./(cycle*lab)

99% 919 459.5 5.795% 598 299.0 3.790% 460 230.0 2.985% 379 189.5 2.480% 322 161.0 2.075% 277 138.5 1.770% 241 120.5 1.565% 210 105.0 1.360% 183 91.5 1.155% 160 80.0 1.050% 139 69.5 0.9

Value500

1/200

91.8%

Co

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f d

ete

ctio

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Detection threshold (#NDV/#TSL)

APHL: Vaccine Strain Selection (VSS) Calculator [Mode 2: Baseline surveillance for novel drift variants]

Desired detection threshold (#NDV/#TSL)

Parameters (enter ONLY in blue boxes)Desired detection threshold (#NDV/#TSL)

Submission cycles remaining

Number of labs participating

Baseline surveillance for novel drift variant (NDV)

Probability of detecting NDV

Data confidence (enter ONLY in blue boxes)Total TSL sample size

919!

598!

460!379!

322!277! 241! 210! 183! 160! 139!

0!100!200!300!400!500!600!700!800!900!

1000!

99%! 95%! 90%! 85%! 80%! 75%! 70%! 65%! 60%! 55%! 50%!

Required total number of TSL samples!

5.7!

3.7!

2.9!2.4!

2.0! 1.7! 1.5! 1.3! 1.1! 1.0! 0.9!

0.0!

1.0!

2.0!

3.0!

4.0!

5.0!

6.0!

7.0!

99%! 95%! 90%! 85%! 80%! 75%! 70%! 65%! 60%! 55%! 50%!

Required average number of TSL samples per cycle per lab!

For a selected TSL, this calculator computes the minimum number of TSL samples required to detect a novel drift variant at a given threshold (#NDV/#TSL). Results are presented as the number of TSL necessary to detect a NDV at the chosen confidence level.!!For example, if we would like to be 85% confident of detecting a NDV at a detection threshold of 1/200, APHL must obtain 460 TSL samples across all labs and submission cycles. With 2 submission cycles remaining and 80 labs participating, the average number of TSL samples each PHL must submit per cycle is 2.4.!

Given the total number of TSL samples (across all labs and submission cycles) to be submitted, the data confidence calculator outputs the probability of detecting a NDV at the detection threshold chosen below. This provides an estimate of data confidence.!

This quick reference chart shows the total minimum number of type/subtype/lineage (TSL) samples needed to achieve baseline surveillance for unknown, novel drift variants (NDVs) at a given detection threshold (#NDV/#TSL) and confidence level. Color shading ranging from green (small number of required samples) to blue (large number of required samples) is provided for visual reference. Larger detection thresholds or lower confidence levels correspond to a smaller required sample size.!

Mode 2 (Baseline surveillance): Step-by-step instructions

Box 3

Box 2

Box 4 Box 5 Box 6

Box 9

Box 1

A color-coded quick reference chart is provided in Box 1 which shows the minimum sample size needed to achieve a given detection threshold at a particular confidence. This can be used for guidance when choosing a detection threshold in Mode 2.

1) To begin, determine a type/subtype/lineage (TSL) on which to perform baseline surveillance for novel drift variants (NDVs). In Box 2, input a desired detection threshold as a ratio of number of NDV samples to TSL samples.

2) In Box 3, input the number of remaining submission cycles and the number of labs providing samples.

3) The calculator computes the minimum number of TSL samples (Box 5) necessary to achieve baseline surveillance at a chosen confidence level (Box 4) using the detection threshold inputted in Box 2. This is plotted in Box 7. Furthermore, a minimum sample size per submission cycle per lab (Box 6) is determined using the values in Box 3 and is plotted in Box 8.

4) A data confidence calculator is also provided. Upon entering a total TSL sample size and desired detection threshold in Box 9, the calculator displays the probability of detecting a NDV at this detection threshold.

