Feature: Implement `Analyze_LinearMixedEffects()` for continuous type KRIs.

[ge-li]

Feature Details

The use cases for this method are similar to the use cases when Analyze_Wilcoxon.R are applicable.

Note: the current Analyze_Wilcoxon.R has issues because it only conducts cross-testing on the level of averaged center KRI values. See my previous issue #558 for details.

The method is proposed in Desmet et al. "Desmet et al. "Linear mixed-effects models for central statistical monitoring of multicenter clinical trials." Statistics in medicine 33.30 (2014): 5265-5279.

The advantage of this method is that the p-value cutoff in the flagging stage will be meaningful in the sense that it conservatively controls the false positive rate (so expect <= 5%) at the given level (0.05), whereas the thresholds for p-values produced by cross-tests will not be interpretable.

This method might become less powerful when the contamination rate (i.e., the proportion of true underlying atypical centers out of all centers) is high, and in the meantime, the departure of atypical centers to typical centers is also extreme.

Example Code

See the method implemented in {csmm} for example. https://github.com/Gilead-BioStats/csmm/blob/b92a50c0a81fa8286bd3ad1191bbf93d45c09274/R/lme_test.R

Possible Implementation

Refactor the example code so that it fits the current analyze_* function pipeline in {gsm}.

Additional Comments

Make sure to use the most up-to-date version in {csmm} for reference.

[mattroumaya]

@jwildfire @gwu05 - is it alright to close this one based on decision to pare down stats methods?

[Zhongkai-Wang]

@mattroumaya @gwu05 @jwildfire - I'm not sure what is our plan for continuous KRIs in the future? Anyway, I have copied the issue to {csmm}: https://github.com/Gilead-BioStats/csmm/issues/38

[mattroumaya]

Closing for now since it's documented in {csmm}, and stats methods are TBD.