Select Page ## Linear Mixed Effects Analysis

Biostatistical Methods BioXpedia is proud to offer data analysis using linear mixed effects models.

This data analysis focuses on using linear mixed effects models to determine the effects of one or more variables of interest for time series data.

The data analyses includes the following components:

• Detailed PDF report.
• Data handling.
• Visualization of the time series data.
• Employment of linear mixed effects models.

One fundamental assumption in a lot of statistical models is, that the datapoints are independent. This is important if the data is analyzed as one single group of datapoints.

Data points are not always independent, though, and when they are not, it is important to account for this in the data analysis.

One common example of non-independent datapoints are timeseries data. If 100 patients are put on a diet and their blood pressure is measured every day for 20 days, this would yield 2000 datapoints. These 2000 datapoints would, however, not be independent. Even though it might be tempting to do simple linear regression on all datapoints to see the diet’s effect on the patients’ blood pressure, this violates the assumptions of linear regression. If a patient’s last blood pressure measurement was a systolic blood pressure of 125 mm Hg, then that patient is more likely to also have a high blood pressure in the next measurement. In independent data, information about the first measurement would not give any information about the second (Fokkema et al., 2018).

One simple solution to the problem of dependent datapoints, is to summarize the information in dependent datapoints into independent datapoint. In the example above the patients are randomly chosen, so summarizing the measurements from each patient e.g. by taking the average, would yield independent datapoints. The problem with this approach is, that the data has been reduced from 2000 data point to a single datapoint from each patient – 100 data points. A lot of information is lost, which makes it harder to reject a null hypothesis.

Another possibility is to analyze measurements from each patient separately. This means, fitting 100 models with only 20 datapoints in each model. This would likely lead to high variance in the models and it adds the trouble of comparing the results from 100 models.

Linear Mixed Effects Models allows for all the data to be used in one single model, even though the measurements are not independent. This means that analysis will have more power to reject a false null hypothesis.

Another advantage of Linear Mixed Effects Models is that they can correct for confounding variables and detect interaction between variables. Confounding variables are variables that are not included in the data but still has an effect on the response. This means that they can disturb the relationship between the explanatory variable and the response – the causal relationship. Interactions happen when the effect of two or more explanatory variables are not additive. That is, the effect on one variable on the response depends on the state of another variable (Sola-Soler et al., 2019).

1. Fokkema, M et al. “Detecting treatment-subgroup interactions in clustered data with generalized linear mixed-effects model trees.” Behavior research methods 50,5 (2018): 2016-2034