Box 7

Box 8

3

H1N1 H3N2 B1 B21/100 1/50 1/200 1/10

X25

13001.9%78%18%

14.0%1

75%0 0 465 0

-0.67448975

99% 459 228 454 4495% 299 149 133 2990% 230 114 0 2285% 189 94 0 1980% 161 80 0 1675% 138 69 0 1470% 120 60 0 1265% 105 52 0 1060% 92 46 0 955% 80 40 0 850% 69 35 0 7

H1N1 H3N2 B1 B2500 100 300 20

1/100 1/50 1/200 1/10

99.3% 86.7% 77.8% 87.8%

55.6%0.810.90

Probability of successful growth of DV in both tissue and eggs

Desired additional successful growth events of DV

Desired confidence for DV growth

DV detected? (if yes, mark with 'X')

Current number of selected DV (not cumulative)

Current number of TSL corresponding to DV (not cumulative)

Current estimated prevalence of DV among TSL

Probability of successful growth of DV in tissue culture

Probability of successful growth of DV in eggs

Growth of known drift variant (DV)

ValuesParameters (enter ONLY in blue boxes)Name of TSL

Desired baseline surveillance detection threshold (#NDV/#TSL)

Additional samples needed for surveillance of novel drift variants (NDVs)

Growth of known drift variant (DV) (using input from rows 15-23)

Probability of achieving desired number of growth events

Number of TSL required for growth at desired confidence

Inverse z-value

Probability of detecting NDV

Co

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DV

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Baseline surveillance for novel drift variants (NDVs)

Data confidence (enter ONLY in blue boxes)Name of TSL

Expected total number of successful growth events

Standard deviation of number of successful growth events

APHL: Vaccine Strain Selection (VSS) Calculator [Mode 3: Hybrid calculator]

Total TSL sample size

Desired baseline surveillance detection threshold (#NDV/#TSL)

Values

Given the total number of TSL samples (across all labs and submission cycles) to be submitted, the data confidence calculator outputs (1) the probability of detecting a NDV at the detection threshold chosen above and (2) the probability of obtaining the number of successful growth events chosen above. This provides an estimate of data confidence. The expected yield and its standard deviation are also provided.!

This hybrid calculator combines sampling for successful growth of known drift variants (DV) in tissue and eggs with baseline surveillance for novel drift variants (NDVs) across all type/subtype/lineages (TSLs).!!Given a set of TSLs and assuming the growth of known drift variants is given full priority, the calculator computes the additional number of samples of each TSL to achieve a desired detection threshold #NDV/#TSL at various confidence levels.!

459!

299!

230!

189!

161!

138!

120!105!

92!80!

69!

228!

149!

114!

94!80!

69!60!

52! 46! 40! 35!

454!

133!

0! 0! 0! 0! 0! 0! 0! 0! 0!

44!29! 22! 19! 16! 14! 12! 10! 9! 8! 7!

0!

50!

100!

150!

200!

250!

300!

350!

400!

450!

500!

99%! 90%! 80%! 70%! 60%! 50%!

Additional number of TSL samples for baseline surveillance of NDVs!

H1N1!

H3N2!

B1!

B2!

Mode 3 (Hybrid calculator): Step-by-step instructions

1) To begin, provide in Box 1 the names of up to four type/subtype/lineages (TSLs) on which to perform baseline surveillance of novel drift variants (NDVs) and the corresponding detection thresholds for each of these TSLs. 2) Upon detecting a drift variant (DV) within a particular TSL, enter an 'X' in the corresponding column of Box 2. Then, input values for all fields in the same column of Boxes 3-5 as described in steps (a)-(c). These fields are identical to those in Mode 1.

a) In Box 3, input the number of samples of this DV obtained in the latest cycle and the corresponding number of samples of the type/subtype/lineage (TSL) to which it belongs. This provides the calculator an estimate of the current prevalence of the DV among its TSL, shown just below Box 3.

b) In Box 4, input the estimated probability of growth of a DV sample in tissue culture, and the probability of growth of a DV sample in eggs (knowing it has already grown in tissue culture). The product of these probabilities is an estimate for the probability of growth in both tissue and eggs, shown just below Box 4.

c) In Box 5, provide the desired number of DV samples to be successfully grown in tissue and eggs and the desired confidence for achieving this number of successful growth events. The calculator then displays the minimum TSL sample size necessary to obtain these growth events immediately below Box 5.

3) TSL samples collected for growing a known DV can also be used for detecting unknown NDVs. Using the values inputted in Boxes 3-5, the calculator determines the minimum number of additional TSL samples (Box 7) necessary to achieve baseline surveillance of NDVs for each TSL at a chosen confidence level (Box 6). These additional sample sizes are plotted in Box 8.

