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Discussion Post-abortion contraception plays a critical role in the provision of quality PAC services. Conclusion Improving the reproductive health of PAC patients requires considerable efforts at policy, service delivery, and individual levels.
Appendix A: Model specification Appendix A1: A Model specification for ordered categorical data Our outcome variable is defined as whether a PAC patient received a highly effective contraceptive method 2 , or a less effective contraceptive method 1 , or whether they did not receive any method at all 0 , and is ordinal in nature.
The ordinal logit model is developed from the general form of the binomial models given as; 1 In ordinal logit regression, the event of interest is observing a particular contraceptive use or less.
Suppose are the ordered categories of contraceptive use, the odds for each category are defined as follows; In general, this can be described in the form 2 Let denote the ordinal contraceptive use for patient i from a facility in county.
Without loss of generality, the probability of an observation for an ordered logit model with county- level random effects can be defined as follows with the error term included;[ 48 ] 4 Rearranging the terms in the above model gives; Replacing the part in the above equation gives; 5 The above probability function can also be written in terms of latent linear response as; Where the errors follow a logistic distribution, gives the ordered logit model and are independent of the random effects.
Thus the likelihood contribution for each county is obtained by integrating out the random effects from the joint density and can be given as; 10 Where The above equation has no closed form.
Therefore, this is extended to the Bayesian framework such that the link function predictor is extended such that; The spatial Bayesian model is defined as follows; The full conditional distribution for our model can be expressed as 11 The prior for the beta coefficients in the model is , thus The unstructured random effects , where with a Gamma function prior used as shown by Banerjee [ 49 ] With a Gamma function prior used , then 12 A Continuous Autoregressive CAR prior is used for the structured spatial random effects.
Thus, as shown in Banerjee and Lawson [ 27 , 50 ]; 13 Within the spatial random effects model, it was considered that as much as facilities within one county are more similar to each other than to facilities in other counties, counties near each other are likely to have higher correlations than counties that are far away from each other. The likelihood of the neighbouring counties is therefore given as; where denotes the adjacency matrix and the subscript shows that the county is a neighbour of county and is the number of neighbours for county.
A Gamma distribution of the conjugate hyper prior is used and whose distribution function can be shown as; 14 Combining the equations above, a full conditional likelihood function for the spatial structured and unstructured model can be given as; 15 The above equation has no closed form and has to be approximated.
Goodness of fit Goodness of fit for all ordered logit models presented in this paper was evaluated by comparing the Deviance Information Criteria DIC value for each model as defined in [ 24 ] where is the posterior deviance expectation with effective parameters. Bivariate patient level characteristics. Appendix B Multivariable model. Supporting information. S1 File.
Acknowledgments The study on which we draw is based on research funded by the Consortium for Research on Unsafe Abortion in Africa and its principal donors, the UK Department for International Development, and the Government of the Netherlands. References 1. Abortion incidence between and global, regional, and subregional levels and trends.
Lancet [Internet]. Elsevier; ;— Ovulation resumption after medical abortion with mifepristone and misoprostol. United States; ;—3. Health [Internet].
Guttmacher Institute; ;—8. Borges ALV. Post-abortion contraception: effects of contraception services and reproductive intention. Saude Publica. Marston C. Creating linkages between incomplete abortion treatment and family planning services in Kenya. Stud Fam Plann [Internet]. Biney AAE. Exploring contraceptive knowledge and use among women experiencing induced abortion in the Greater Accra Region, Ghana.
Olenick I. JSTOR; ;— View Article Google Scholar Contraceptive use among women seeking repeat abortion in Addis Ababa, Ethiopia. Effect of previous induced abortions on postabortion contraception selection.
Marston C, Cleland J. Relationships between contraception and abortion: a review of the evidence. JSTOR; ;6— Kenya Demographic and Health Survey. Elsevier; ;—9. Schunmann C, Glasier A. Specialist contraceptive counselling and provision after termination of pregnancy improves uptake of long-acting methods but does not prevent repeat abortion: a randomized trial. Oxford University Press England; ;— Elsevier; ;—e1.
The effect of patient-centered contraceptive counseling in women who undergo a voluntary termination of pregnancy. Patient Educ. Elsevier; ;—8. Impact of post-abortion family planning services on contraceptive use and abortion rate among young women in China: a cluster randomised trial.
Kenya Service Provision Assessment Survey Nairobi, Kenya; Contraceptive technology. Ardent Media; Baltimore and Geneva; Stata Statistical Software: Release College Station, TX; Software for Bayesian inference in structured additive regression models.
Version 2. Basu S. Bayesian and Frequentist Regression Methods. Bayesian image restoration, with two applications in spatial statistics. Springer; ;— Lawson AB.
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