[R-sig-ME] Linear mixed model query

[Etn bot]

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





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).

Any advice is greatly appreciated,

Many thanks

Etn

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