eqv.ssd {PK}R Documentation

Establishing Bioequivalence in Serial Sampling Designs

Description

Calculation of a confidence interval for the ratio of two AUCs assessed in a serial sampling design.

Usage

eqv.ssd(conc, time, group, method=c("fieller", "asymp", "boott"), 
        conf.level=0.90, strata=NULL, nsample=1000, data)            

Arguments

conc Time points of concentration assessment.
time Levels of concentrations.
group Grouping variable with two levels.
method Character string specifying the method for calculation of confidence intervals (default=fieller).
conf.level Confidence level (default=0.90).
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 the ration of two AUCs (from 0 to the last time point) 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. Details for calculation can be found in Wolfsegger (2007) and in Jaki et al.

The fieller method is based on Fieller"s theorem (1954) using the critical value from a t-distribution with Satterthwaite"s approximation (1946) to the degrees of freedom for calculation of confidence intervals.

The asymp method is based on the limit distribution for the ratio using the critical value from a normal distribution for calculation of confidence intervals.

The boott method uses the standard error of the limit distribution for the ratio where the critical value is obtained by the bootstrap-t approach. Using boott an additional strata variable for bootstrapping can be specified.

Value

A data frame consisting of:

ratio estimate for ratio of two AUCs.
lower lower limit of confidence interval.
upper upper limit of confidence interval.
df degrees of freedom when using method fieller.

Note

Records including missing values are omitted.

Author(s)

Martin J. Wolfsegger and Thomas Jaki

References

Fieller E. C. (1954). Some problems in interval estimation. Journal of the Royal Statistical Society, Series B, 16:175-185.

Jaki T., Wolfsegger M. J. and Ploner M. (In press). Confidence intervals for ratios of AUCs in the case of serial sampling: A comparison of seven methods. Pharmaceutical Statistics, epub ahead of print.

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.

Wolfsegger M. J. (2007). Establishing bioequivalence in serial sacrifice designs. Journal of Pharmacokinetics and Pharmacodynamics, 34(1):103-113.

See Also

ptest.ssd, auc.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)

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$dose
eqv.ssd(conc=data$concadj, time=data$time, group=data$dose, method="asymp")
eqv.ssd(conc=data$concadj, time=data$time, group=data$dose, method="fieller")

set.seed(310578)
eqv.ssd(conc=data$concadj, time=data$time, group=data$dose, method="boott", nsample=1E3)

set.seed(310578)
eqv.ssd(conc=data$concadj, time=data$time, group=data$dose, method="boott",
        strata=data$sex, nsample=1E3)

[Package PK version 1.00 Index]