4) A data confidence calculator is also provided. Given total TSL sample sizes and desired detection thresholds in Box 9, the calculator displays the probability of detecting a NDV immediately below. In addition, using values inputted in Boxes 1-4, the probability of growing the desired number of DV samples in tissue and eggs is shown along with the expected value and standard deviation of DV samples grown.

Box 1

Box 2Box 3

Box 4

Box 5Box 8

Box 6 Box 7

Box 9

4

Upon using the standard calculator to determine sample sizes to obtained for each type/subtype/lineage (TSL) under consideration, the advanced calulator can be used to allocate sample requests by TSL among participating PHLs. Allocations are generated according to a scheme to be chosen by the user.

The calculator requires user input in the following two tabs.

• Input PHL Specimen Availability: In this tab, the user submits a list of labs and their sample availability by TSL.

• Calculate Allocations: The user specifies the total number of samples desired for each TSL, and selects one of three schemes (proportional to sample availability, proportional to population, or equal-effort per lab) by which to compute the allocation.

Advanced calculator [VSS.Advanced.xls]

user input tabs computed allocations

5

APHL: Vaccine Strain Selection (VSS) Calculator Advanced ModeInstructions: Input lab IDs (in any order) in the first column for those labs reporting sample availability. In the remaining columns, enter sample availability for (up to 12) type/subtype/lineages. Active cells will automatically be highlighted.

IDA(subtype unknown) A(H3) 2009 H1N1 H3N2v B-Yamagata B-Victoria Total

1104 83 13 68 1 27 27 2193613 116 23 57 0 29 29 2544818 94 15 49 0 26 26 2100603 100 17 70 0 14 14 2150610 136 26 87 0 42 42 3330612 171 27 152 0 43 43 4363611 188 21 270 0 37 37 5534202 210 20 419 0 55 55 7594815 330 28 472 0 41 41 9125303 726 32 988 0 67 67 18805504 815 54 1279 0 50 50 22483204 1584 50 2142 0 65 65 39065305 1711 46 2939 0 93 93 48820101 1514 82 3398 0 84 84 51620201 1247 105 3345 0 83 83 48630401 1117 117 3069 0 110 110 45230502 992 124 2486 0 154 154 39100611 745 88 1837 0 157 157 29840805 530 116 1479 0 199 199 25230901 469 92 1078 0 202 202 20431002 331 91 799 0 236 236 16931201 253 96 543 0 257 257 14061203 201 99 394 0 284 284 12621206 158 134 338 0 318 318 12661207 185 161 198 0 422 422 13881302 179 175 145 0 477 477 14531501 129 231 106 0 514 514 14941601 158 222 48 0 548 548 15241704 130 215 30 0 458 458 12911708 124 186 17 0 428 428 11831709 123 140 13 0 394 394 10641801 91 106 7 0 276 276 7561901 89 50 0 0 200 200 539

Type/subtype/lineages under consideration (additional entries to the right)

Input PHL Specimen Availability: Step-by-step instructions

1) To begin, provide in Box 1 the names of up to 12 type/subtype/lineages (TSLs) for which samples are available. These TSLs will automatically appear in the Calculate Allocations tab. 2) In Box 2, submit the 4-digit IDs (in any order) of any number of participating labs. These IDs will be cross-referenced by the calculator with a (hidden) list of PHLs that includes information about their name and location. Upon entering a lab ID, the corresponding cell with automatically be highlighted in green to show that it is active.

3) In Box 3, input the number of samples available by lab for each TSL. Enter '0' if no samples of a given TSL are available at the lab. Active cells will automatically be highlighted in blue.

4) The total number of samples available at each lab is shown in Box 4.

5) Continue by clicking on the Calculate Allocations tab.

Box 2

Box 3

Box 4

Box 1

6

APHL: Vaccine Strain Selection (VSS) Calculator Advanced ModeInstructions: Input minimum number of samples per lab to collect (if available), and desired number of samples per type/subtype/lineage. Warnings in red will appear if desired number of samples exceeds availability.

Summary of sample availability by type/subtype/lineage

A(subtype unknown) A(H3) 2009 H1N1 H3N2v B-Yamagata B-Victoria

Total across labs 15029 3002 28322 1 6390 6390

Average/lab 455.4 91.0 858.2 0.0 193.6 193.6

Enter desired number of samples by type/subtype/lineage


Minimum per lab (if available) 1 1 1 1 1 1Total across labs 60 80 120 100 40 70

Enter sheet name for allocation (31 character limit)

Select allocation scheme

1

Allocation 1

Proportional to sample availability!

