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Mixed Linear Models

Mixed Linear Models. An Introductory Tutorial. Mixed Models in Context. Other options for longitudinal Repeated Measures ANOVA MANOVA GEE (we won’t talk about this) Univariate analysis of Longitudinal Data ANCOVA Change score. Drop out and You.

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Mixed Linear Models

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  1. Mixed Linear Models An Introductory Tutorial

  2. Mixed Models in Context • Other options for longitudinal • Repeated Measures ANOVA • MANOVA • GEE (we won’t talk about this) • Univariate analysis of Longitudinal Data • ANCOVA • Change score

  3. Drop out and You Drop out is a reality in any study, and so far we have ignored it. Drop out creates missing values in a subjects data. Some data analysis methods deal with this better than others Why do subjects drop out • Missing Completely At Random: MCAR • Drop out is completely unrelated to the outcomes of interest • e.g. Poor record keeping, Forgot to administer the measure, Moving • Missing At Random: MAR • Drop out is related to the observed outcomes • e.g. Subjects with a poor outcome at baseline tend to drop out • Missing Not At Random: MNAR • Drop out is related to unobserved outcomes (Bad news for the data analyst) • e.g. Subjects whose outcome decreases after a visit are less likely to come in for the next one Mixed models are okay if the drop out is either MCAR or MAR

  4. Drop out in Citalopram So there were 102 subjects at baseline, and 74 at week 12. Thus 27% of our subjects drop out

  5. Repeated Measures ANOVA (rANOVA) • A group by time rANOVA is similar to our random intercept model. • Time is treated as a factor (I.e. dummy coded) • Hypotheses that can be tested are: • Different treatment progressions • Pair wise comparisons / endpoint / change from baseline • Sphericity (Compound Symmetry) is assumed • All time points have equal correlation to all other time points (slightly more complicated, but essentially this) • Missing completely at random is assumed is assumed • Each subject must be observed at all time points to be included in analysis. • Option 1: Analyze only the complete cases • Option 2: Impute values into the missing time points (e.g. Last Observation carried forward (LOCF)

  6. MANOVA • A MANOVA is similar to a treatment by time mixed model with unstructured covariance • Time is treated as a factor (i.e. dummy coded) • Hypotheses that can be tested are: • Different treatment progressions • Missing completely at random is assumed is assumed • Each subject must be observed at all time points to be included in analysis. • Option 1: Analyze only the complete cases • Option 2: Impute values into the missing time points (e.g. Last Observation carried forward (LOCF)

  7. ANCOVA • Analysis of the last observation • Covariate on the baseline observation to increase precision • Hypothesis tested is: • Are subjects different at the last time point • Missing completely at random is assumed is assumed • Each subject must be observed at all time points to be included in analysis. • Option 1: Analyze only the subjects that make it to the end • Option 2: Analyze the last observed time point for each subject

  8. Change score • Analysis of the change score (Y at endpoint – Y at baseline) • t-test of the change scores • Hypothesis tested is: • Are subjects different at the last time point • Missing completely at random is assumed is assumed • Each subject must be observed at all time points to be included in analysis. • Option 1: Analyze only the subjects that make it to the end • Option 2: Analyze the last observed time point for each subject as the endpoint

  9. Random Intercept Mixed model vs. rANOVA HAM: 3 time points. Treatment vs placebo Random intercept MM rANOVA: Complete cases

  10. Unstructured Mixed vs. MANOVA Mixed model: UNR MANOVA: Complete Cases

  11. Mixed model vs. ANCOVA ANCOVA with complete cases Mixed model with unstructured errors

  12. Change Score Mixed Model t-test

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