Trajectory analysis incorporating non-response weights via a non-parametric feature-based approach and a Bayesian finite mixture model approach

Author

Samia Sultana

Date

2025

Document Type

Dissertation

Degree Name

Doctor of Philosophy

Department

Public Health

Committee Chair

Meredith Ray

Committee Member

Drew Westmoreland

Committee Member

Hongmei Zhang

Committee Member

Yu Jiang

Abstract

While conducting longitudinal population-based research, the most insight concerning a phenomenon can be achieved by analyzing the changing patterns of outcomes over time, rather than depending on overall measures that may mask significant within- and between-individual variation. Trajectory analyses address this need by grouping individuals into sub-populations with similar temporal patterns. In population surveys, dropout and wave non-response can distort estimated trajectories and their prevalence. Non-response weights, defined as the inverse probabilities of response, adjust the representation of under-represented individuals and mitigate the impact of over-represented ones, so restoring the population representativeness of the resultant patterns. Nonetheless, conventional trajectory analysis approaches seldom incorporate weights, and often produce descriptive rather than inferential clusterings. This dissertation presents two methodologies for identifying groups of individuals with similar longitudinal patterns while explicitly incorporating non-response weights into trajectory analysis. These methods included a traditional non-parametric feature-based trajectory analysis approach and a Bayesian finite mixture model approach. The first approach adapts the non-parametric, feature-based method implemented in the R package traj, which partitions subjects by summary measures. Individual trajectories are summarized by change indices, reduced via principal component analysis (PCA), and then clustered using k-means. Since the original traj algorithm does not natively incorporate weights or extend beyond a default linear summary, we extend the implementation to (i) support polynomial summaries (linear, quadratic, and cubic) and (ii) allow weighting throughout each model type. In simulation studies, the method recovered the correct number of clusters and achieved high accuracy in scenarios with well-separated patterns, with broadly similar behavior under weighted and unweighted runs. The real data analysis of log-transformed AUDIT scores from the Together 5,000 cohort revealed two trajectories (both cubic) characterized by different levels and trends in the later era; both weighted and unweighted mean curves were visually analogous, indicating equivalent cluster sizes and minimal weight variation. Motivated by the limitations of our first approach, in our second approach, we proposed a Bayesian finite–mixture model framework that models trajectories directly as linear, quadratic, or cubic functions of time while scaling error variances by the non-response weights. The method automatically determines the number of clusters using the birth-death clustering algorithm, yields interpretable coefficients with uncertainty, and natively incorporates weights. Simulation studies demonstrated nearly perfect outcomes for clustering for two and three clusters, and decent accuracy for four clusters with overlap, with weighting yielding a modest although constant improvement in stability. In the T5K real data investigation, the weighted model demonstrated improved separation and added dynamics compared to the unweighted version, indicating that weights improve cluster assignments and enhance the population representativeness of detected patterns.

Comments

Data is provided by the student.”

Library Comment

Dissertation or thesis originally submitted to ProQuest.

Notes

Open Access

Recommended Citation

Sultana, Samia, "Trajectory analysis incorporating non-response weights via a non-parametric feature-based approach and a Bayesian finite mixture model approach" (2025). Electronic Theses and Dissertations. 3906.
https://digitalcommons.memphis.edu/etd/3906