Table 4 Final model to predict crude death rate, South Sudan (2013–2018)

Intercept

0.00014

0.00008 to 0.00022

 < 0.001

Region

Northeast

[Ref.]

Northwest

0.54

0.41 to 0.72

 < 0.001

Southern

0.80

0.51 to 1.25

0.326

Main livelihood type

Agriculturalists

[Ref.]

Agro-pastoralists

0.82

0.55 to 1.22

0.329

Pastoralists

1.24

0.69 to 2.23

0.478

Displaced to Protection of Civilians camps

0.52

0.34 to 0.81

0.004

Rate of insecurity events (per 100,000 people per month, lag = 4 months)

0

[Ref.]

0.01 to 0.99

1.16

1.02 to 1.32

0.021

 ≥ 1.00

1.32

1.08 to 1.62

0.008

Uptake of measles vaccine (doses administered per 100,000 people per month)

0

[Ref.]

0.1 to 199.9

0.83

0.69 to 0.99

0.042

200.0 to 399.9

0.76

0.60 to 0.97

0.025

 ≥ 400.0

0.56

0.43 to 0.74

 < 0.001

Terms of trade purchasing power index (Kg of white wheat flour that an average goat can be exchanged for; 3 months running average, lag = 3 months)

0.992

0.987 to 0.996

 < 0.001

Rate of violent incidents affecting humanitarian staff (per 100,000 per month, lag = 4 months)

0

[Ref.]

 ≥ 0

1.19

1.04 to 1.36

0.010

Incidence rate of confirmed or probable measles cases (per 100,000 per month)

0

[Ref.]

 ≥ 0

1.30

1.15 to 1.47

 < 0.001

Dawid–Sebastiani score (internal prediction)

\(\frac{{\left( {{\text{observed }} - {\text{predicted}}} \right)^{2} }}{{{\text{variance}}}} + 2 \times \log \left( {{\text{variance}}} \right)\)

Dawid–Sebastiani score (out-of-sample prediction)

Based on tenfold cross-validation (CV)

Relative bias (on CV)

\(\frac{{{\text{predicted}} - {\text{observed}}}}{{{\text{observed}}}}\)

Relative 95% precision (mean across strata on CV)

\(\frac{{0.5 \times \left( {{\text{upper}} 95\% {\text{CI}} - {\text{lower}} 95\% CI} \right)}}{{{\text{predicted}}}}\)

Coverage of 80% confidence intervals (on CV)

Proportion of stratum observations falling within the confidence interval of the prediction

Coverage of 95% confidence intervals (on CV)