Proportional to population!

Equal-effort per lab!

Proportional to sample availability: For each type/subtype/lineage, samples are allocated to labs proportional to their current availability.!!Proportional to population: For each type/subtype/lineage, samples are allocated to labs proportional to the (state) population represented by each lab. If multiple labs from a single state report availability, the state's population is split amongst these labs proportional to their sample availability for each given type/subtype/lineage.!!Equal-effort per lab: Samples are allocated across type/subtype/lineages with the goal of apportioning total sample requests equally for all labs.!

Calculate Allocations: Step-by-step instructions

Box 1

Box 2Box 3

Box 4

Box 5

7

1) Having provided the appropriate information in the Input PHL Specimen Availability tab, in Box 1 the calculator displays the total number of samples available by type/subtype/lineage (TSL) across all labs and the average availability per lab. 2) In Box 2, enter the minimum number of samples of each TSL to be requested from every submitting lab. These inputs can be used to ensure that at least this number of TSL samples is allocated to each lab, provided that enough samples are available. If a lab does not have enough samples of a particular TSL available, it is allocated the maximum number that it can contribute.

3) In Box 3, input the total number of samples of each TSL to be obtained across all labs. If the requested number for a given TSL exceeds its total availability, the corresponding cell will automatically be highlighted in red as a warning. Note that the allocation will still be computed in this case but the total number allocated will not satisfy the user's desired number.

4) In Box 4, submit a unique name for the allocation.

5) Select an allocation scheme in Box 5. Desired samples per TSL beyond the minimum values entered in Box 2 will be allocated to labs using this chosen scheme. The choices are:

Proportional to sample availability: For each TSL, samples are allocated to labs proportional to their current availability.

Proportional to population: For each TSL, samples are allocated to labs proportional to the (state) population represented by each lab. If multiple labs from a single state report availability, the state's population is split amongst these labs proportional to their sample availability for each given TSL.

Equal-effort per lab: Samples are allocated across TSLs with the goal of apportioning total sample requests equally for all labs. This ensures that most labs will be requested to submit nearly the same number of samples.

6) To finish, click the 'Generate allocation' button. A new sheet with the name entered in Box 4 will be created containing the computed sample allocation. Examples of allocations using each of the three schemes are provided in the subsequent pages.

Allocation using scheme: Proportional to sample availabilityGenerated at 06/26/2014 11:49:24 PM. This allocation was created using the desired sample values in the box shown below.



Total across labs 15029 3002 28322 1 6390 6390Average/lab 455.4 91.0 858.2 0.0 193.6 193.6

Desired number of samples by type/subtype/lineage


Minimum per lab (if available) 1 1 1 1 1 1Total across labs (requested) 60 80 120 100 40 70Total across labs (allocated) 60 80 120 1 40 70


1104 2 1 1 1 1 1 73613 2 1 1 0 1 1 64818 2 1 1 0 1 1 60603 2 1 1 0 1 1 60610 2 1 1 0 1 1 60612 1 2 1 0 1 1 63611 1 1 3 0 1 1 74202 1 1 3 0 1 1 74815 2 1 2 0 2 1 85303 2 2 4 0 2 1 115504 2 2 5 0 2 1 123204 4 2 8 0 1 2 175305 4 2 10 0 1 3 200101 4 2 12 0 1 2 210201 3 3 11 0 1 2 200401 3 3 11 0 1 2 200502 3 3 9 0 1 2 180611 2 2 7 0 1 2 140805 2 3 6 0 1 2 140901 2 2 4 0 1 2 111002 2 2 3 0 1 2 101201 1 3 3 0 1 2 101203 1 3 2 0 1 3 101206 1 3 2 0 1 3 101207 1 4 2 0 1 3 111302 1 4 1 0 2 4 121501 1 5 1 0 2 4 131601 1 4 1 0 2 4 121704 1 4 1 0 2 4 121708 1 4 1 0 1 3 101709 1 3 1 0 1 3 91801 1 3 1 0 1 3 91901 1 2 0 0 1 2 6

Allocation by type/subtype/lineage

Example 1: Allocation proportional to sample availability

The chosen allocation scheme and a timestamp for the generated allocation are shown in Box 1.

