Re: Confidence interval calculations
Dear Dennis,
there is probably a nice formula with linear approximation to convert the
uncertainty in your parameters (the slopes of the regression lines) into the CI
at different concentrations, but linearization is so "last century" :), it may
be just easier to run a simulation with uncertainty.
I would suggest is that you
1. first obtain uncertainty in both your parameters and importantly the
correlation between the two uncertainty terms.
2. you simulate out your response at all values of Cp including this
uncertainty in the parameters. You do this a bunch of times (n=500 should do)
3. you obtain the CI at each concentration level just by using the empirical
percentiles of the simulation (2.5th and 97.5th).
It is very important to include the correlation value because that would affect
greatly your confidence interval, and it will prevent the generation of
implausible values.
For the estimation of the joint uncertainty (2x2 covariance matrix), you can do
things parametrically by assuming that your joint distribution is a
multi-variate Gaussian distribution, and for you could even use the values of
precision provided by the covariance step of NONMEM. However, I would strongly
discourage you from doing this - and I am sure Nick Holford would agree :)
What I suggest is that you estimate your precision in the slope of the
regression lines by using a bootstrap, and then you use each single set of
parameter estimates from the bootstrap in your simulation. This way you will
make no assumptions on the distributions, and you will automatically keep the
correlation into account.
I think the SSE (stochastic simulation and estimation) script in Perl Speaks
NONMEM has a tool to do this kind of simulations with uncertainty, and you can
in fact use as an input values the output estimates from a bootstrap. Option
-raw_res, or something like that.
Good luck and greetings from Cape Town,
Paolo
Quoted reply history
On 2015/12/10 18:23, Fisher Dennis wrote:
Colleagues
I have fit an exposure response model using NONMEM — the optimal model is a
segmented two-part regression with Cp on the x-axis and response on the y-axis.
The two regression lines intercept at the cutpoint.
The parameters are:
slope of the left regression
cutpoint between regressions
“intercept” — y value at the cutpoint
slope of the right regression (fixed at zero; models in which the value was
estimated yielded similar values for the objective function)
I have been asked to calculate the confidence interval for the response at
various Cp values.
Above the cutpoint, this seems straightforward:
a. if NONMEM yielded standard errors, the only relevant parameter is the y
value at the cutpoint and its standard error
b. if NONMEM did not yield standard errors, the confidence interval could come
from either likelihood profiles or bootstrap
My concern is calculating at Cp values below the cutpoint, for which both slope
and intercept come into play. Any thoughts as to how to do this in the
presence or absence of NONMEM standard errors?
The reason that I mention with / without presence of SE’s is that this model
was fit to two different datasets, one of which yielded SE’s, the other not.
Any thoughts on this would be appreciated.
Dennis
Dennis Fisher MD
P < (The "P Less Than" Company)
Phone: 1-866-PLessThan (1-866-753-7784)
Fax: 1-866-PLessThan (1-866-753-7784)
http://www.plessthan.com/
--
------------------------------------------------
Paolo Denti, PhD
Pharmacometrics Group
Division of Clinical Pharmacology
Department of Medicine
University of Cape Town
K45 Old Main Building
Groote Schuur Hospital
Observatory, Cape Town
7925 South Africa
phone: +27 21 404 7719
fax: +27 21 448 1989
email: [email protected]<mailto:[email protected]>
------------------------------------------------
Disclaimer - University of Cape Town This e-mail is subject to the UCT ICT
policies and e-mail disclaimer published on our website at
http://www.uct.ac.za/about/policies/emaildisclaimer/ or obtainable from +27 21
650 9111. If this e-mail is not related to the business of UCT it is sent by
the sender in the sender's individual capacity.