[R-sig-ME] Linear mixed model query

[Ben Bolker]

On Thu, Sep 24, 2015 at 10:06 AM, Etn bot <etnbot1 at gmail.com> wrote:
> Hi all,
>
> My study looks at allergy levels of skin patches from patients and readings
> (repeated 5 times) are measured over 4 time points
>
> I need to determine if the allergy level for skin patch changes over time
> (e.g. if allergy level from skin patch 1 for patient 1 at time 0 is
> different from allergy level for skin patch 1 for patient 1 at time 1 etc.)
> I do not want to see the difference between skin patch 1 and skin patch
> 2....
>
> using package lmer:
> model<-lmer(allergy_level ~ time +(time|patient/patch))
>
> Results from this model indicate that time is not significant - the average
> patient allergy level for individual skin patches does not change over
> time:
>
> Random effects:
>
>  Groups   Name        Variance Std.Dev. Corr
>
>  ID:patch (Intercept) 17.4109  4.1726
>
>           time1        2.7109  1.6465   -0.30
>
>           time2        3.0082  1.7344   -0.26  0.60
>
>           time3        5.7643  2.4009   -0.35  0.15  0.54
>
>  patch    (Intercept) 19.1576  4.3769
>
>           time1        0.2103  0.4586   -0.56
>
>           time2        0.4372  0.6612   -0.94  0.48
>
>           time3        0.5895  0.7678   -0.48  0.96  0.49
>
>  Residual              4.9467  2.2241
>
> Number of obs: 2956, groups:  ID:patch, 149; patch, 16
>
>
>
> Fixed effects:
>
>             Estimate Std. Error t value
>
> (Intercept)  6.44763    1.15028   5.605
>
> time1       -0.01907    0.21237  -0.090
>
> time2       -0.03172    0.24759  -0.128
>
> time3       -0.01124    0.29940  -0.038
>
>
   I was going to ask if you wanted to treat time as linear, but there's
not much evidence that it will help you here.
>
>
>
> model1: Force ~ 1 + (1 + time | patch/ID)
>
> model2: Force ~ time + (1 + time | patch/ID)
>
>          Df   AIC   BIC  logLik deviance  Chisq Chi Df Pr(>Chisq)
>
> model11 22 14281 14413 -7118.5    14237
>
> model12 25 14287 14437 -7118.4    14237 0.0208      3     0.9992
>
> I have extracted the random coefficients from model 1:
>
> ranef(model1)
>
> $`ID:patch`
>
>       (Intercept)       time1        time2        time3
>
> 1:11    5.9845070  0.34088535  0.431998708  1.590906238
>
> 1:12    5.1236456 -0.03178611 -0.149784278 -0.116150278
>
> 1:13    6.3746877 -0.76853294 -0.550037715  0.842518786
>    :
>    :
> However, I need to be able to tell if there is a significant difference for
> individual patches for individual patients over time
>
> e.g.
> If I run individual linear regression on patient 1 for skin patch 1,
> results show that that time is significant:
>
> Coefficients:
>
>             Estimate Std. Error t value Pr(>|t|)
>
> (Intercept)  18.0800     0.6523  27.717 5.95e-15 ***
>
> time1         0.3600     0.9225   0.390 0.701502
>
> time2         1.2400     0.9225   1.344 0.197641
>
> time3        -4.3400     0.9225  -4.705 0.000239 ***
>
> ---
>
> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>
>
>
> Residual standard error: 1.459 on 16 degrees of freedom
>
> Multiple R-squared:  0.7323,    Adjusted R-squared:  0.6821
>
> F-statistic: 14.59 on 3 and 16 DF,  p-value: 7.679e-05
>
>
> If I run individual regression models for each skin patch for each patient,
> this will result in a large number of models as I have There are 16 skin
> patches per patient. (10 patients in total) 5 readings are taken at each of
> the 4 time points.
>
> I thought linear mixed models would be an appropriate method to answer my
> question (I need to be able to tell if there is a significant difference
> for individual patches for individual patients over time).
>

  When you adopt a random-effects formulation, you forego the ability
to perform significance tests on individual levels -- that's the price you
pay for the benefits of doing shrinkage estimation.  If you need significance
tests on individual patch/patient combinations, you're going to be
stuck with 160 significance tests (you should probably consider some
kind of multiple-comparisons correction ...)

 Ben Bolker