# Proportional similarity index Compute proportional similarity index. ```r epi.psi(dat, itno = 99, conf.level = 0.95) ``` ## Arguments - `dat`: a data frame providing details of the distributions to be compared (in columns). The first column (either a character of factor) lists the levels of each distribution. Additional columns list the number of events for each factor level for each distribution to be compared. - `itno`: scalar, numeric defining the number of bootstrap simulations to be run to generate a confidence interval around the proportional similarity index estimate. - `conf.level`: scalar, numeric defining the magnitude of the returned confidence interval for each proportional similarity index estimate. ## Details The proportional similarity or Czekanowski index is an objective and simple measure of the area of intersection between two non-parametric frequency distributions (Feinsinger et al. 1981). PIS values range from 1 for identical frequency distributions to 0 for distributions with no common types. Bootstrap confidence intervals for this measure are estimated based on the approach developed by Garrett et al. (2007). ## Returns A five column data frame listing: `v1` the name of the reference column, `v2` the name of the comparison column, `est` the estimated proportional similarity index, `lower` the lower bound of the estimated proportional similarity index, and `upper` the upper bound of the estimated proportional similarity index. ## References Feinsinger P, Spears EE, Poole RW (1981) A simple measure of niche breadth. Ecology 62: 27 - 32. Garrett N, Devane M, Hudson J, Nicol C, Ball A, Klena J, Scholes P, Baker M, Gilpin B, Savill M (2007) Statistical comparison of Campylobacter jejuni subtypes from human cases and environmental sources. Journal of Applied Microbiology 103: 2113 - 2121. DOI: 10.1111/j.1365-2672.2007.03437.x. Mullner P, Collins-Emerson J, Midwinter A, Carter P, Spencer S, van der Logt P, Hathaway S, French NP (2010). Molecular epidemiology of Campylobacter jejuni in a geographically isolated country with a uniquely structured poultry industry. Applied Environmental Microbiology 76: 2145 - 2154. DOI: 10.1128/AEM.00862-09. Rosef O, Kapperud G, Lauwers S, Gondrosen B (1985) Serotyping of Campylobacter jejuni, Campylobacter coli, and Campylobacter laridis from domestic and wild animals. Applied and Environmental Microbiology, 49: 1507 - 1510. ## Examples ```r ## EXAMPLE 1: ## A cross-sectional study of Australian thoroughbred race horses was ## carried out. The sampling frame for this study comprised all horses ## registered with Racing Australia in 2017 -- 2018. A random sample of horses ## was selected from the sampling frame and the owners of each horse ## invited to take part in the study. Counts of source population horses ## and study population horses are provided below. How well did the geographic ## distribution of study population horses match the source population? state <- c("NSW","VIC","QLD","WA","SA","TAS","NT","Abroad") srcp <- c(11372,10722,7371,4200,2445,1029,510,101) stup <- c(622,603,259,105,102,37,22,0) dat.df01 <- data.frame(state, srcp, stup) epi.psi(dat.df01, itno = 99, conf.level = 0.95) ## The proportional similarity index for these data was 0.88 (95% CI 0.86 to ## 0.90). We conclude that the distribution of sampled horses by state ## was consistent with the distribution of the source population by state. ## Not run: ## Compare the relative frequencies of the source and study populations ## by state graphically: library(ggplot2) dat.df01$psrcp <- dat.df01$srcp / sum(dat.df01$srcp) dat.df01$pstup <- dat.df01$stup / sum(dat.df01$stup) dat.df01 <- dat.df01[sort.list(dat.df01$psrcp),] dat.df01$state <- factor(dat.df01$state, levels = dat.df01$state) ## Data frame for ggplot2: gdat.df01 <- data.frame(state = rep(dat.df01$state, times = 2), pop = c(rep("Source", times = nrow(dat.df01)), rep("Study", times = nrow(dat.df01))), pfreq = c(dat.df01$psrcp, dat.df01$pstup)) gdat.df01$state <- factor(gdat.df01$state, levels = dat.df01$state) ## Bar chart of relative frequencies by state faceted by population: ggplot(data = gdat.df01, aes(x = state, y = pfreq)) + theme_bw() + geom_bar(stat = "identity", position = position_dodge(), color = "grey") + facet_grid(~ pop) + scale_x_discrete(name = "State") + scale_y_continuous(limits = c(0,0.50), name = "Proportion") ## End(Not run) ```

epi.psi function