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

[Cole, Tim]

Michelle,

You may like to try my sitar growth curve model (see CRAN sitar package, based on nlme). It estimates a mean growth curve as a B-spline, assuming that each individual growth curve differs from the average in three respects - a random intercept on the weight scale, and two random effects on the age scale, location and scale. This matches the biology of individuals growing at different rates, which arise from differences on both the weight and time scales. A multiplicative (i.e. log) age scale makes best sense biologically.

The random effects have associated fixed effects which can also be modelled, e.g. to include the effect of the toxin. So for example rats with the toxin may be developmentally delayed, so the age scale is stretched relative to that for the control group.

Note that to avoid confounding of the random intercepts on the weight and age scales, the mean growth curve needs to be nonlinear. If that does not hold, the age location random effect can be dropped.

Best wishes,
Tim
---
Tim.Cole at ucl.ac.uk<mailto:Tim.Cole at ich.ucl.ac.uk> Phone +44(0)20 7905 2666 Fax +44(0)20 7905 2381
Population Policy and Practice Programme
UCL Institute of Child Health, London WC1N 1EH, UK

Date: Tue, 21 Apr 2015 21:21:40 +0000
From: "Gosse, Michelle" <Michelle.Gosse at foodstandards.gov.au<mailto:Michelle.Gosse at foodstandards.gov.au>>
To: "'John Maindonald'" <john.maindonald at anu.edu.au<mailto:john.maindonald at anu.edu.au>>
Cc: "R-sig-mixed-models at r-project.org<mailto:R-sig-mixed-models at r-project.org>"
<R-sig-mixed-models at r-project.org<mailto:R-sig-mixed-models at r-project.org>>
Subject: Re: [R-sig-ME] mixed effect models where time ordering is
important
Thanks John,

I'll follow that approach,  and also see if the resulting error structure fits logically with the biology, in particular with the control groups.

Cheers
Michelle, note: I do not work Fridays

-----Original Message-----
From: John Maindonald [mailto:john.maindonald at anu.edu.au]
Sent: Wednesday, 22 April 2015 8:35 AM
To: Gosse, Michelle
Cc: R-sig-mixed-models at r-project.org<mailto:R-sig-mixed-models at r-project.org>
Subject: Re: [R-sig-ME] mixed effect models where time ordering is important

A quick initial response!  The starting point needs to be plots of weight vs time for each rat separately, distinguished by treatment group.  These may not be linear.  You may want to look at log(weight) vs time.  You may need to transform the time scale to get something close to linear.  Sort out the error structure (is there a consistent difference in the pattern of change with time?) once you have a reasonable model for the pattern of change with time, for individual mice, perhaps somewhat separately for each dose.

John Maindonald             email: john.maindonald at anu.edu.au<mailto:john.maindonald at anu.edu.au>


On 22/04/2015, at 08:14, Gosse, Michelle <Michelle.Gosse at foodstandards.gov.au<mailto:Michelle.Gosse at foodstandards.gov.au>> wrote:
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


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