I had ran NLME model to assess BMI growth as a function of age using
gompertz function. Then I calculated peak growth time - usin nlme
model estimates, second
derivative of gompertz function and uniroot function in Splus.
I'd like to know if there is a way to calculate confidence limits for
peak growth time? Any reference or programming assistance would
be greatly appreciated. I used win NT SPLUS 4.0 RELEASE 3.
Thanks in advance, WayWay M. Hlaing
University of South Florida
Program used to calculate PGT (peak growth time) is as follows:
# GOMPERTZ: f(AGE) = A + exp(B-exp(C+D * (AGE-6)))
# f"(age)=exp(B-exp(C+D(age-6)))*exp(C+D(age-6))*D^2*(exp(C+D(age-6))-1)
sderiv<-function(gamma, t){exp(gamma[1]-exp(gamma[2]+gamma[3]*(t-6)))*exp(gamma[2]+gamma[3]*(t-6))*gamma[3]**2*(exp(gamma[2]+gamma[3]*(t-6))-1)} # 1
sderiv2<-function(t){exp(2.3-exp(1.75-0.32*(t-6)))*exp(1.75-0.32*(t-6))*-0.32**2*(exp(1.75-0.32*(t-6))-1)}
t<-seq(6, 22, 0.25)
# bmi model
# gamma[1]=B, gamma[2]=C=, gamma[3]=D : estimates from BMI model
# B=2.30, C=1.75, D=-0.32: for females
uniroot(sderiv2, c(6,22))
# uniroot result was 11.5 years =PGT FOR FEMALES
# confidence limits for PGT=11.5???????
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