Summary information of TSL sample availability and user-inputted values from the Calculate Allocations tab used to generate the allocation are displayed in Box 2. The last row in Box 2 shows the total number of samples by TSL allocated by the calculator. The values in this row will be identical to that the sample request numbers in the previous row, except when the user request exceeds availability (in which case the desired value is highlighted in red).

In Box 3, the number of samples to request by TSL from each lab is shown. Note that these values will reflect the choice of apportioning sample requests proportional to availability after having met the minimum request per lab. The total number of samples requested from each lab is given in Box 4.

Box 2

Box 4

Box 1

Box 3

8

Allocation using scheme: Proportional to populationGenerated at 06/26/2014 11:49:34 PM. This allocation was created using the desired sample values in the box shown below.








1104 0 1 1 1 1 1 53613 1 4 3 0 1 3 124818 2 3 3 0 1 3 120603 1 2 2 0 2 1 80610 2 3 2 0 2 2 110612 2 3 2 0 2 2 113611 3 3 9 0 2 3 204202 3 4 7 0 2 3 194815 4 5 12 0 2 4 275303 1 2 2 0 1 2 85504 2 2 4 0 1 2 113204 1 2 2 0 1 2 85305 2 2 3 0 1 2 100101 2 2 3 0 1 2 100201 1 1 1 0 1 1 50401 2 3 4 0 1 2 120502 1 2 2 0 1 2 80611 4 6 16 0 2 5 330805 2 2 3 0 1 2 100901 2 2 3 0 1 2 101002 1 1 1 0 1 1 51201 2 2 4 0 1 2 111203 2 2 3 0 1 2 101206 2 2 3 0 1 2 101207 2 3 2 0 1 2 101302 2 3 6 0 1 3 151501 1 1 2 0 1 1 61601 1 1 2 0 1 1 61704 2 2 4 0 1 2 111708 2 2 3 0 1 2 101709 2 2 2 0 1 2 91801 2 3 4 0 1 2 121901 1 2 0 0 1 2 6


Example 2: Allocation proportional to population



In Box 3, the number of samples to request by TSL from each lab is shown. Note that these values will reflect the choice of apportioning sample requests proportional to the population represented by each lab, having met the minimum request. The total number of samples requested from each lab is given in Box 4.

Box 2

Box 4

Box 1

Box 3

9

Allocation using scheme: Equal-effort per labGenerated at 06/26/2014 11:49:43 PM. This allocation was created using the desired sample values in the box shown below.








1104 2 2 4 1 0 2 113613 3 3 3 0 0 2 114818 3 3 3 0 0 2 110603 3 3 4 0 0 2 120610 3 3 3 0 1 1 110612 3 3 4 0 1 1 123611 2 2 6 0 1 1 124202 2 2 6 0 1 1 124815 2 2 6 0 0 0 105303 3 2 6 0 0 0 115504 2 2 6 0 0 0 103204 3 2 6 0 0 0 115305 2 2 7 0 0 1 120101 2 1 6 0 0 1 100201 1 1 6 0 0 1 90401 1 1 6 0 0 1 90502 1 1 6 0 0 1 90611 2 2 6 0 0 1 110805 2 2 5 0 1 2 120901 2 2 5 0 1 2 121002 2 2 4 0 1 2 111201 2 3 4 0 2 3 141203 1 3 3 0 2 3 121206 1 3 2 0 2 3 111207 1 3 1 0 3 4 121302 1 3 1 0 3 4 121501 1 3 1 0 3 4 121601 1 3 0 0 3 4 111704 1 4 0 0 3 4 121708 1 3 0 0 3 4 111709 1 3 0 0 3 4 111801 1 3 0 0 3 4 111901 2 3 0 0 3 5 13


Example 3: Allocation according to equal-effort per lab



In Box 3, the number of samples to request by TSL from each lab is shown. The total number of samples requested from each lab is given in Box 4. Note that these values will reflect the choice of apportioning sample requests to ensure that the total number of samples requested from each lab is as uniform as possible while meeting the user's desired total sample requests.

Box 2

Box 4

Box 1

Box 3

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APHL: Vaccine Strain Selection (VSS) Calculator Advanced ModeInstructions: Do not edit sheet, except to add PHL labs and modify corresponding information.

