[R-sig-ME] mixed effect models where time ordering is important

[Steve Candy]

There is an intercept parameter, say beta0, then there is a beta1 parameter
associated with the regressor variable NotContr_d  (even though it's a dummy
variable), then there is a beta2 parameter for the regressor LogDose. The
control and dosed treatments have separate spline shapes and due to the
loglinear form of the model the product of 

exp(beta0+beta1)*exp(beta2*LogDose)*exp(s(time, Control_f=="1"))

gives the dose-time response for Weight for the dosed treatments.

For these dosed treatments this allows varying trajectories for Weight but
strictly according to this common shape model. The control time response
curve is

exp(beta0)*exp(s(time, Control_f=="0")). 

Therefore setting LogDose to zero for the Control makes sure this term does
not contribute to the predicted response since beta2*0=0. Note that beta1
takes care of the fact that LogDose for  a dosed treatment may be less than
zero i.e. one could always scale the Doses up by a constant so that LogDose
is always positive and this would have a complementary effect on beta1.

Note that "log(.)" is the natural not base10 logarithm.

See as an example Table 1 of the paper below in a toxicological application
that models survival rather than weight growth.

Hope that is clearer.

Modelling grouped survival times in toxicological studies using Generalized
Additive Models . Environmental and Ecological Statistics. DOI
10.1007/s10651-014-0306-3

On Wednesday, 22 April 2015 9:42 PM, Emmanuel Curis wrote:

>I'm confused by the second model, the LogDose = 0 if control seems strange
to me. How does it distinguish, in the intercept term, the < control > (0 +
0) and < dose = 10^-1 > (1 + -1) groups? And if the intercept is monotonic >
>with dose, wouldn't be an annoyance to have the < dose = 0 > just somewhere
between other points, depending on the exact doses used (and the log basis
and the unit used...)?

>On Wed, Apr 22, 2015 at 09:16:09PM +1000, Steve Candy wrote:

< To model the dose response component and assuming a common time response <
shape on the log scale you might want to consider; 1). specify a dummy (1,0)
< for Control (0) vs Dosed (1) as "NotContr_d" (i.e. the intercept gives the
< control intercept), 2). LogDose  is set to zero for the control and is the
< log of the actual dose (low, medium, high) for the dosed treatments, and <
define Control_f <- as.factor(NotContr_d)  then 3). replace the above gamm <
with < < < < gamm_01 <- gamm(formula = log(Weight) ~ NotContr_d + LogDose +
s(time, < by=Control_f, bs="cr"), data=data, random=list(subject=~1), < 
<      correlation=corCAR1(form= ~ time | subject))
<
<
<
< The log transforms used above are just suggestions which can be compared
to < using raw Weights or Doses.
<
<
<
<
<
< > Hi all,
<
< >
<
< > I have repeated measures weight data on rats who were in a 28-day toxin
< study. I have one control group and the toxin was administered at one of <
three doses (low, medium, high). This is not a cross-over design, so (for <
example) the rats who were in the low dose group always got the low dose <
over the course of the study.
<
< >
<
< > The rats were not fully grown when the study started. Body weights were
< measured every fourth day.
<
< >
<
< > The interest is in seeing if the toxin has an influence on body weight.
I < am looking at using lmer to analyse this data, however I am unsure how
to < handle the ordering of time, as this will be correlated with increasing
body < weight.
<
< >
<
< > If I did not have to worry about time ordering, I thought this model
would < work:
<
< >
<
< > Weight ~ dose + (1|subject)
<
< >
<
< > The doses are being treated as fixed effects as I am not wanting to <
extrapolate the impact of dose beyond what was administered in the study.
<
< >
<
< > I was wondering if the appropriate model for my data would be:
<
< >
<
< > Weight ~ dose * time + (1|subject)
<
< >
<
< > However, time is measured as days from initial dose administration (e.g.
< day 1 = first day of dosing). While the rats are all very similar in age,
I < do not believe they were all born on the same day, and so I am unsure
about < time as a proxy for age (assuming an intercept in the model). And
day is < measured discontinuously (every fourth day). I feel that omitting
day will < remove one obvious explanatory variable from the model, which may
bias the < results as well as producing a model that poorly fits the data.
<
< >
<
< > I have tried to find an example of a toxicology study that uses a mixed
< effects model in R on repeated measures, that specifies the model. I have
< been unable to locate one.
<
< >
<
< > I would appreciate any advice/recommendations on how to handle this
data.
< I have already advised that a series of separate ANOVAs are not <
statistically defensible given that the weights are likely to be <
auto-correlated and the statistical analysis needs to account for this.
<
< >
<
< > Cheers
<
< > Michelle, note: I do not work Fridays < < < < Dr Steven G. Candy < <
Director/Consultant < < SCANDY STATISTICAL MODELLING PTY LTD < < (ABN: 83
601 268 419) < < 70 Burwood Drive < < Blackmans Bay, TASMANIA, Australia
7052 < < Mobile: (61) 0439284983 < < < < 
< 	[[alternative HTML version deleted]]
<
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-- 
                                Emmanuel CURIS
                                emmanuel.curis at parisdescartes.fr

Page WWW: http://emmanuel.curis.online.fr/index.html