Variant detection
Figure 1. Identifying the key question (detection vs prevalence) is the second step in designing a pathogen surveillance system. Determining the sample size needed to answer this question then requires determining the sampling frequency, i.e., if samples will be collected and sequenced just once (cross-sectional sampling) or with some regularity over a period of time (periodic surveillance).
By specifying sampling_freq = "cont", the
vartrack_samplesize_detect() function can be used to
calculate the sample size needed to detect a particular variant in the
population within a specific number of days since its introduction, OR
by the time a variant reaches a specific frequency. As when specifying
cross-sectional sampling with sampling_freq = "xsect" (see
Estimating the sample size needed for variant monitoring: cross-sectional
sampling for details), applying the
vartrack_samplesize_detect() function to calculate a sample
size assuming periodic sampling (Figure 1) requires
knowledge of the coefficient of detection ratio between two pathogen
variants (or, more commonly, one variant and the rest of the pathogen
population). The coefficient of detection ratio for two variants can be
calculated using the vartrack_cod_ratio() function (see Estimating bias in observed
variant prevalence). Since we are only interested in the ratio
of the coefficients of detection, applying this function only requires
providing parameters which are expected to differ between variants. The
ratio between any variants not provided is assumed to be equal to
one.
Once we have an estimate of the coefficient of detection ratio, we can calculate the sample size needed for detection from the following parameters:
| Param | Variable Name | Description |
|---|---|---|
| \(p\) | prob | the desired probability of detection |
| \(t\) | t | the number of days after introduction a variant should be detected by |
| \(P_{V_1}\) | p_v1 | the desired prevalence to detect a variant by |
| \(P_{0_{V_1}}\) | p0_v1 | the initial variant prevalence (# introductions / population size) |
| \(r_{V_1}\) | r_v1 | the estimated logistic growth rate of the variant (per day) |
| \(\omega\) | omega | the sequencing success rate |
| \(\frac{C_{V_1}}{C_{V_2}}\) | c_ratio | the coefficient of detection ratio, calculated as the ratio of the
coefficients of variant 1 to variant 2 (can be calculated using
calc_cod_ratio()) |
To calculate the sample size needed for detection assuming periodic sampling, we must provide either the number of days after introduction a variant should be detected by (\(t\)) OR the desired prevalence to detect a variant by (\(P_{V_1}\)), but not both. All other parameters listed above are required.
Therefore, if we would like to know the sample size needed per day to
ensure detection of a variant by the time it reaches 1% prevalence in
the population, we can apply the
vartrack_samplesize_detect() function as follows:
library(phylosamp)c1_c2 <- vartrack_cod_ratio(phi_v1=0.975, phi_v2=0.95, gamma_v1=0.8, gamma_v2=0.6)
vartrack_samplesize_detect(prob=0.95, p_v1=0.01, p0_v1=3/10000, r_v1=0.1,
omega=0.8, c_ratio=c1_c2, sampling_freq="cont")## Calculating sample size for variant detection assuming periodic sampling## [1] 25.81341In other words, 26 samples per day are needed to detect a variant at 1% (or higher) in a population with 95% probability of detection, given a coefficient of detection ratio (\(\frac{C_{V_1}}{C_{V_2}}\)) of 1.368 (as calculated from parameters listed above). This assumes that all samples sequenced (or otherwise characterized) will be successful. We assume an 80% success rate (\(\omega = 0.8\)), which ensures the 21 high quality data points that can be used to detect the presence of a pathogen variant from a selection of 27 samples. If sequencing will occur on a weekly basis, this means we need to process \(26*7=182\) samples per week (ideally from infections spread evenly over the 7 days) to ensure we detect a variant by the time it reaches 1% frequency in the population.
