[R-sig-ME] Another case of -1.0 correlation of random effects

[Kevin E. Thorpe]

Ben Bolker wrote:
> Kevin E. Thorpe wrote:
>> Hello.
>>
>> I know this has come up a couple times recently, but I'm still not sure 
>> what to do about it in my data.  Note that my sessionInfo() will be at 
>> the bottom.
>>
>> My data come from a crossover trial and are balanced.
>>
>>  > str(gluc)
>> 'data.frame':	96 obs. of  4 variables:
>>   $ Subject  : int  1 2 3 5 6 7 10 11 12 13 ...
>>   $ Treatment: Factor w/ 2 levels "Barley","Oat": 1 1 1 1 1 1 1 1 1 1 ...
>>   $ Dose     : int  8 8 8 8 8 8 8 8 8 8 ...
>>   $ iAUC     : num  110 256 129 207 244 ...
>>
>>  > xtabs(~Treatment+Dose,data=gluc)
>>           Dose
>> Treatment  0  2  4  8
>>     Barley 12 12 12 12
>>     Oat    12 12 12 12
>>
>> I plot the data (attached as gluc.pdf, if it comes through).
>>
>>  From the plot, I think I want to fit the model as:
>>
>> lmer(iAUC~Treatment+Dose+(Treatment|Subject)+(Dose|Subject),data=gluc)
>>
>> It could possibly be argued that the (Treatment|Subject) part is not 
>> needed.  When I fit this, I got -1.0 correlation within the Dose random 
>> effects.  To simplify, I will fit a simpler model, since the issue persists.
>>
>>  > lmer(iAUC~Dose+(Dose|Subject),data=gluc,subset=Treatment=="Oat")
>> Linear mixed model fit by REML
>> Formula: iAUC ~ Dose + (Dose | Subject)
>>     Data: gluc
>>   Subset: Treatment == "Oat"
>>     AIC   BIC logLik deviance REMLdev
>>   562.6 573.9 -275.3    563.1   550.6
>> Random effects:
>>   Groups   Name        Variance Std.Dev. Corr
>>   Subject  (Intercept) 8274.324 90.9633
>>            Dose          16.214  4.0266  -1.000
>>   Residual             4862.319 69.7303
>> Number of obs: 48, groups: Subject, 12
>>
>> Fixed effects:
>>              Estimate Std. Error t value
>> (Intercept)  309.352     30.539  10.130
>> Dose         -14.424      3.596  -4.012
>>
>> Correlation of Fixed Effects:
>>       (Intr)
>> Dose -0.647
>>
>> Now, a plot created by (and attached as lmlist.pdf):
>>
>> plot(confint(lmList(iAUC~Dose|Subject,data=gluc,subset=Treatment=="Oat"),pooled=TRUE),order=1)
>>
>> shows (I think) a strong negative correlation between the intercept and 
>> slope random effects for Dose.
>>
>> So, I would appreciate some advice on how I might specify these random 
>> effects correctly.
> 
>   It's not entirely clear whether Subjects are unique within Treatments
> (OK, maybe we should say "nested") or whether the same Subject can have
> both Treatments  -- what would xtabs(~Subject+Dose+Treatment) look like?
> 
>   *If* each Subject appears in only one Treatment (i.e., 5 doses per
> Subject, each Subject is either Oat or Barley, 12 Subjects per
> Treatment), which is what I initially took for granted, then it makes
> perfect sense to me that you can't specify Treatment|Subject, because
> Treatment does not vary within Subject -- there doesn't seem to be any
> way you can recover information about how the effect of Treatment varies
> among Subject.
> 
>   Since your plots do look reasonably linear within Subject,
> 
> iAUC~Treatment*Dose+(Dose|Subject)
> 
>  seems best to me.
> For what it's worth, this example closely parallels the Orthodont
> example in the nlme package ...

It is a true crossover.  There are 12 patients and each patient gets 
both treatments and all four doses.

I will look at the Orthodont example too.


-- 
Kevin E. Thorpe
Biostatistician/Trialist, Knowledge Translation Program
Assistant Professor, Dalla Lana School of Public Health
University of Toronto
email: kevin.thorpe at utoronto.ca  Tel: 416.864.5776  Fax: 416.864.3016