All,

I have concentration-time data on N=26 subjects with 3 measurements per subject (t=0,t=1, and t=6,8, or 12 hours). The measurement at t=0 is taken right before an IV bolus.

If t=0 measurement (and more) had been taken soon after IV bolus, perhaps the biexponential self-start function (SSbiexp) could have been used (see indomethacin ex., p.277, Pinheiro & Bates).  Also, for 1st order open compartment model w/ oral dosing there exists self-start funtion SSfol (theophylline ex., p.351, P&B). However, as shown in equation 8.2 (p.351), this model includes an absorbtion rate consant (Ka) due to oral dosing.

I'd like to proceed w/ a similar anlaysis but for IV bolus.  As there does not appear to exist an appropriate self-start function, does anyone know the functional form of the corresponding fixed-effects model, or is it as simple as setting Ka in equation 8.2 to a specific constant?  Below is the reproducible example, showing the fitting of a single exponential via nlme after dropping t = 0 (unappealing given it results in only two points per subect).

Thanks,
David



--
David Afshartous, Ph.D.
Research Associate Professor
PSTATŽ: ASA Accredited Professional Statistician
Department of Biostatistics
Vanderbilt University Medical Center


conc <- c(2.66, 3.99, 1.23, 0.81, 0.81, 2.77, 2.31, 1.48, 5.34, 5.57, 2.84, 4.54, 2.36, 1, 1.26, 9.4, 6.7, 3.48, 16.37, 12.1, 10.77, 7.55, 7.07, 10.43, 7.9, 11.37, 16.73, 19.29, 7.48, 12.39, 10.86, 19.54, 11.06, 10.65, 20.86, 17.08, 10.76, 18.01, 11.45, 14.72, 11.7, 26.31, 36.45, 30.79, 32.39, 20.05, 25.17, 23.41, 18.66, 24.89, 16.51, 26.86, 3.65, 3.66, 1.02, 0.56, 1.38, 2.83, 1.8, 2.58, 4.61, 6.35, 3.76, 3.25, 2.49, 1.19, 2.05, 10.53, 6.09, 4.09, 12.48, 10.78, 9.69, 7.4, 8.57, 10.21, 8.25, 11.52)
Subject <- c(rep(1:26, 3))
Time <- c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 8, 12, 12, 12, 8, 12, 8, 8, 6, 8, 8, 8, 8, 8, 8, 12, 12, 6, 8, 8, 8, 8, 8, 8, 8)
Dose <- c(500, 500, 250, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 1000, 500, 500, 500, 500, 500, 500, 500, 500, 500, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)

dat.all <- data.frame(Subject, Time, conc, Dose)
dat.all.grp <- groupedData(conc ~ Time | Subject, data = dat.all,
       labels = list(x = "Time (hours)", y = "Concentration", order.groups = FALSE))
dat.all.after.0.grp <- dat.all.grp[!dat.all.grp$Time == 0, ]

single.exp.fit.1 <- nlme(conc ~ 0 + A* exp(-B * Time),
     fixed = c(A + B  ~ 1),
     random = pdDiag(A ~ 1),
     start = c(30, .3),
     data = dat.all.after.0.grp)




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