swash (version 1.1.0)

compare_countries: Two-country Comparison of Swash-Backwash Model Parameters

Description

This function enables bootstrap estimates for the mean difference of Swash-Backwash Model parameters of two countries to be compared.

Usage

compare_countries(
  sbm1, 
  sbm2, 
  country_names = c("Country 1", "Country 2"), 
  indicator = "R_0A", 
  iterations = 100, 
  samples_ratio = 0.8, 
  alpha = 0.05, 
  replace = TRUE
  )

Value

object of class countries, see countries-class

Arguments

sbm1

A sbm object for country 1

sbm2

A sbm object for country 2

country_names

list with user-given country names (two entries)

indicator

character, indicator to be analyzed ("S_A", "I_A", "R_A", "t_LE", "t_LE", or "R_0A" (default and recommended: "R_0A"))

iterations

Number of iterations for resampling (default: 100)

samples_ratio

Proportion of regions included in each sample (default: 0.8)

alpha

Significance level \(\alpha\) for the confidence intervals (default: 0.05)

replace

Resampling with replacement (TRUE or FALSE, default: TRUE = bootstrap resampling)

Author

Thomas Wieland

Details

The combination of the Swash-Backwash Model and bootstrap resampling allows the estimation of mean differences of a user-specified model parameter (e.g., spatial reproduction number \(R_{OA}\)) between two countries. This makes it possible to check whether the spatial spread velocity of a communicable disease is significantly different in one country than in another country. Since the initial data in the Swash-Backwash Model should be balanced, entity-based bootstrap sampling is carried out in the compare_countries() function. This means that not, for example, 80% of all observations are included in each sample at a sample ratio equal to \(p\) = 0.8, but rather all observations for 80% of the regions. For both countries, \(B\) bootstrap samples (default: 100) are drawn for which the Swash-Backwash Model is calculated. Based on the distribution of indicators, confidence intervals are calculated at the user-specified significance level \(\alpha\). The compare_countries() function calculates the differences of the user's desired indicator between the two samples, \(D\), and also calculates \(\alpha\) confidence intervals for this.

References

Swash-Backwash Model:

Cliff AD, Haggett P (2006) A swash-backwash model of the single epidemic wave. Journal of Geographical Systems 8(3), 227-252. tools:::Rd_expr_doi("https://doi.org/10.1007/s10109-006-0027-8")

Smallman-Raynor MR, Cliff AD, Stickler PJ (2022) Meningococcal Meningitis and Coal Mining in Provincial England: Geographical Perspectives on a Major Epidemic, 1929–33. Geographical Analysis 54, 197–216. tools:::Rd_expr_doi("https://doi.org/10.1111/gean.12272")

Smallman-Raynor MR, Cliff AD, The COVID-19 Genomics UK (COG-UK) Consortium (2022) Spatial growth rate of emerging SARS-CoV-2 lineages in England, September 2020–December 2021. Epidemiology and Infection 150, e145. tools:::Rd_expr_doi("https://doi.org/10.1017/S0950268822001285").

Bootstrapping und bootstrap confidence intervals:

Efron B, Tibshirani RJ (1993) An Introduction to the Bootstrap.

Ramachandran KM, Tsokos CP (2021) Mathematical Statistics with Applications in R (Third Edition). Ch. 13.3.1 (Bootstrap confidence intervals). tools:::Rd_expr_doi("https://doi.org/10.1016/B978-0-12-817815-7.00013-0")

See Also

swash, countries-class

Examples

data(COVID19Cases_geoRegion)
# Get Swiss COVID19 cases at NUTS 3 level

data(Oesterreich_Faelle)
# Get Austrian COVID19 cases at NUTS 3 level
# (first wave, same final date as in Swiss data: 2020-05-31)

COVID19Cases_geoRegion <- 
  COVID19Cases_geoRegion[!COVID19Cases_geoRegion$geoRegion %in% c("CH", "CHFL"),]
# Exclude CH = Switzerland total and CHFL = Switzerland and Liechtenstein total

COVID19Cases_geoRegion <- 
  COVID19Cases_geoRegion[COVID19Cases_geoRegion$datum <= "2020-05-31",]
# Extract first COVID-19 wave

CH_covidwave1 <- 
  swash (
    data = COVID19Cases_geoRegion, 
    col_cases = "entries", 
    col_date = "datum", 
    col_region = "geoRegion"
    )
# Swash-Backwash Model for Swiss COVID19 cases
# Spatial aggregate: NUTS 3 (cantons)

AT_covidwave1 <- 
  swash (
    data = Oesterreich_Faelle,
    col_cases = "Faelle",
    col_date = "Datum",
    col_region = "NUTS3"
  )
# Swash-Backwash Model for Austrian COVID19 cases
# Spatial aggregate: NUTS 3

AT_vs_CH <- 
  compare_countries(
    CH_covidwave1, 
    AT_covidwave1,
    country_names = c("Switzerland", "Austria"))
# Country comparison Switzerland vs. Austria
# default config: 100 iterations, alpha = 0.05, sample ratio = 80%,
# indicator: R_0A

summary(AT_vs_CH)
# Summary of country comparison

plot(AT_vs_CH)
# Plot of country comparison