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Model Schematic

Source: vignettes/model-schematic.Rmd
model-schematic.Rmd

Schematic overview

The figure below summarises the modelling assumptions in vrcmort.

  • Covariates (especially conflict intensity and measures of system functioning) can affect both the latent mortality rate and the reporting completeness.
  • The latent mortality rate generates true deaths given exposure (population or person-time).
  • The reporting process governs what fraction of true deaths appear in VR.
  • The observed VR counts are modelled with a negative binomial likelihood around the expected value.

How to read the diagram

Nodes

  • Exposure Er,t,a,sE_{r,t,a,s} is the person-time at risk.
  • Latent mortality rate λr,t,a,s,g\lambda_{r,t,a,s,g} is the death rate per unit exposure.
  • True deaths Dr,t,a,s,gD_{r,t,a,s,g} are the deaths that truly occur.
  • Reporting completeness ρr,t,a,s,g\rho_{r,t,a,s,g} is the probability a true death is recorded in VR.
  • Observed VR counts Yr,t,a,s,gY_{r,t,a,s,g} are what you analyse.

Edges

  • The arrow from covariates to λ\lambda represents the mortality submodel, for example a positive effect of conflict on trauma mortality.
  • The arrow from covariates to ρ\rho represents the reporting submodel, for example conflict reducing the completeness of non-trauma registration.
  • The arrows from exposure and λ\lambda to DD represent the death-generating process.
  • The arrow from ρ\rho to YY represents under-reporting.

Key equation

The expected observed count is the product of exposure, latent mortality, and completeness:

μr,t,a,s,g=Er,t,a,s⋅λr,t,a,s,g⋅ρr,t,a,s,g. \mu_{r,t,a,s,g} = E_{r,t,a,s} \cdot \lambda_{r,t,a,s,g} \cdot \rho_{r,t,a,s,g}.

This is the mathematical representation of the idea that conflict can increase true mortality while reducing observed VR counts.

Where does age-selective reporting fit?

The base model includes an age-selective reporting penalty applied after conflict begins (usually only for non-trauma causes). In the diagram this is part of the reporting node ρ\rho.

A practical way to think about it is:

  • if the observed VR age distribution suddenly shifts younger,
  • and there is no plausible demographic explanation on the population side,
  • then the model will tend to attribute this to lower completeness for older ages.

The vignette Under-reporting and Age Structure goes through this in detail.