# Confidence intervals for the area under the concentration versus time curve in complete data designs Examples to find confidence intervals for the area under the concentration versus time curve (AUC) in complete data designs. ```r auc.complete(conc, time, group=NULL, method=c("t", "z", "boott"), alternative=c("two.sided", "less", "greater"), conf.level=0.95, nsample=1000, data) ``` ## Arguments - `conc`: Levels of concentrations as a vector. - `time`: Time points of concentration assessment as a vector. One time point for each concentration measured needs to be specified. - `group`: A grouping variable as a vector (default=`NULL`). If specified, a confidence interval for the difference of independent AUCs will be calculated. - `method`: A character string specifying the method for calculation of confidence intervals (default=`c("t", "z", "boott")`). - `alternative`: A character string specifying the alternative hypothesis. Possible values are `"less"`, `"greater"` and `"two.sided"` (the default). - `conf.level`: Confidence level (default=`0.95`). - `nsample`: Number of bootstrap iterations for method `boott` (default=`1000`). - `data`: Optional data frame containing variables named as `conc`, `time` and `group`. ## Details This function computes confidence intervals for an AUC (from 0 to the last time point) or for the difference between two AUCs in complete data designs. To compute confidence intervals in complete data designs the design is treated as a batch design with a single batch. More information can therefore be found under `auc`. A corresponding reminder message is produced if confidence intervals can be computed, ie when at least 2 measurements at each time point are available. The above approach, though correct, is often inefficient and so we will illustrate alternative methods in this help file. A general implementation is not provided as the most efficient analysis strongly depends on the context. The interested reader is refered to chapter 8 of Cawello (2003). If `data` is specified the variable names `conc`, `time` and `group` are required and represent the corresponding variables. ## See Also `auc`, `estimator`, `ci` and `test` ## Returns An object of the class PK containing the following components: - **est**: Point estimates. - **CIs**: Point estimates, standard errors and confidence intervals. - **conc**: Levels of concentrations. - **conf.level**: Confidence level. - **design**: Sampling design used. - **group**: Grouping variable. - **time**: Time points measured. ## References Cawello W. (2003). **Parameters for Compartment-free Pharmacokinetics. Standardisation of Study Design, Data Analysis and Reporting**. Shaker Verlag, Aachen. Gibaldi M. and Perrier D. (1982). **Pharmacokinetics**. Marcel Dekker, New York and Basel. ## Author(s) Thomas Jaki and Martin Wolfsegger ## Examples ```r ## example from Gibaldi and Perrier (1982, page 436) for an individual AUC time <- c(0, 0.165, 0.5, 1, 1.5, 3, 5, 7.5, 10) conc <- c(0, 65.03, 28.69, 10.04, 4.93, 2.29, 1.36, 0.71, 0.38) auc.complete(conc=conc, time=time) ## dataset Indometh of package datasets ## calculate individual AUCs require(datasets) row <- 1 res <- data.frame(matrix(nrow=length(unique(Indometh$Subject)), ncol=2)) colnames(res) <- c('id', 'auc') for(i in unique(Indometh$Subject)){ temp <- subset(Indometh, i==Subject) res[row, 1] <- i res[row, 2] <- auc.complete(data=temp[,c("conc","time")])$est[1,1] row <- row + 1 } print(res) # function to get geometric mean and corresponding CI gm.ci <- function(x, conf.level=0.95){ res <- t.test(x=log(x), conf.level=conf.level) out <- data.frame(gm=as.double(exp(res$estimate)), lower=exp(res$conf.int[1]), upper=exp(res$conf.int[2])) return(out) } # geometric mean and corresponding CI: assuming log-normal distributed AUCs gm.ci(res[,2], conf.level=0.95) # arithmetic mean and corresponding CI: assuming normal distributed AUCs # or at least asymptotic normal distributed arithmetic mean t.test(x=res[,2], conf.level=0.95) # alternatively: function auc.complete set.seed(300874) Indometh$id <- as.character(Indometh$Subject) Indometh <- Indometh[order(Indometh$id, Indometh$time),] Indometh <- Indometh[order(Indometh$time),] auc.complete(conc=Indometh$conc, time=Indometh$time, method=c("t")) ## example for comparing AUCs assessed in a repeated complete data design ## (dataset: Glucose) ## calculate individual AUCs data(Glucose) res <- data.frame(matrix(nrow=length(unique(Glucose$id))*2, ncol=3)) colnames(res) <- c('id', 'date', 'auc') row <- 1 for(i in unique(Glucose$id)){ for(j in unique(Glucose$date)){ temp <- subset(Glucose, id==i & date==j) res[row, c(1,2)] <- c(i,j) res[row, 3] <- auc.complete(data=temp[,c("conc","time")])$est[1,1] row <- row + 1 } } res <- res[order(res$id, res$date),] print(res) # assuming log-normally distributed AUCs # geometric means and corresponding two-sided CIs per date tapply(res$auc, res$date, gm.ci) # comparison of AUCs using ratio of geometric means and corresponding two-sided CI # repeated experiment res1<-reshape(res, idvar = "id", timevar = "date", direction = "wide") model <- t.test(Pair(log(auc.1),log(auc.2))~1,data=res1) exp(as.double(model$estimate)) exp(model$conf.int) ```

auc.complete function