ID Name State Population0101 Alabama Department of Public Health AL 48220230201 Alaska State Public Health Laboratory AK 7314490401 Arizona Department of Health Services AZ 65532550502 Public Health Laboratory, Arkansas Department of Health AR 29491310603 San Diego County Public Health Laboratory CA 380414300610 Los Angeles County Department of Public Health CA 380414300611 California Department of Health Services CA 380414300612 San Luis Obispo Public Health Services CA 380414300805 Colorado Department of Public Health and Environment CO 51875820901 Connecticut State Department of Health CT 35903471002 Delaware Public Health Laboratory DE 9170921104 DC Public Health Lab DC 6323231201 State of Florida Department of Health FL 193175681203 Bureau of Public Health Laboratories - Tampa FL 193175681206 Pensacola Branch Laboratory FL 193175681207 Miami Branch Laboratory FL 193175681302 Georgia Public Health Laboratory GA 99199451501 State of Hawaii Department of Health HI 13923131601 Idaho Department of Health and Welfare ID 15957281704 Illinois Department of Public Health- IL 128752551708 Illinois Department of Public Health-Springfield IL 128752551709 Illinois Department of Public Health-Carbondale IL 128752551801 Indiana State Department of Health IN 65373341901 State Hygenic Laboratory, University of Iowa IA 30741862001 Kansas Department of Health and Environment KS 28859052102 Kentucky Department for Public Health KY 43804152201 Louisiana Department of Health LA 46018932301 Maine Department of Health and Environmental Testing Laboratory ME 13291922401 Maryland State Department of Health and Mental Hygiene MD 58845632502 Massachusetts State Laboratory MA 66461442601 Michigan Department of Public Health MI 98833602702 Minnesota Department of Health MN 53791392802 Mississippi Department of Health MS 29849262904 Missouri Department of Health MO 60219883002 Montana Public Health Laboratory MT 10051413102 Nebraska Public Health Laboratory NE 18555253203 Nevada State Health Department NV 27589313204 Southern Nevada Health District NV 27589313302 New Hampshire Public Health Laboratories NH 13207183402 New Jersey State Department of Health and Senior Services NJ 88645903502 New Mexico Department of Health NM 20855383601 State of New York Department of Health NY 195702613611 Westchester County Deptartment of Laboratories and Research NY 195702613613 NYC Department of Health and Mental Hygiene Public Health Laboratory NY 195702613702 North Carolina State Laboratory of Public Health NC 97520733802 North Dakota Public Health Laboratory ND 6996283902 Ohio Department of Health OH 115442254001 Oklahoma State Department of Public Health OK 38148204101 Oregon Department of Human Services OR 38993534201 Pennsylvania State Public Health Laboratory PA 127635364202 Allegheny County Department of Laboratories PA 127635364402 Rhode Island State Public Health Laboratory RI 10502924502 South Carolina Department of Health SC 47237234602 South Dakota State Health Laboratory SD 8333544703 Tennessee Department of Health TN 64562434804 Texas Department of Health TX 260592034815 Tarrant County Public Health TX 260592034818 City of Houston Department of Health and Human Services TX 260592034819 Texas Department of Health - South TX Lab TX 260592034902 Utah State Department of Health UT 28552875001 Vermont Department of Health Laboratory VT 6260115102 Division of Consolidated Laboratory Services VA 81858675301 Washington State Department of Health WA 68970125303 Seattle-King County Public Health Laboratory WA 68970125305 Spokane Regional Health District WA 68970125403 West Virginia Department of Health WV 18554135501 Wisconsin State Laboratory of Hygiene WI 57263985504 City of Milwaukee Health Department WI 57263985602 Wyoming Public Health Laboratory WY 5764127201 Puerto Rico Dept of Health PR 3667084

Hidden tab: PHL List (contains lab IDs, names, location by state, and corresponding state population)

Note: To reveal this tab, right click any of the tabs in the calculator and select 'Unhide...'. Then select PHL List and click 'OK'.

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Appendix A: Model and formulas for Mode 1

Mode 1 addresses the following problem: For a selected drift variant (DV) of a given type/sub-type/lineage (TSL), what is the minimum number of TSL specimens to request in order to havea high confidence that the number of events of a given drift variant successfully grown in tissueculture and eggs is greater than some desired number?

