Suggest load per case assumption using wastewater data and case numbers

This helper function uses a crude heuristic to infer the load_per_case based on the relationship between measured concentrations and case counts. The goal is to obtain a load_per_case assumption that is on the right order of magnitude - this will not be sufficient for accurate prevalence estimation from wastewater, but fully sufficient for monitoring trends and estimating Rt.

Usage

suggest_load_per_case(
  measurements,
  cases,
  flows = NULL,
  flow_constant = NULL,
  ascertainment_prop = 1,
  measurement_shift = seq(-7, 7),
  shift_weights = 1/(abs(measurement_shift) + 1),
  date_col = "date",
  concentration_col = "concentration",
  flow_col = "flow",
  case_col = "cases",
  signif_fig = 2
)

Arguments

measurements: A data.frame with each row representing one measurement. Must have at least a column with dates and a column with concentration measurements. If multiple measurements per date are provided, their arithmetic mean is used.
cases: A data.frame with each row representing one day. Must have at least a column with dates and a column with case numbers.
flows: A data.frame with each row representing one day. Must have at least a column with dates and a column with flow measurements.
flow_constant: Fixed flow volume, as an alternative to flows, if no regular flow measurements are available.
ascertainment_prop: Proportion of all cases that get detected / reported. Can be used to account for underreporting of infections. Default is ascertainment_prop=1, meaning that 100% of infections become confirmed cases.
measurement_shift: The specific timing between wastewater concentrations and case numbers depends on reporting delays and shedding profiles and is typically uncertain. This argument allows to shift the concentration and case number time series relative to each other and to average over several potential lags/leads, as specified by an integer vector. The default is measurement_shift = seq(-7,7), i.e. a shift of concentrations between up to one week before and after case numbers.
shift_weights: Weights for the shifted comparisons. Must be an numeric vector of the same length as measurement_shift. If NULL (default), the weights are chosen to be approximately inversely proportional to the shift distance.
date_col: Name of the date column in all provided data frames.
concentration_col: Name of the column containing the measured concentrations.
flow_col: Name of the column containing the flows.
case_col: Name of the column containing the case numbers.
signif_fig: Significant figures to round to. Since this heuristic only provides crude estimates which should not be overinterpreted, the result gets rounded. Default is rounding to the 2 most significant figures.

Value

A suggested load_per_case that can be used as an assumption in load_per_case_assume().

Details

In the EpiSewer model, the load_per_case serves as a scaling factor describing how many pathogen particles are shed by the average infected individual overall and how much of this is detectable at the sampling site. This depends both on biological factors as well as on the specific sewage system. It is therefore almost always necessary to assume the load per case based on a comparison of measured concentrations/loads and case numbers.

The heuristic used here is to fit a linear regression model with loads (computed using concentrations and flows) as dependent variable and case numbers as independent variable over all measurements. This does not explicitly account for shedding profiles or reporting delays, but the measurement_shift argument allows to average over a set of relative shifts between the two time series.

The flow volume unit should be the same as for the concentration measurements, e.g. if concentrations are measured in gc/mL, then the flow should be in mL as well.