Linear Mixed Model - can someone please explain?

[97tbird]

in simple to understand terms, if someone can?

I read about it, but i think i need a simpler language version
I have to present a journal article, and the authors used a LMM to do the statistics between treatment results in 3 different grps of patients who received 3 different drugs in sequence.

I just need to explain to my audience what they did with this LMM, why they did it, etc, in simple terms.

here's the passage from the article where they talk about it:

Statistical analysis
The preplanned main analysis compared pain scores for
combination treatment versus monotherapy for patients
on the maximum tolerated dose. On the basis of previous
variance estimates and accounting for two pairwise
comparisons (combination treatment vs gabapentin or
nortriptyline), we calculated that 40 patients would
provide an 80% probability of detecting a mean diff erence
between treatments of about half of a clinically
signifi cant20 amount of pain reduction (α=0·05, twosided).
Dropout rates in previous studies were about 10%
per 4–6-week treatment period, therefore we anticipated
that enrolment of 58 patients would yield 40 who
completed the study.
Patients completing at least two study treatment
periods (providing one pairwise comparison) were
included in the effi cacy analysis; analysis was by intention
to treat. Patients receiving at least one dose of any study
drug were included in analyses of adverse events. Mean
pain intensity was calculated from patient diaries while
patients were on the maximum tolerated dose. For
inclusion, more than 50% of the scores had to be
available; otherwise, the mean daily pain intensity was
treated as missing. A linear mixed model21 was formed
with fi xed eff ects of drug treatment, treatment sequence,
treatment period, and the fi rst-order carryover term, and
the random eff ect as patient (nested in sequence); the
model was fi rst fi tted with the pain intensity data. If the
carryover eff ect was not signifi cant, then a reduced model
excluding the carryover term was refi tted.
According to Jones and Kenward,21 the extent of the
carryover factor in the second and third treatment
period was defi ned as treatment received in the fi rst
and second period, respectively; the extent of carryover
in the fi rst period was the same but an arbitrary
treatment for all patients. The model was identifi able
since treatment period was another factor in the model.
The eff ect of carryover was fi rst tested, and if it was not
statistically signifi cant, this term was dropped from the
linear mixed model. The least-square mean (SD)
estimated from the initial or reduced model was
calculated for every drug treatment. For treatment
eff ects, according to Fisher’s least signifi cant diff erence
method for multiple comparisons,22 the global diff erence
between all the treatment groups was fi rst tested in the
model. Only when this test was signifi cant, all three
pairwise comparisons were made with the estimated
contrast from the initial or reduced model. As a
secondary analysis, change in pain during each
treatment period was calculated as the diff erence
between pain at treatment period baseline (mean of last
3 days of baseline before study start, or mean of last
3 days of washouts preceding periods B and C) and pain
on treatment (mean of last 3 days on maximum
tolerated dose). The percentage change in pain (change
in pain/treatment period baseline) was analysed as per
the above linear mixed model. Secondary continuous
outcome measures were analysed in the same way with
baseline scores included as an additional fi xed eff ect
in the model. Proportion data were analysed by
Fisher’s exact method.23 All reported p values are twosided.
All analyses were done with SAS software
(version 8.0)

 

[Boomer]

I get a pain reading this!

 

[97tbird]

yeah i had to cut/paste from a pdf, and it breaks words in the middle...idk why

 

[JayhawkRoy]

Here's a short overview that explains it, courtesy of the NC State math dept:
Linear mixed models (LMM) handle data where observations are not independent. That is, LMM correctly models correlated errors, whereas procedures in the general linear model family (GLM) usually do not. (GLM includes such procedures as t-tests, analysis of variance, correlation, regression, and factor analysis, to name a few.) LMM is a further generalization of GLM to better support analysis of a continuous dependent for:

Random effects: where the set of values of a categorical predictor variable are seen not as the complete set but rather as a random sample of all values (ex., the variable "product" has values representing only 5 of a possible 42 brands). Through random effects models, the researcher can make inferences over a wider population in LMM than possible with GLM.

Hierarchical effects: where predictor variables are measured at more than one level (ex., reading achievement scores at the student level and teacher-student ratios at the school level; or sentencing lengths of offenders, gender of judges, and budgets of judicial districts).

Repeated measures: where observations are correlated rather than independent (ex., before-after studies, time series data, matched-pairs designs)

It is true that GLM has been adapted to handle these models also, but problematically so and therefore LMM is preferred. For instance, GLM in SPSS does support random effects but estimates their parameters as if they were fixed, calculating variance components based on expected mean squares; LMM, in contrast, uses maximum likelihood estimation to estimate these parameters. GLM in SPSS supports repeated measures but the LMM module supports more variations and data options. Hierarchical models in SPSS require LMM implementation. Linear mixed models include a variety of multi-level modeling (MLM) approaches, including hierarchical linear models, random coefficients models (RC), and covariance components models. Differences between LMM and GLM are discussed further in the FAQ section.
Note that multi-level mixed models are based on a multi-level theory which specifies expected direct effects of variables on each other within any one level, and which specifies cross-level interaction effects between variables located at different levels. That is, the researcher must postulate mediating mechanisms which cause variables at one level to influence variables at another level (ex., school-level funding may positively affect individual-level student performance by way of recruiting superior teachers, made possible by superior financial incentives). Multi-level modeling tests multi-level theories statistically, simultaneously modeling variables at different levels without necessary recourse to aggregation or disaggregation. It should be noted, though, that in practice some variables may represent aggregated scores.

 

[eljefino]

Work has been proceeding in order to bring perfection to the crudely conceived idea of a machine that would not only supply inverse reactive current for use in unilateral phase detractors, but would also be capable of automatically synchronizing cardinal grammeters. Such a machine is the Linear Mixed Model.












Sorry dude. Whatever they're going to pay you as a pharmacist, it's not enough.

 

[Gary Allan]

This is something you need an instructor that deals with this ..who is also human. They can give you digestible examples that will allow you to integrate the master's level paper rhetoric.

You're not geek'd out enough.

 

[JayhawkRoy]

Three take-aways:
1. Given the nature of the testing being done, LMM is a more appropriate modeling technique than GLM. It accounts for the difference in variables better than GLM.
2. Because of the before/after aspect of the testing and combining those results with the questions on whether pain is better, worse, etc, makes LMM a better modeling technique. GLM might be able to replicate the results, but the modeling would be more complicated with results that would not necessarily be improved.
3. LMM assumes a certain amount of dependence amongst the variables, whereas GLM doesn't. Clearly there is dependence between the medicine and the pain level.

That's about as good as I can do before I got a brain freeze....

 

[97tbird]

Guys - all your answers DID help!!! Thanks - I just needed a very brief overview of it.

Thanks again!!!