Joint research project

Spatial partition models in the construction of maps for neonatal deaths in Minas Gerais

Project leaders
Fabrizio Ruggeri, Marcia Branco
BRASILE - CNPq - Conselho Nacional Desenvolvimento Cientifico y Tecnologico
CNR/CNPq 2012-2013
Thematic area
Biomedical sciences
Status of the project

Research proposal

The proposed project arises from the common interest of Italian and Brazilian researchers in developing innovative (Bayesian) statistical models to address issues in healthcare practice. The research stems from a recent discussion among the senior Italian and Brazilian researchers about aspects in neonatal mortality in a Brazilian state; they found out that different statistical methods, from their current or recent research, could be exploited to address the issues and propose new methodologies.

As discussed in [1], early neonatal deaths are closely related to the access to good quality prenatal, hospital delivery and newborn healthcare. In Minas Gerais, one of the healthiest Brazilian states with respect to economy, the early neonatal mortality rate (ENMR) is higher than in any other state of the southeast region of the country. Hospitals in the Minas Gerais state are heterogeneously distributed; this may result in various levels of neonatal mortality across the state's micro-regions. The coverage of information about births and infant deaths is also heterogeneous.

It is important to investigate early neonatal hospital mortality behavior, obtained from the Hospital Information System of the National Health System (SIH/SUS), and assess possible associations between its rate of occurrence and factors like care to pregnant women (such as number of doctors per person, percentage of children whose mother did seven or more prenatal doctor evaluations, percentage of population registered in the government program for family health assistance, etc.), socioeconomic conditions of the region (such as income distribution, percentage of population with salary below 50% of the minimum by law, level of analphabetism) and newborn characteristics (such as percentage of children born with low weight in the region). The SIH/SUS was used to obtain the number of births and deaths according to place of residence in the micro-regions of the Minas Gerais state in 1999-2001. Due to the heterogeneous characteristics of Minas Gerais, the early neonatal hospital mortality rate presents different behaviors throughout the state, originating clusters. In order to define an efficient policy to diminish the number of early neonatal deaths and properly distribute the financial resources, one of our main goals is to identify the clusters where the early neonatal hospital mortality rate presents similar behavior.

The geographical distribution of the number of early neonatal hospital mortality death can be studied through mapping as in [2] and [3], or considering clustering approaches as in [4] and [5]. The Poisson distribution is the usual model for count data, whereas gamma or log-normal prior distributions are considered to model the prior uncertainty about the relative risk. Here we plan to undertake a Bayesian approach since we are willing to incorporate information not only from data but also from experts; in a Bayesian framework both sources of information, expressed respectively by the likelihood and the prior distribution, are joined in the posterior distribution which will be used to perform inferences or make decisions.

Our main proposal is to extend the approach in [4] assuming a skew-log-normal prior for the relative risk and considering correlation among the clusters. The approach is based on spatial version of product partition models which allow to split a set (here all the micro-regions) into a cluster of homogeneous elements. The skew-log-normal distribution can be seen as a multiplicative contamination of the log-normal distribution. Thus another goal of this work is to measure the robustness (i.e. the lack of significant changes) of the Bayesian estimators for the number and positions of the clusters when letting the prior distribution for the relative risk vary in class (see [6]). We plan a novel cluster method based on the concentration function, a tool to compare distributions, used e.g. in [7] and in a chapter of [6]. Furthermore, we plan to apply the Bayesian nonparametric approach, via Dirichlet process and Dirichlet process mixture models, to define clusters. The use of the Dirichlet process allows for more flexibility with respect to a parametric model, simple simulations based on the "stick-breaking" technique and "natural" clustering since it chooses discrete distributions a.s.

The two teams combine different level of expertise, with senior and junior researchers in both. Furthermore, there are common fields of interest like Bayesian statistics and use of statistical methods in healthcare practice, although the focuses of the two teams are quite distinct and complementary within the project. The Brazilian team has a longstanding experience in developing new methods, and performing statistical analyses, based on product partition models, skewed distributions and, recently, in Bayesian robustness (e.g. [7]); furthermore, a member of the team has already studied, through a descriptive study, basic aspects of infant hospital mortality in Minas Gerais. The Italian team has a wide experience in Bayesian nonparametrics, inference on stochastic processes, with an increasing interest in issues in healthcare practice, like classifying hospitals according to in-hospital mortality of patients subject to acute myocardial infarction; furthermore, one of its members has been one of the pioneers of Bayesian robustness studies in the 90's (see [6]).

[1] Campos, D., Loschi, R.H. and França, E. (2007), Mortalidade neonatal precoce
hospitalar em Minas Gerais: associação com variáveis assistenciais e a questão da subnotificação, Revista Brasileira de Epidemiologia, 10, 223-38.
[2] Knorr-Held, L. and Ra²er, G. (2000), Bayesian detection of clusters and discontinuities in disease maps, Biometrics, 56, 13-21.
[3] Besag, J., York, J. and Mollié, A. (1991), A Bayesian image restoration, with two applications in spatial statistics, Annals of the Institute of Statistical Mathematics, 43, 1-20.
[4] Hegarty, A. and Barry, D. (2008), Bayesian disease mapping using product partition models, Statistics in Medicine, 27, 3868 - 3893.
[5] Denison, D.G.T. and Holmes, C.C. (2001), Bayesian partitioning for estimating disease risk, Biometrics, 57, 143-149.
[6] Rios Insua, D. and Ruggeri, F. (2000), Robust Bayesian Analysis, Springer, New York.
[7] Godoy, L. G. (2010), Análise bayesiana de sensibilidade sob distribuições a priori assimétricas, Ph. D. Theses, Universidade de São Paulo.

Research goals

The proposed project has two main goals: develop novel statistical models and apply them to a relevant problem in healthcare practice. We plan to build maps of neonatal hospital mortality, based upon clusters of micro-regions in the Minas Gerais state, using product partition models (PPMs) and a Bayesian nonparametric approach. In the former case, we plan to extend the approach by Hegarty and Barry (2008), considering correlation among the different clusters (which is a relevant research theme in PPMs nowadays) and introducing a robustness study (a novelty in PPMs) to check for influence of different prior specifications on clustering. This research will stem from the work of the Brazilian researchers in PPMs (which intrinsically define clusters), skew-log-normal distributions and Bayesian robustness (on which the senior Italian researcher has a longstanding experience). In the latter case, we plan to explore the possibility of applying Dirichlet processes (like in a recent work involving an Italian researcher about performance of hospitals with respect to survival of acute myocardial infarction patients) or semi-parametric mixture models (as studied by the other Italian researcher) to classify the micro-regions in clusters, as a "natural" consequence induced by the entertained nonparametric processes. We plan also to use the concentration function (studied by the recent Brazilian Ph.D. recipient and, extensively, by the senior Italian researcher) to compare distributions and define clusters out of it (this would be a new, challenging contribution). We will try to cooperate with local authorities to validate our models, get experts' opinions useful in a Bayesian statistical approach and discuss the findings of our research, with the aim of making an impact on their policy, if possible.

Last update: 27/11/2021