Childhood Mortality in DRC: Bayesian Geo-additive Survival Model

1. OUTLINE • Background andcontext • The country in focus (DRC) 3. Geoadditive regressionmodels4. Applications: Results Childhood mortality in the Democratic Republic of Congo (DRC): An application of a Bayesian Geo-additive discrete-time survival model Ngianga-Bakwin Kandala, PhD Warwick Medical School, The University of Warwick N-B.Kandala@warwick.ac.uk

2. Crude under-five mortality rates by provincesOverall mortality rates: 148 death/per 1000 live birth Kinshasa , 31 Bas-Congo, 66 Bandundu, 57 Equateur, 74 Orientale, 100 Nord Kivu, 47 Sud Kivu, 68 Maniema, 103 Katanga, 66 Kasai Orientale, 68 Kasai Occidentale, 69

3. Background • Overall, the number of under-five deaths worldwide has declined from more than 12 million in 1990 to 7.6 million in 2010. • Nearly 21,000 children under five died every day in 2010 – about 12,000 fewer a day than in 1990. • The highest rates of child mortality are still in sub-Saharan Africa – where 1 in 8 children dies before age 5, more than 20 times the average for industrialized countries (1 in 167) – and South Asia (1 in 15). • As under-five mortality rates have fallen more sharply elsewhere, the disparity between these two regions and the rest of the world has grown. • Several factors (sanitary conditions, socio-economic factors, cultural, environmental and distal characteristics. etc.) Source: UN Inter-agency Group for Child Mortality Estimation, 20111

4. 70-fold difference Infant Mortality Rate (< 1 year of age) DR Congo: 205 WHO, The World Health Report 2006

5. Infant Mortality • A key measure of the health of any population, usually possible to measure even in very low income countries • Infant mortality has an important effect on the overall life expectancy of a population

6. Main objectives • Highlight provinces inequalities in child’s mortality in DRC • Investigate spatial patterns at a disaggregated provinces-level • Explore the effects of unobserved and unmeasured factors such as conflict using flexible Bayesian approach.

7. Why spatial analysis and geo-additive modelling? • A number of statistical models have been proposed when analyzing the risk of child mortality in the first five years of life and its determinants. • Time to event (death), and • To capture exposure to the risk of dying or follow the evolution of the subject’s state over time. • More appropriately, survival models (Cox) can be used to analyse the hazards of child survival. • Both the logistic and survival analysis can be implemented within the basic generalized linear models (GLM) framework.

8. Why spatial analysis and geo-additive modelling? • Cox and recent modern survival techniques have other advantages including analysis of censored and truncated response data, and time-varying effects. • The inclusion of random effects permits modelling of unmeasured and unobserved contextual factors in the models. • These may act at family, community, district, province or national levels since the underlying causes of neonatal mortality are multi-sectorial and complex. • Observations are spatially referenced

9. Spatio-temporal regression data • Regression in a general sense: – Generalised linear models, – Multivariate (categorical) generalised linear models, – Regression models for survival times (Cox-type models, AFT models). • Common structure:Model a quantity of interest in terms of categorical and continuous covariates, e.g. E(y|u) = h(u'γ) (GLM) or λ(t|u) = λ0(t) exp(u'γ) (Cox model) • Spatio-temporal data: Temporaland spatial informationas additional covariates.

10. Spatio-temporal regression models should allow: • - to account for spatialand temporal correlations, • - for time- and space-varyingeffects, • - for non-lineareffects of continuous covariates, • - for flexible interactions, • - to account for unobserved heterogeneity.

11. Geo-additive regression • General Idea: Replace usual parametric predictor with a flexible semi-parametric predictor containing: • – Nonparametric effects of time scalesand continuous covariates, • – Spatial effects, • – Interaction surfaces, • – Varying coefficient terms (continuous and spatial effect modifiers), • – Random intercepts and random slopes. • All effects can be cast into one general framework.

12. The observation model

13. The observation model cont’d

14. The observation model cont’d

15. The model • “Usual assumption for Generalised Linear Models” • Response: Binomial • Replace the linear predictor • By a semi-parametric geo-additive predictor

16. •Penalised splines. – Approximate f(x) by a weighted sum of B-spline basisfunctions. – Employ a large number of basis functions to enable flexibility. – Penalise differencesbetween parameters of adjacent basis functions to ensure smoothness. • 2 -1 0 1 2 • 2 -1 0 1 2 • 2 -1 0 1 2 -3 -1.5 0 1.5 3 -3 -1.5 0 1.5 3 -3 -1.5 0 1.5 3

17. . Spatial effect for regional data: Markov random fields. – Bivariate extension of a first order random walk on the real line. – Define appropriate neighbourhoodsfor the regions. – Assume that the expected value of fspat(s) is the average of the function evaluations of adjacent sites.

