Estimate measurement noise for digital PCR data with priors for assay parameters

This option models concentration measurements using an error model specialized for digital PCR (e.g. digital droplet PCR). This option also jointly estimates the uncertain parameters of the dPCR assay. For a faster approximation assuming fixed assay parameters, see noise_estimate_dPCR().

This model predicts more relative variation at smaller concentrations, which often leads to a better model fit, even for measurements from other quantification methods such as qPCR.

If multiple measurements (replicates) per sample are provided, EpiSewer can also explicitly model variation before the replication stage.

Usage

noise_estimate_dPCR_params(
  replicates = FALSE,
  cv_prior_mu = 0,
  cv_prior_sigma = 1,
  total_partitions_observe = FALSE,
  max_partitions_prior_lower = 20000,
  max_partitions_prior_upper = 40000,
  partition_loss_mean_prior_lower = 0.05,
  partition_loss_mean_prior_upper = 0.3,
  partition_loss_variation_prior_lower = 0.5,
  partition_loss_variation_prior_upper = 2,
  partition_loss_max = 0.5,
  volume_scaled_prior_lower = 1e-06,
  volume_scaled_prior_upper = 1e-04,
  pre_replicate_cv_prior_mu = 0,
  pre_replicate_cv_prior_sigma = 1,
  prePCR_noise_type = "log-normal",
  use_taylor_approx = TRUE,
  modeldata = modeldata_init()
)

Arguments

replicates: Should replicates be used to explicitly model variation before the replication stage?
cv_prior_mu: Prior (mean) on the coefficient of variation of analyzed concentrations (pre-PCR noise). Note that this does not include the technical noise of the digital PCR. This is because the dPCR noise is explicitly modeled (using the total number of partitions and conversion factor). Moreover, when replicates=TRUE, noise before the replication stage is separately modeled, so cv_prior_mu only describes any remaining pre-PCR noise (see details for more explanation).
cv_prior_sigma: Prior (standard deviation) on the coefficient of variation of analyzed concentrations.
total_partitions_observe: If TRUE, the total number of partitions is taken from the supplied measurements data.frame. This requires that the argument total_partitions_col is specified in concentrations_observe().
max_partitions_prior_lower: Prior (lower bound) for the maximum total number of dPCR partitions. This is usually defined by the manufacturer of the dPCR system/chip used, which supports a certain maximum number of partitions. If you know the exact dPCR system and its maximum partition number, you can set both max_partitions_prior_lower and max_partitions_prior_upper to this value. Otherwise, this prior can be used to set a broad lower and upper bound for the maximum number of partitions, to reflect a range of popular dPCR systems/chips.
max_partitions_prior_upper: Prior (upper bound) for the maximum total number of dPCR partitions (see max_partitions_prior_lower for details.)
partition_loss_mean_prior_lower: Prior (5% quantile) for the mean relative partition loss. A certain proportion of partitions in a dPCR run is typically invalid and discarded from the concentration estimate. This prior can be used to set a lower and upper bound for the mean proportion of partitions lost. Note that for proportions close to 0 or to partition_loss_max (see below), the resulting mean partition loss can differ from what is specified here, because we internally translate this prior to the logit scale.
partition_loss_mean_prior_upper: Prior (95% quantile) for the mean relative partition loss (see partition_loss_mean_prior_lower for details). In well-functioning dPCR assays, the mean proportion of lost partitions should not be very high (definitely below 50%).
partition_loss_variation_prior_lower: Prior (5% quantile) for the variation in the number of invalid partitions across dPCR runs. The proportion of partitions lost typically varies between dPCR runs. We thus model this proportion as logit-normal distributed, with mean (approximately) defined by partition_loss_mean_prior and logit-level standard deviation sigma. You can use partition_loss_variation_prior_lower and partition_loss_variation_prior_upper to set a lower and upper bound for sigma.
partition_loss_variation_prior_upper: Prior (95% quantile) for the variation in the number of invalid partitions across dPCR runs (see partition_loss_variation_prior_lower for details).
partition_loss_max: The maximum proportion of partitions that can be lost in a valid dPCR run. During quality control, runs where the proportion of invalid partitions is above some threshold (e.g. 50%) are often discarded. This parameter can be used to represent such a QC threshold.
volume_scaled_prior_lower: Prior (lower bound) on the conversion factor (partition volume scaled by the dilution of wastewater in the assay) for the dPCR reaction. See details for further explanation.
volume_scaled_prior_upper: Prior (upper bound) on the conversion factor (partition volume scaled by the dilution of wastewater in the assay) for the dPCR reaction. If this is identical to volume_scaled_prior_lower, the conversion factor will be fixed and not estimated.
pre_replicate_cv_prior_mu: Prior (mean) on the coefficient of variation of concentrations before the replication stage.
pre_replicate_cv_prior_sigma: Prior (standard deviation) on the coefficient of variation of concentrations before the replication stage.
prePCR_noise_type: The parametric distribution to assume for noise before the PCR assay. Currently supported are "log-normal" and "gamma". The choice of the parametric distribution typically makes no relevant difference for the noise model, but can make a relevant difference for the LOD model if LOD_estimate_dPCR() is used.
use_taylor_approx: If TRUE (default), a Taylor expansion approximation is used to estimate the CV of measurements under pre-PCR noise. The approximation is very accurate, unless concentrations are extremely high (so high that the quality of the measurements from dPCR would anyway be questionable).
modeldata: A modeldata object to which the above model specifications should be added. Default is an empty model given by modeldata_init(). Can also be an already partly specified model returned by other EpiSewer modeling functions.

Value

A modeldata object containing data and specifications of the model to be fitted. Can be passed on to other EpiSewer modeling functions to add further data and model specifications.

The modeldata object also includes information about parameter initialization (.init), meta data (.metainfo), and checks to be performed before model fitting (.checks).

Details

The conversion factor (see volume_scaled_prior_lower, volume_scaled_prior_upper) is the partition volume v multiplied with a scaling factor s. The scaling factor accounts for concentration differences between the sample and the reaction mix, for example due to extraction or adding of reagents. For example, if the partition volume is 4.5e-7 mL and the scaling factor is 100:3 (i.e. 100 gc/mL in the original sample correspond to 3 gc/mL in the PCR reaction), then the overall conversion factor is 4.5e-7 * 100 / 3 = 1.5e-5.

When replicates=TRUE, two coefficients of variation are estimated:

the CV before the replication stage (see pre_replicate_cv_prior_mu)
the CV after the replication stage (see cv_prior_mu)

The meaning of these CV estimates depends on the type of replicates. If the replicates are biological replicates (i.e. independently processed), then cv estimates the noise in the preprocessing before the PCR, and pre_replicate_cv estimates the noise from anything before preprocessing (e.g. sampling noise and all other unexplained variation). In contrast, if the replicates are technical replicates (i.e. several PCR runs of the same preprocessed sample), then cv estimates only unexplained PCR noise (should be close to zero), and pre_replicate_cv estimates all other noise (including preprocessing noise.)

The priors of this component have the following functional form:

coefficient of variation of concentration measurements (cv): Truncated normal
maximum number of total partitions in dPCR: Uniform
mean proportion of lost partitions in dPCR: Normal (logit-level)
variation of proportion of lost partitions: Truncated normal (logit-level)
conversion factor for dPCR: Uniform
coefficient of variation of concentration before the replication stage (pre_replicate_cv): Truncated normal

Estimate measurement noise for digital PCR data with priors for assay parameters

Usage

Arguments

Value

Details

See also