Relating multivariate time-series by linear three-way decomposition (LTD) and partial least squares (PLS) analysis

Area of Science:

• Multivariate statistics
• Chemometrics
• Pharmacometrics

Background:

• Drug development frequently involves analyzing complex multivariate time-series data.
• Relating such data often requires analyzing two three-way tables with shared objects and time-points but unique variables.
• Existing methods may not optimally leverage the commonalities between these tables.

Purpose of the Study:

• To address the challenge of relating multivariate time-series data in drug development.
• To present a modified linear three-way decomposition (LTD) algorithm that incorporates shared objects and time-points.
• To compare the modified LTD algorithm with partial least squares (PLS) analysis.

Main Methods:

• A modified linear three-way decomposition (LTD) algorithm was developed.
• The algorithm was designed to directly incorporate common objects and time-points across two three-way tables.
• The modified LTD was compared theoretically and practically with partial least squares (PLS) using three real datasets.

Main Results:

• The modified LTD algorithm effectively relates multivariate time-series data by leveraging common objects and time-points.
• The modified LTD demonstrated advantages over partial least squares (PLS) in applied analyses.
• Limitations of LTD, such as the trilinearity constraint, were identified.

Conclusions:

• The modified LTD algorithm offers an improved approach for analyzing drug development time-series data.
• The method effectively handles the complexity of relating two three-way tables with shared dimensions.
• Future research should explore relaxing the trilinearity constraint and expanding LTD applications.