auc.ssd {PK} | R Documentation |
Calculation of a confidence interval for an AUC or for the difference between two AUCs assessed in a serial sampling design.
auc.ssd(conc, time, group=NULL, method=c("tang.burke", "bailer", "boott"), alternative=c("two.sided", "less", "greater"), conf.level=0.95, strata=NULL, nsample=1000, data)
conc |
vector of concentrations. |
time |
vector of time points. |
group |
vector of grouping variable, if specified a confidence interval for the difference will be calculated; default=NULL. |
method |
character string specifying the method for calculation of confidence intervals; default=tang.burke . |
alternative |
character string specifying the alternative hypothesis; default=two.sided . |
conf.level |
confidence level; default=0.95 . |
strata |
vector of one strata variable, only available for method boott . |
nsample |
number of bootstrap iterations for method boott ; default=1000 . |
data |
optional data frame containing variables named as conc , time , group and strata . |
Calculation of a confidence interval for an AUC (from 0 to the last time point) or for the difference between two AUCs assessed in a serial sampling design.
In a serial sampling design only one measurement is available per analysis subject at a specific time point. The AUC (from 0 to the last time point) is calculated using the linear trapezoidal rule on the arithmetic means at the different time points.
If group=NULL a confidence interval for an AUC is calculated. If group specifies a factor variable (with two levels), a confidence interval for the difference between two AUCs is calculated.
The tang.burke
method uses the critical value from a t-distribution with Satterthwaite's approximation (1946) to the degrees of freedom for calculation of confidence intervals as presented in Tang-Liu and Burke (1988) or in Nedelman et al. (1995).
The bailer
method uses the critical value from a normal distribution for calculation of confidence intervals as presented in Bailer (1988).
The boott
method uses bootstrap-t confidence intervals. Using boott
an additional strata variable for bootstrapping can be specified.
A data frame consisting of:
est |
estimate for AUC or estimate for difference between two AUCs. |
stderr |
standard error for estimate. |
lower |
lower limit of confidence interval. |
upper |
upper limit of confidence interval. |
df |
degrees of freedom when using method tang.burke . |
Records including missing values are omitted.
Martin J. Wolfsegger and Thomas Jaki
Bailer A. J. (1988). Testing for the equality of area under the curves when using destructive measurement techniques. Journal of Pharmacokinetics and Biopharmaceutics, 16(3):303-309.
Nedelman J. R., Gibiansky E. and Lau D. T. W. (1995). Applying Bailer's method for AUC confidence intervals to sparse sampling. Pharmaceutical Research, 12(1):124-128.
Satterthwaite F. E. (1946). An approximate distribution of estimates of variance components. Biometrics Bulletin, 2:110-114.
Tang-Liu D. D.-S. and Burke J. P. (1988). The effect of azone on ocular levobunolol absorption: calculating the area under the curve and its standard error using tissue sampling compartments. Pharmaceutical Research, 5(4):238-241.
## example from Nedelman et al. (1995) m.030 <- c(391, 396, 649, 1990, 3290, 3820, 844, 1650, 75.7, 288) f.030 <- c(353, 384, 625, 1410, 1020, 1500, 933, 1030, 0, 80.5) m.100 <- c(1910, 2550, 4230, 5110, 7490, 13500, 4380, 5380, 260, 326) f.100 <- c(2790, 3280, 4980, 7550, 5500, 6650, 2250, 3220, 213, 636) time <- c(1, 1, 2, 2, 4, 4, 8, 8, 24, 24) auc.ssd(conc=m.030, time=time, method=c('bailer', 'tang.burke')) auc.ssd(conc=f.030, time=time, method=c('bailer', 'tang.burke')) auc.ssd(conc=m.100, time=time, method=c('bailer', 'tang.burke')) auc.ssd(conc=f.100, time=time, method=c('bailer', 'tang.burke')) data <- data.frame(conc=c(m.030, f.030, m.100, f.100), time=rep(time, 4), sex=c(rep('m', 10), rep('f', 10), rep('m', 10), rep('f', 10)), dose=c(rep(30, 20), rep(100, 20))) data$concadj <- data$conc / data$dose auc.ssd(conc=data$concadj, time=data$time, group=data$dose, method=c('bailer', 'tang.burke')) set.seed(260151) auc.ssd(conc=data$concadj, time=data$time, group=data$dose, method='boott', strata=data$sex) ## example from Bailer (1988) time <- c(rep(0, 4), rep(1.5, 4), rep(3, 4), rep(5, 4), rep(8, 4)) grp1 <- c(0.0658, 0.0320, 0.0338, 0.0438, 0.0059, 0.0030, 0.0084, 0.0080, 0.0000, 0.0017, 0.0028, 0.0055, 0.0000, 0.0037, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000) grp2 <- c(0.2287, 0.3824, 0.2402, 0.2373, 0.1252, 0.0446, 0.0638, 0.0511, 0.0182, 0.0000, 0.0117, 0.0126, 0.0000, 0.0440, 0.0039, 0.0040, 0.0000, 0.0000, 0.0000, 0.0000) grp3 <- c(0.4285, 0.5180, 0.3690, 0.5428, 0.0983, 0.0928, 0.1128, 0.1157, 0.0234, 0.0311, 0.0344, 0.0349, 0.0032, 0.0052, 0.0049, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000) auc.ssd(conc=grp1, time=time, method='bailer') auc.ssd(conc=grp2, time=time, method='bailer') auc.ssd(conc=grp3, time=time, method='bailer') data <- data.frame(conc=c(grp1, grp2, grp3), time=rep(time, 3), group=c(rep(1, length(grp1)), rep(2, length(grp2)), rep(3, length(grp3)))) ## function call with data frame using simultaneous confidence intervals based on bonferroni adjustment auc.ssd(data=subset(data, group==1 | group==2), method=c('bailer', 'tang.burke'), conf.level=1-0.05/3) auc.ssd(data=subset(data, group==1 | group==3), method=c('bailer', 'tang.burke'), conf.level=1-0.05/3) auc.ssd(data=subset(data, group==2 | group==3), method=c('bailer', 'tang.burke'), conf.level=1-0.05/3)