<p>Separate and marginal model for malaria.</p>

This approach allowed for the simultaneous modeling of the marginal probability of each illness and the latent correlations among them. The model incorporated a range of child-, household-, and maternal-level covariates. Average Marginal Effects (AMEs) were calculated to facilitate interpretation.

The copula correlation (ρ) between anaemia and malaria from the copula structure was estimated to quantify the dependence between the two illnesses. Descriptive analyses revealed substantial co-occurrence: 13.8% of children experienced both illnesses simultaneously. The joint copula model detected significant positive copula correlations (ρ ≈ 0.19) between anaemia and malaria.

Several covariates displayed differential effects in the joint versus separate models. For instance, the association between maternal anaemia and child malaria risk reversed direction once interdependence was accounted for. Joint modeling yielded more stable and plausible estimates across outcomes.

This study highlights the critical importance of accounting for outcome dependence in the analysis of child morbidity. The significant correlations among malaria and anaemia suggest that these illnesses are influenced by common or interacting risk factors. Joint modeling using a Gaussian copula framework enhances both the precision of marginal effect estimates and the understanding of comorbidity patterns.

These findings support the design of integrated health interventions that address the interconnected nature of childhood illnesses in high-burden settings.</p></div>