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

[Gosse, Michelle]

Thanks again for the advice. I have Pinheiro and Bates which I normally find sufficient, but not in this case. The recommendations for other books are very helpful.

Cheers
Michelle, note: I do not work Fridays

From: Ken Beath [mailto:ken.beath at mq.edu.au]
Sent: Thursday, 23 April 2015 11:20 AM
To: Steven J. Pierce
Cc: Gosse, Michelle; r-sig-mixed-models at r-project.org
Subject: Re: [R-sig-ME] mixed effect models where time ordering is important

Yes, first rule of statistics: start with the easy models first, and check the diagnostics. So order of models would be linear, quadratic, nonlinear (there are several used in infant growth modelling which may be applicable), regression splines, then anything else. All of these may fit better with log Weight as the response. I would also recommend Pinheiro and Bates ":Mixed-Effects Models in S and S-Plus", and Verbeke and Molenberghs "Linear Mixed Models for Longitudinal Data".

On 22 April 2015 at 22:31, Steven J. Pierce <pierces1 at msu.edu<mailto:pierces1 at msu.edu>> wrote:
Michelle,

This looks like a fairly straightforward growth curve modeling problem. The first half of the Singer & Willett (2003) book is an excellent source on using mixed effects models for these sorts of analyses. You can describe each rat's individual longitudinal trajectory for weight in terms of starting weight (intercept) plus parameters that describe the shape of the trajectory over time (e.g., slope if the trajectory is linear). All of those parameters may vary across rats, but should also have some average value that describes a "typical" trajectory. If you introduce dose as a categorical variable, you can allow dose to predict parameters of the individual rats' trajectories, essentially allowing you to compare the average trajectories across the dose groups. You may want to consider allowing the time slope to vary across rats, as in the formula Weight ~ dose * time + (time + 1|subject).

You should also consider non-linear shapes for the trajectory. Right now, assuming time is a continuous variable, you appear to be considering only linear trends. You could account for the variation in age at the start of the trial by carefully considering how you code time. See Singer & Willett for excellent coverage of various methodological details that are relevant.

Singer, J. D., & Willett, J. B. (2003). Applied longitudinal data analysis: Modeling change and event occurrence. New York, NY: Oxford University Press.


Steven J. Pierce, Ph.D.
Associate Director
Center for Statistical Training & Consulting (CSTAT)
Michigan State University
Web: http://www.cstat.msu.edu

-----Original Message-----
From: Gosse, Michelle [mailto:Michelle.Gosse at foodstandards.gov.au<mailto:Michelle.Gosse at foodstandards.gov.au>]
Sent: Tuesday, April 21, 2015 4:14 PM
To: 'R-sig-mixed-models at r-project.org<mailto:R-sig-mixed-models at r-project.org>'
Subject: [R-sig-ME] mixed effect models where time ordering is important

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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Ken Beath
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MACQUARIE UNIVERSITY NSW 2109, Australia

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