[R-sig-ME] mixed effect models where time ordering is important
Steve Candy
burwood70 at gmail.com
Fri Apr 24 04:12:02 CEST 2015
Emmanuel
I think you make an interesting point that the exp(-beta1/beta2) appears to
be a "problem dose" if its within the range of doses tested but it doesn't
turn out to problematic as for example given the estimates in Table 1 of the
paper I referred to (DOI 10.1007/s10651-014-0306-3). The predictions for the
control and the data for one of the actual doses (=0.56), where this dose
is very close to exp(-beta1/beta2), are quite different and the fit to the
data is very good in each case (see Figure 1). That is because the ratio of
predictions for control to that of dosed at a dose of exactly
exp(-beta1/beta2) is not 1 but is, as you note,
exp(s(time, Control_f=="0"))/ exp(s(time, Control_f=="1")).
Incorporating a Control directly into a dose-response model that
incorporates a log(Dose) term is difficult since the control can be assumed
to have zero dose. The model I suggest is a workaround. One can ask why not
simply fit the control data separately, however, there are benefits in
modelling these data jointly with the dosed data. These include automatic
adjustment for control mortality in the case of survival data and pooled
estimates of error variance for determining confidence bounds on
predictions.
-----Original Message-----
From: Emmanuel Curis [mailto:emmanuel.curis at parisdescartes.fr]
Sent: Wednesday, 22 April 2015 11:23 PM
To: Steve Candy
Cc: r-sig-mixed-models at r-project.org
Subject: Re: [R-sig-ME] mixed effect models where time ordering is important
I'm sorry if I'm slow, but I don't see how the exponential writing solves
the problem - it's just a rewrite that does not change the behaviour of the
system, since exp is bijective, right?
It is always possible with the first model to fine a given dose such that
gives the same pre-exponential model that the second one. If treatment has
no effect on the shape part, this means that we have a strong discontinuity
at 0 with a singular point having the same value that another one on the
curve --- in other words, it seems that this assume that, for instance, at
low dose subjects grow more slowly than unexposed, but at high dose they
grow more quickly, and somewhere between the dose has no effect... Of
course, this may be compensated for/hidden by the different spline models,
but it seems a strange assumption, no?
I guess in several situations, the problematic dose exp(-beta1/beta2) is not
observed and may be not in the range of tested doses, so it may not always
be a concern, but may be it can in some circumstances?
On Wed, Apr 22, 2015 at 10:18:10PM +1000, Steve Candy wrote:
< 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]]
< <
< < _______________________________________________
< < R-sig-mixed-models at r-project.org mailing list < <
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<
< --
< Emmanuel CURIS
< emmanuel.curis at parisdescartes.fr
<
< Page WWW: http://emmanuel.curis.online.fr/index.html
--
Emmanuel CURIS
emmanuel.curis at parisdescartes.fr
Page WWW: http://emmanuel.curis.online.fr/index.html
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