Bayesian hierarchical model of abortions classification by safety

Global, regional, and subregional classification of abortions by safety, 2010–14: estimates from a Bayesian hierarchical model

всё, что нужно знать о байесовой иерархии, но страшно спросить,
можно найти в этой ланцетной статейке

data sources that informed the .estimation models:

обследования

Russian Federation (2006-2012)√√ Data point

Serbanescu F, Avdeev A, Traskaia I. Induced abortion in reproductive health survey Russia 2011: Final report draft. Atlanta, GA, USA: Federal State Statistic Service (ROSSTAT), and Centre for Disease Control and Prevention (CDC), 2013

+официальная статистика

DATA REPORTED FROM MINISTRIES OF HEALTH OR NATIONAL STATISTICAL

OFFICES

Russia (2013) √ Data point Ministry of Health, personal communication
трудно поверить, но так написано (с. 34)

из вики:
Bayesian hierarchical modelling is a statistical model written in multiple levels (hierarchical form) that estimates the parameters of the posterior distribution using the Bayesian method. The sub-models combine to form the hierarchical model, and the Bayes’ theorem is used to integrate them with the observed data, and account for all the uncertainty that is present. The result of this integration is the posterior distribution, also known as the updated probability estimate, as additional evidence on the prior distribution is acquired.
Frequentist statistics, the more popular foundation of statistics, has been known to contradict Bayesian statistics due to its (i.e., the Bayesian's) treatment of the parameters as a random variable, and its use of subjective information in establishing assumptions on these parameters. However, Bayesians argue that relevant information regarding decision making and updating beliefs cannot be ignored and that hierarchical modeling has the potential to overrule classical methods in applications where respondents give multiple observational data. Moreover, the model has proven to be robust, with the posterior distribution less sensitive to the more flexible hierarchical priors.
Hierarchical modeling is used when information is available on several different levels of observational units. The hierarchical form of analysis and organization helps in the understanding of multiparameter problems and also plays an important role in developing computational strategies.

по существу:

Background

Global estimates of unsafe abortions have been produced for 1995, 2003, and 2008. However, reconceptualisation of the framework and methods for estimating abortion safety is needed owing to the increased availability of simple methods for safe abortion (eg, medical abortion), the increasingly widespread use of misoprostol outside formal health systems in contexts where abortion is legally restricted, and the need to account for the multiple factors that affect abortion safety.

Methods

We used all available empirical data on abortion methods, providers, and settings, and factors affecting safety as covariates within a Bayesian hierarchical model to estimate the global, regional, and subregional distributions of abortion by safety categories. We used a three-tiered categorisation based on the WHO definition of unsafe abortion and WHO guidelines on safe abortion to categorise abortions as safe or unsafe and to further divide unsafe abortions into two categories of less safe and least safe.

Findings

Of the 55· 7 million abortions that occurred worldwide each year between 2010–14, we estimated that 30·6 million (54·9%, 90% uncertainty interval 49·9–59·4) were safe, 17·1 million (30·7%, 25·5–35·6) were less safe, and 8·0 million (14·4%, 11·5–18·1) were least safe. Thus, 25·1 million (45·1%, 40·6–50·1) abortions each year between 2010 and 2014 were unsafe, with 24·3 million (97%) of these in developing countries. The proportion of unsafe abortions was significantly higher in developing countries than developed countries (49·5% vs 12·5%). When grouped by the legal status of abortion, the proportion of unsafe abortions was significantly higher in countries with highly restrictive abortion laws than in those with less restrictive laws.

Interpretation

Increased efforts are needed, especially in developing countries, to ensure access to safe abortion. The paucity of empirical data is a limitation of these findings. Improved in-country data for health services and innovative research to address these gaps are needed to improve future estimates.

Funding

UNDP/UNFPA/UNICEF/WHO/World Bank Special Programme of Research, Development and Research Training in Human Reproduction; David and Lucille Packard Foundation; UK Government; Dutch Ministry of Foreign Affairs; Norwegian Agency for Development Cooperation.[список, конечно, заворажывает]