Project 01 - DHS Access-Demand Decomposition for Immunisation

1) Decision Objective

Primary policy decision: determine which regions need demand-generation interventions versus service-delivery/access interventions first, to improve full immunisation fastest.

Unit of Analysis

Child-level outcome modeling with mother/household covariates and region-level hierarchical effects.

2) Latent Structure (Current Core)

Access: latent/partially latent dimension informed by MHAQI-style barriers.
Demand: modeled conditional on access and uptake behavior.
Trust/service reliability: proxied in current core, not explicitly separate latent factors.

3) Indicator Mapping

Access-side indicators include permission, money, distance, accompaniment, ANC/delivery proxies, wealth, and residence.

Outcome side uses dose indicators:

y_{i,d} in {imm_bcg, ..., imm_mcv1}

interpreted as uptake behavior conditional on schedule eligibility and access.

4) Missingness and Eligibility Handling

Dose values are set to missing for ineligible ages (schedule-based masking). For child i and dose d:

e_{i,d} = 1[age_i >= a_d^*], y_{i,d} = NA if e_{i,d} = 0

Downstream predictor steps use model defaults and complete-case behavior where required.

5) Access Model

Let A_i denote access propensity (or access probability scale):

logit(P(A_i = 1)) = alpha_0 + alpha^T x_i + u_{r(i)}

u_r ~ N(0, sigma_A^2)

with x_i including MHAQI-related constraints and sociodemographic covariates.

6) Demand Model (Conditional on Access)

For each dose d:

logit(P(D_{i,d}=1 | A_i=1)) = beta_{0,d} + beta_d^T x_i + v_{r(i),d}

v_{r,d} ~ N(0, sigma_d^2)

D_{i,d} captures demand-side uptake probability once access is available.

7) Access/Demand Decomposition

Observed dose-uptake probability is decomposed as:

P(y_{i,d}=1) = e_{i,d} * P(A_i=1) * P(D_{i,d}=1 | A_i=1)

Observed full-immunisation probability for eligible schedule S_i:

P_i^{obs} = prod_{d in S_i} P(y_{i,d}=1)

Counterfactual full-access probability:

P_i^{cf-access} = prod_{d in S_i} P(D_{i,d}=1 | A_i=1)

Region-level access gap:

Gap_r^{access} = E_i[P_i^{cf-access} - P_i^{obs} | r(i)=r]

Demand shortfall under full access:

Gap_r^{demand} = 1 - E_i[P_i^{cf-access} | r(i)=r]

8) Identifiability and Priors

Identifiability is maintained through latent scale constraints and fixed model structure (dose ordering plus hierarchical pooling).

Standardized latent dimensions.
Monotone dose/schedule logic constraints.
Domain-driven constraints for age and schedule plausibility.
Weakly informative priors for generic regression/random-effect components.

9) Validation and Robustness

Strongest model check:

PPC dose calibration by region + dropout-pattern PPC

Posterior predictive discrepancy form:

D = sum_{r,d} (y_bar_{r,d} - y_hat_{r,d})^2

10) Sensitivity Strategy

Threshold sweeps: 10 / 50 / 80 / 90 / 99.
Alternate model specifications (M1-M4).
Alternate latent item sets and prior choices.
Consistency via LOO + PPC agreement.

11) Biases, Uncertainty, and Interpretation Guardrails

Known Bias Sources

Vaccination measurement error (card vs recall).
Selection/survivorship effects.
Age-reporting noise.

Uncertainty Communication

95% credible intervals.
Probabilistic rankings.
Map overlays highlighting overlap/instability, not only point estimates.

Wrong-but-Plausible Interpretation to Avoid

"Low coverage implies low parental demand" can be false when access/service constraints are dominant.

12) Most Important Heterogeneity and Core Contribution

Most important subgroup heterogeneity dimensions: region, wealth/SES, urban-rural, and maternal education.

One-sentence contribution: The project provides a hierarchical, uncertainty-aware decomposition of child immunisation gaps into access and demand, enabling region-specific policy targeting.