# Lethal Concentration Probit Calculates lethal concentration (LC) and its fiducial confidence limits (CL) using a probit analysis according to Finney 1971, Wheeler et al. 2006, and Robertson et al. 2007. ```r LC_probit(formula, data, p = NULL, weights = NULL, subset = NULL, log_base = NULL, log_x = TRUE, het_sig = NULL, conf_level = NULL, conf_type = NULL, long_output = TRUE) ``` ## Arguments - `formula`: an object of class `formula` or one that can be coerced to that class): a symbolic description of the model to be fitted. The details of model specification are given under Details. - `data`: an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which `LC_probit` is called. - `p`: Lethal Concentration (LC) values for given p, example will return a LC50 value if p equals 50. If more than one LC value wanted specify by creating a vector. LC values can be calculated down to the 1e-16 of a percentage (e.g. LC99.99). However, the tibble produced can round to nearest whole number. - `weights`: vector of 'prior weights' to be used in the fitting process. Only needs to be supplied if you are taking the response / total for your response variable within the formula call of `LC_probit`. Otherwise if you use cbind(response, non-response) method you do not need to supply weights. If you do the model will be incorrect. If you don't supply weights there is a warning that will help you to make sure you are using one method or the other. See the following StackExchanges post about differences [cbind() function in R for a logistic regression](https://stats.stackexchange.com/questions/259502/in-using-the-cbind-function-in-r-for-a-logistic-regression-on-a-2-times-2-t) and [input format for binomial glm](https://stats.stackexchange.com/questions/322038/input-format-for-response-in-binomial-glm-in-r). - `subset`: allows for the data to be subseted if desired. Default set to `NULL`. - `log_base`: default is `10` and will be used to calculate results using the anti of `log10()` given that the x variable has been `log10` transformed. If `FALSE` results will not be back transformed. - `log_x`: default is `TRUE` and will calculate results using the antilog of determined by `log_base` given that the x variable has been `log()` transformed. If `FALSE` results will not be back transformed. - `het_sig`: significance level from person's chi square goodness-of-fit test (pgof) that is used to decide if a heterogeneity factor is used. `NULL` is set to 0.15. - `conf_level`: adjust confidence level as necessary or `NULL` set at 0.95. - `conf_type`: default is `"fl"` which will calculate fudicial confidence limits per Finney 1971. If set to `"dm"` the delta method will be used instead. - `long_output`: default is `TRUE` which will return a tibble with all 17 variables. If `FALSE` the tibble returned will consist of the p level, n, the predicted LC for given p level, lower and upper confidence limits. ## Returns Returns a tibble with predicted LC for given p level, lower CL (LCL), upper CL (UCL), Pearson's chi square goodness-of-fit test (pgof), slope, intercept, slope and intercept p values and standard error, and LC variance. ## Examples ```r head(lamprey_tox) # within the dataframe used, control dose, unless produced a value # during experimentation, are removed from the dataframe, # as glm cannot handle values of infinite. Other statistical programs # make note of the control dose but do not include within analysis # calculate LC50 and LC99 m <- LC_probit((response / total) ~ log10(dose), p = c(50, 99), weights = total, data = lamprey_tox[lamprey_tox$nominal_dose != 0, ], subset = c(month == "May")) # OR m1 <- LC_probit(cbind(response, survive) ~ log10(dose), p = c(50, 99), data = lamprey_tox[lamprey_tox$nominal_dose != 0, ], subset = c(month == "May")) # view calculated LC50 and LC99 for seasonal toxicity of a pisicide, # to lamprey in 2011 m # these are the same m1 # dose-response curve can be plotted using 'ggplot2' # library(ggplot2) # lc_may <- subset(lamprey_tox, month %in% c("May")) # p1 <- ggplot(data = lc_may[lc_may$nominal_dose != 0, ], # aes(x = log10(dose), y = (response / total))) + # geom_point() + # geom_smooth(method = "glm", # method.args = list(family = binomial(link = "probit")), # aes(weight = total), colour = "#FF0000", se = TRUE) # p1 # calculate LC50s and LC99s for multiple toxicity tests, June, August, and September j <- LC_probit((response / total) ~ log10(dose), p = c(50, 99), weights = total, data = lamprey_tox[lamprey_tox$nominal_dose != 0, ], subset = c(month == "June")) a <- LC_probit((response / total) ~ log10(dose), p = c(50, 99), weights = total, data = lamprey_tox[lamprey_tox$nominal_dose != 0, ], subset = c(month == "August")) s <- LC_probit((response / total) ~ log10(dose), p = c(50, 99), weights = total, data = lamprey_tox[lamprey_tox$nominal_dose != 0, ], subset = c(month == "September")) # group results together in a dataframe to plot with 'ggplot2' results <- rbind(m[, c(1, 3:8, 11)], j[,c(1, 3:8, 11)], a[, c(1, 3:8, 11)], s[, c(1, 3:8, 11)]) results$month <- factor(c(rep("May", 2), rep("June", 2), rep("August", 2), rep("September", 2)), levels = c("May", "June", "August", "September")) # p2 <- ggplot(data = results, aes(x = month, y = dose, # group = factor(p), fill = factor(p))) + # geom_col(position = position_dodge(width = 0.9), colour = "#000000") + # geom_errorbar(aes(ymin = LCL, ymax = UCL), # size = 0.4, width = 0.06, # position = position_dodge(width = 0.9)) # p2 ``` ## References Finney, D.J., 1971. Probit Analysis, Cambridge University Press, Cambridge, England, ISBN: 052108041X Wheeler, M.W., Park, R.M., and Bailey, A.J., 2006. Comparing median lethal concentration values using confidence interval overlap or ratio tests, Environ. Toxic. Chem. 25(5), 1441-1444.10.1897/05-320R.1 Robertson, J.L., Savin, N.E., Russell, R.M. and Preisler, H.K., 2007. Bioassays with arthropods. CRC press. ISBN: 9780849323317

LC_probit function