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Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills
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Derivation of a multivariate longitudinal causal effects model.

Halima S Twabi1, Samuel O M Manda2, Dylan S Small3

  • 1School of Natural and Applied Sciences, Department of Mathematical Science, University of Malawi, Zomba, Malawi.

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|September 10, 2025
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Summary

This study introduces a new causal inference method for longitudinal studies with multiple outcomes. The method, joint marginal structural models with inverse probability treatment weights (MSM-IPTWs), accurately estimates effects and found HIV awareness increases condom use.

Keywords:
MLSFHMultivariate outcomescausal effectsmarginal structural models

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Area of Science:

  • Biostatistics
  • Epidemiology
  • Causal Inference

Background:

  • Longitudinal observational studies with multiple outcomes present challenges in causal effect estimation.
  • Existing methods may not adequately address time-varying confounders, treatment exposures, and outcome correlations.

Purpose of the Study:

  • To develop and evaluate a novel causal inference method for longitudinal observational studies with multiple outcomes.
  • To estimate the causal effect of HIV positivity awareness on condom use and number of sexual partners.

Main Methods:

  • Proposed a joint marginal structural model with inverse probability treatment weights (MSM-IPTWs).
  • Weights are redefined as a product of inverse weights at each time point.
  • Method accounts for time-varying confounders, treatment exposures, and correlations between/within multiple outcomes.

Main Results:

  • Simulation studies showed the joint MSM-IPTW performs well with good coverage for large sample sizes and moderate to strong outcome correlations.
  • The method performed comparably to standard joint models when treatment effect estimates were consistent across outcomes.
  • Application to Malawi Longitudinal Study of Families and Health data indicated HIV positivity awareness increased condom use but did not affect the number of sexual partners.

Conclusions:

  • The proposed joint MSM-IPTW method is effective for estimating causal effects in longitudinal studies with multiple outcomes.
  • The method correctly controls for time-varying treatments and confounders.
  • HIV positivity awareness positively impacts condom usage, highlighting the importance of public health messaging.