Use potency to calculate fold change for plasma titer

Basic formula

• individual fold change = individual control potency / individual experimental potency for NT or NC
• individual fold change = individual experimental potency / individual control potency for IC
• median fold change = median(individual fold changes) for NT, NC or IC when paired
• median fold change = geomean control potency / geomean experimental potency for NT or NC when unpaired
• median fold change = geomean experimental potency / geomean control potency for IC when unpaired
• geomean potency = geomean(each quirk2(individual potency)) for NT, NC or IC
• quirk2(individual potency) = (individual potency < threshold && len(individual potencies) > 1) ? sqrt(individual potency) : individual potency for NT or NC

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Parameters that will change the formula

Pairing

1. control and experiment points are linked one by one if they're using the same test sample. (paired)
2. control and experiment points are not linked. It's hard to know if two points are the results of using the same plasma sample. (unpaired)

Grouping

1. the potency value is for one sample. (non-cumulative)
   • if it's paired, first calculate fold change for each pair, then calculate average fold change
   • if it's unpaired, first calculate geo mean titer for control and experiment group, then calculate fold change
2. the potency value is for a group of samples. (cumulative)
   • if it's paired, first calculate fold change for each pair, then calculate weighted average fold change
   • if it's unpaired, first calculate weighted geo mean titer for control and experiment group, then calculate fold change

Quirks (Things I hate but have to be this way)

1. Although the median fold and geometric mean titer are calculated separately, the compare symbol of median fold is solely determined by the geometric mean of experimental titer, so these two can be consistent. (hivdb/chiro-frontend#40)
2. Square-root titer value is taken when calculating the geometric mean titer if:
   • The potency type is NT or NC;
   • Number of titers in the group is greater than one;
   • The titer value is lower than potency_lower_limit.

Lowest test threshold (indicated in the reference)

1. both the control and experiment potencies are above the lowest test threshold. (both effective)
2. the control potency is below the lowest test threshold, but not the experiment potency. (control ineffective)
   • if it's paired, both control and experimental potency will be excluded
   • if it's not paired, the control potency and the less or same amount of experimental lower-than-threshold experimental potency will be excluded
3. the experiment potency is below the lowest test threshold, but not the control potency. (experiment ineffective)
   • Note this affects the calculation of geomean for titer, see Quirks #2
4. both the control and experiment potencies are below the lowest test threshold. (both ineffective)
   • if it's paired, both control and experiment potency will be excluded
   • if it's not paired, only the control experiment will be excluded

We define 1 as the lowest value for neutralization titer. Any value below 1 or equal to 0 will be adjusted to 1.

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Definition of names

• sample: convalescent plasma (CP) or vaccinee plasma (VP) which is described in the reference
• potency: commonly, NT50 for CP or VP. The potencies are extracted from figures, tables, or body text.
• point: point from figures in reference, which is used to extract potency value.
• reference: paper, report, press release, etc.

Note

The calculated fold change result may be different from the original reference. That depends on these conditions below:

• the paper provided accurate potency value and detailed pairing information
• the paper was using the same methods as the methods described here

For complex data, we may apply additional rules for calculating fold change.