Model inputs

Assume we are given:

• A choice of drift variant (DV) to track

• The number #DV of samples of the selected DV (not cumulative)

• The number #TSL of TSL samples corresponding to the selected DV (not cumulative)

This allows to find the proportion µ of DV samples among the TSL samples:

µ =#DV#TSL

.

Note that µ is an estimate for the true prevalence of the DV among its TSL in the entire population.

We also require:

• The probability πtissue of successful growth of DV in tissue culture

• The probability πeggs of successful growth of DV in eggs

Assuming these processes are independent , the probability π of successful growth of DV in bothtissue culture and eggs is

π = πtissueπeggs.

The assumption of independence seems reasonable, particularly if no data exist regarding correla-tions between the two growth processes. Alternatively, if πeggs actually represents the conditionalprobability that a DV sample sucessfully grows in eggs after having grown in tissue culture we donot need to make any further assumptions.

Lastly, we require:

• The desired number d of additional successful growth events of DV in tissue/eggs

Given this information, we can determine the minimum number n∗ of samples to be requested intotal across all PHLs in order to detect the selected drift variant at a given confidence level.

The calculator also has input fields for:

• The remaining number w of submission cycles

• The number b of PHLs participating

1

This yields the average number of samplesn∗

wbto request per lab per remaining submission cycle,

assuming enough samples are available at each submission.

Basic model and sample size formulas

We would like to find the minimum number of samples n∗ to be requested out of all available TSLsamples such that the probability of obtaining at least d successful growth events of DV is greaterthan some given confidence level p.

Note that this is only one choice of a metric (dependent on the distribution of the number ofsuccessful growth events) that we can use to determine a desired number of samples. Other choicesmay be more desirable based on the purpose. As an example, we can easily modify our analysisto determine the minimum number of samples required so that the expected number of growthevents is at least d.

Let S be the number of successful growth events in one time period. We will characterize thedistribution of S below. To do this, first define N to be the number of DV samples drawn from nrequested TSL samples. Since each TSL sample has probablity µ of being DV, we have that

N ∼Binomial(n, µ).

This holds if n is small relative to the total number of TSL samples in the entire population (whichis certainly true). Now given N , we have that

S |N ∼Binomial(N, π),

where we have assumed that each DV sample leads to a successful growth event independently ofother DV samples.

Putting these two steps together implies that

S∼Binomial(n, µπ).

This makes sense, since each selected TSL sample has probability µπ of resulting in a successfulgrowth event. We can use this to explicitly compute the minimum number of samples n∗ to berequested to have at least confidence p of an additional d successful growth events in one timeperiod:

n∗=min {n≥ 0 : P (S ≥ d)≥ p}

where

P (S ≥ d)= 1−∑

k=0

d−1(

nk

)

(µπ)k(1− µπ)n−k.

Under the right conditions, a normal approximation or Poisson approximation can be used toobtain reasonable estimates of n∗. If n is reasonably large (greater than say, 20) then S is dis-tributed approximately normal with mean m = nµπ and variance σ2 = nµπ(1 − µπ). Using acontinuity correction,

P (S ≥ d)≈P

(

Z ≥d− 1

2−m

σ

)

= 1−Φ

(

d− 1

2−nµπ

nµπ(1− µπ)√

)

and

n∗≈min

{

n≥ 0 :d− 1

2−nµπ

nµπ(1− µπ)√ ≤Φ−1(1− p)

}

.

2

LetK =nµπ, τ =Φ−1(1− p), ν = 1− µπ, and γ = d− 1

2. The constraint above requires us to solve

K2−(

2d + ντ2)

K + γ2 = 0, whose solution is

K =12

{

(

2γ + ντ2)

±(

2γ + ντ2)

2− 4γ2

√

}

=12

{

(

2γ + ντ2)

± |λ| 4νγ + ν2τ2√

}

.

Therefore,

n∗≈

⌈

K

µπ

⌉

=

⌈

12µπ

{

(

2γ + ντ2)

−λ 4νγ + ν2τ2√

}

⌉

.

While a Poisson or skew-normal approximation may be marginally better since µπ is likely to besmall, it will not lead to a closed-form expression for n∗ which is useful for a simple worksheetimplementation. Regardless, it appears n∗ will generally be large enough for a normal approxima-tion to suffice.

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APHL Vaccine Strain Selection (VSS) Calculators: User