18. MCMC SIMULATION • Based on a flexible geo-additive model using the province as the geographic unit of analysis, which allows to separate smooth spatial structured effects from random effect. • Inference is fully Bayesian and uses Markov random field priors for spatial effect, P(enalised)-spline priors for nonlinear smooth effects and Deviance Information Criterion for model checking (Fahrmeir and Lang, 2001; Brezgeret al., 2005). • Implemented in the software package BayesX. • Available from http://www.stat.uni-muenchen.de/~bayesx

19. Childhood mortality in the DRC • Data from the 2007 Demographic and Health Survey (DHS) in the DRC. • Retrospective questionnaireon the health status of women in reproductive age and survival of their children. • Survival time of n = 8992 children with 1005 observed deaths • Numerous covariates including spatial information. • Analysis based on the Cox model:λ(t; u) = λ0(t) exp(u'γ).

20. • Limitationsof the classical Cox model: – Restricted to right censored observations. – Post-estimation of the baseline hazard. – Proportional hazards assumption. – Parametric form of the predictor. – No spatial correlations. ⇒ Geoadditive hazard regression.

21. Interval censored survival times • In theory, survival times should be available in days. • Retrospective questionnaire⇒ most uncensored survival times are rounded(Heaping). • In contrast: censoring times are given in days/months. • ⇒ Treat survival times as interval censored.

22. RESULTS

23. without interval censoring with interval censoring 0 500 1000 1500 survival time in days

24. Figure 1: Left: Estimated nonparametric effect of baseline hazard time of child survival. Right: Estimated nonparametric effect of mother’s age at child’s birth. Shown is the posterior mean within 80% credible regions.

25. Figure 1 Estimated OR of Structured (left) and unstructured (right) residual spatial provincial effects of child survival. Red – high prevalence Green – low prevalence

26. Figure 2 Estimated OR of total residual spatial provincial effects (left) and 95% posterior probability map (right) of survival. Black – significant positive effect Grey – not significant White – significant negative effect Red – high prevalence Green – low prevalence

27. Baseline characteristics by U5 mortality status

28. Baseline characteristics by U5 mortality status

29. Summary • We have shown that variation in childhood survival probability in DRC is spatially structured. • It implies that adjusted mortality risks are similar among neighbouring provinces, which may partly be explained by: • General health care conditions • common morbidity prevalence • common environmental/cultural risk factors • other explanation: variation in unmeasured province-specific characteristics such as conflict. • In the light of this, a standard multilevel model with random effects which assume independence among provinces is bound to yield bias estimates

30. ACKNOWLEDGEMENT: This work is supported by the British Council under the DelPHE (Development Partnership in Higher Education) scheme). Thank you to the IAS, University of Warwick for providing additional support

31. Comment rédiger un Article Scientifique dans une Revue Internationale ?Conférence débat organisée par le Secrétaire Général Académique avec la collaboration de l’Ecole Doctorale / ISTM KIN Animée par Prof. Ngianga – Bakwin KANDALA, Ph D Warwick Medical School, The University of Warwick N-B.Kandala@warwick.ac.uk • Jeudi 25/04/2019 à 12h30, le Secrétaire Général Académique entre au local 18 qui affiche complet pour un début de la conférence débat portant sur « Comment rédiger un Article Scientifique dans une Revue Internationale ? » • Après la présentation de l’orateur par Professeur MBADU membre de l’Ecole doctorale, le Professeur N-B KANDALA a présenté ses civilités aux participants. • L’article scientifique qui a servi de modèle est intitulé «Childhood mortality in the Democratic Republic of Congo (DRC): An application of a Bayesian Geo-additive discrete-time survival model” publié au BMC Public Heath • Structuré de l’article : Abstract (Résumé) composé de : - Background ( 300 mots) qui explique la problématique, le contexte de l’étude ; la revue de la littérature devra aider à présenter le problème.

32. Methods : présente les sources de données et les méthodes statistiques utilisées pour exploiter les informations. La collaboration avec d’autres scientifiques est indispensable afin de mieux exploiter et présenter les données. • Resultats : cette partie expose les résultats obtenus au regard des variables définies et d’autres études de la sous région. • Conclusion : on formuler les recommandations aux décideurs afin d’inclure dans la politique de santé du pays avec l’objectif principal de réduire la mortalité infantile • Après ce résumé, le Prof. KANDALA est passé à la description détaillée de ces quatre points du résumé, puis a suivi le débat très animé. CT Robert KIBALE Participant