auc.ssd {PK}R Documentation

Estimation of AUC in Serial Sampling Designs

Description

Calculation of a confidence interval for an AUC or for the difference between two AUCs assessed in a serial sampling design.

Usage

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)            

Arguments

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.

Details

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.

Value

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.

Note

Records including missing values are omitted.

Author(s)

Martin J. Wolfsegger and Thomas Jaki

References

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.

See Also

ptest.ssd, eqv.ssd.

Examples

## 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)

[Package PK version 0.04 Index]