[R-sig-ME] Fitting linear mixed model to longitudinal data with very few data points

[Steven J. Pierce]

I don't see any hope of drawing trustworthy conclusions from a dataset this
small given the complexity of the model you want to use and the long list of
things you want to know. 

Maybe the least-worst approach is to accept that this data should not be
analyzed and go search the literature for previously published evidence
pertaining to your question instead, or to advocate for obtaining the
resources required to plan a study with an appropriate sample size and
research design. 

For most of your questions (e.g., pairwise comparisons at each time point),
you have two relevant data points, one with and one without treatment. It
would take a pretty extraordinary set of circumstances to convince me that
this sample is the best evidence one can acquire to answer your questions.
Barring that, doing statistics on data this sparse and using them to support
any serious decision-making seems unethical to me.


Steven J. Pierce, Ph.D.
Associate Director
Center for Statistical Training & Consulting (CSTAT)
Michigan State University
E-mail: pierces1 at msu.edu
Web: http://www.cstat.msu.edu 

-----Original Message-----
From: David Westergaard [mailto:david at harsk.dk] 
Sent: Sunday, November 24, 2013 9:44 AM
To: Steven J. Pierce
Cc: r-sig-mixed-models at r-project.org
Subject: Re: [R-sig-ME] Fitting linear mixed model to longitudinal data with
very few data points

I agree, but I won't be getting any more data, so I'm trying to find
the least-worst solution, so to speak.

Any suggestions/ideas are most welcome.

Regards,
David

2013/11/24 Steven J. Pierce <pierces1 at msu.edu>:
> You probably need data from a lot more subjects to get good estimates of
the
> parameters in that model.
>
>
> Steven J. Pierce, Ph.D.
> Associate Director
> Center for Statistical Training & Consulting (CSTAT)
> Michigan State University
> E-mail: pierces1 at msu.edu
> Web: http://www.cstat.msu.edu
>
> -----Original Message-----
> From: David Westergaard [mailto:david at harsk.dk]
> Sent: Sunday, November 24, 2013 2:55 AM
> To: r-sig-mixed-models at r-project.org
> Subject: [R-sig-ME] Fitting linear mixed model to longitudinal data with
> very few data points
>
> Hello everyone,
>
> First off, I've posted a similar question to StackExchange
>
(http://stats.stackexchange.com/questions/76980/analysis-of-longitudinal-dat
> a-with-very-few-points),
> but I received no answers.
>
> To summarise the data: From 2 subjects, 8 response values were
> measured at time points T0, T1, T2, T3. At T1, subject 1 underwent
> treatment. Subject 1 received no further treatment after T1.
>
> I've reasoned that this is a repeated measures mixed model kind of
> design, so I tried to fit a linear model with random effects, using
> lme4:
>
> lm1 <- lmer(Response ~ Treatment * Timepoint + (1|Subject),
> data=my_data,REML=FALSE)
>
> However, I am not sure if this model is "correct," I have entered time
> points as factorial values, but I am ensure if they should instead be
> numerical values. They are quite spread. On a side note, if I don't
> set REML=FALSE, I get an error "Computed variance-covariance matrix is
> not positive definite" when I try to run "summary(lm1)". I'm guessing
> this may have something to do with my sample size.
>
> I am a bit unsure of how to evaluate the model. The number of data
> points is extremely low. My naive approach was to make an alternative
> model, which does not include treatment:
>
> lm2 <- lmer(Response ~  Timepoint + (1|subject_id), data=test,REML=FALSE)
>
> And do an ANOVA to see which one fits the data better. This is the output:
> anova(lm1,lm2)
>         Df     AIC     BIC  logLik deviance  Chisq Chi Df Pr(>Chisq)
> lm2  6   87.12   87.60 -37.561    75.12
> lm1 10 -453.72 -452.93 236.860  -473.72 548.84      4  < 2.2e-16 ***
>
> >From this, can I conclude that lm1 fits the data significantly better,
> and is a reliable model?
>
> What I'm trying to investigate, is:
>
> 1. Is there any observable effect after administering the drug (i.e.
> is the difference between response values significantly greater than
> zero)
> 2. If there is an effect, what is the effect size at each time point
> (i.e. what is the difference between response values)
> 3. How does the effect vary over time
> 4. If there is an effect, is the effect observed from the drug at T1
> still persistant at T3
>
> Any help on this matter is much appreciated.
>
> Regards,
> David
>
>
>