Study setting

The data are drawn from the Incidence and Magnitude of Unsafe Abortion (IMUA) study conducted in 2012 in Kenya, targeting a nationally representative sample of 350 facilities. The Ministry of Health in Kenya classifies public and private healthcare facilities providing preventive and curative services into six categories based on their operational capacity. These classifications are community health services (Level I); primary care facilities (Level II and III) comprised of dispensaries, clinics, health centers and maternity homes; county referral health facilities (Levels IV and V), comprised of district/county hospitals, sub-district/sub-county and provincial hospitals; and Level VI (comprised of national referral and teaching hospitals) [20]. As at January 31, 2012, when sampling was undertaken, there were a total of 2,838 facilities classified as between Level II (the lowest level of healthcare facilities) and Level IV (the highest referral level).

Sampling

According to the IMUA Study whose data is used in this analysis, the sample of 350 facilities allowed for detection of a 10% difference in the severity of complications. Sampling fractions ps = 0.1233 (350 out of 2,828 facilities), together with survey response rate pr = 94% (328 out of 350 facilities), were used to compute sampling weights used in this analysis sw = 1/ (ps*pr) = 8.6279. These sampling weights were then normalized and applied differentially for all facilities in the same strata, according to facility level and geographic location. The study collected data from 328 facilities (94 in Level II, 124 in Level III, 94 in Level IV, 14 in Level V and 2 in Level VI); 22 of the 350 sampled facilities did not participate in the study. The sample was stratified by both facility level and region.

Data

Data were collected from all participating facilities and all PAC patients treated in these facilities over a 30 day period in each facility. Data collection was conducted between April and August 2012. Field interviewers collected facility information by interviewing facility managers or senior staff informed about PAC service delivery in these facilities. Data collected included facility’s infrastructure for PAC, staff training on PAC, number of cases the facilities managed in an average/typical month, common practices of services offered to PAC patients, and information on how these facilities cope with demands for PAC services. One or two PAC service providers in each facility were identified and trained to collect data on all PAC patients who presented in these participating facilities. These service providers collected data from their PAC patients using fully structured questionnaires on women’s socio-economic background characteristics, fertility experiences and planning, contraceptive use, and abortion histories, as well as data on the step-by-step management of these patients until they were discharged from their facility. By the end of the data collection period, the study had gathered patient data for 2,568 patients who sought PAC over the 30 days at 281 of the 328 participating facilities, with the other 47 facilities either not reporting any PAC cases during the observation period, or only reporting cases of patients that sought termination of pregnancy. This study focuses on post-abortion care patients only in order to assess the management of patients presenting with complications resulting unsafe abortions. Consequently, an additional 466 patients (15.4%) who sought termination of pregnancies were excluded from this analysis.

Variables

The primary outcome variable, contraceptive use, was based on responses to three questions on whether a patient treated for PAC received a modern contraceptive method: 1) whether the patient was counseled for FP before leaving the health facility: 2) whether the patient was given a modern method of FP before leaving the health facility; and 3) type of contraceptive method the patient received. The outcome variable is defined as a patient who was counseled for and given a highly effective method of FP. All other patients were classified into those who received a “less effective” method or no method at all. According to Hatcher’s classification of contraceptives based on use or actual effectiveness rather than theoretical effectiveness [21], highly effective contraceptive methods include methods that, irrespective of user’s compliance or consistency, reduce pregnancy risk by 99%. These include only long-acting and reversible contraceptives (LARCs) or long-acting and permanent methods (LAPM) that guarantee high efficacy for pregnancy prevention in typical use scenario. These include contraceptive implants, IUCD, and female sterilization [11,22]. These methods all address user challenges related to human error, distance to health facility, and inconsistent use. This outcome variable is considered ordinal, measuring a latent continuum of the efficacy of a contraceptive method in preventing unintended or unwanted pregnancy. A patient discharged on a highly effective method is therefore considered at the lowest risk of repeat abortion, while one who received a less effective method is at moderate risk. A patient who did not receive any method was considered to be at the highest risk of unintended pregnancy and hence at risk of repeat abortion. Since data collection was completed by service providers, who were integral in determining whether a patient received a highly effective contraceptive method or not, we measured certain provider and facility characteristics that we hypothesized influenced this outcome of interest. These include facility level, ownership, whether a facility had a gynecological or FP unit, number of staff trained to offer PAC, and whether or not such trained providers were always available to attend to PAC patients. We also considered demographic information of the main service provider at the facility: gender, age, and duration of service in the facility.

At the county-level, data were collected on three main categories. Proximate determinants of contraceptive use measures of health care seeking behavior and socio-economic determinants of contraceptive use were both considered. Among these variables were measures such as county level of unmet need for contraception, fertility intention, and exposure to contraceptive information. We also included a measure of women’s agency in decision-making for contraceptive use and community-level measures of access to healthcare, such as the percent of deliveries conducted by a skilled provider and the number of pregnant women in the past five years who received a tetanus toxoid injection. Finally, to account for any socio-economic variability among the counties, a measure of county level religious affiliation was considered, by including the percentage of Christians (the main religion in the country), a relative self-reported measure of food security, household size, and a measure of county-level of investment in health through county budgetary allocation to health. These measures were first tested for serial correlation and then selected based on the level of correlation between each other, using a 0.7 correlation coefficient cutoff with any other variable within the above three subcategories.

Survey ethics considerations

The parent study on which this analysis is based was reviewed and approved by the Ethical Review Boards of the Kenya Medical Research Institute, the University of Nairobi/ Kenyatta National Hospital, Moi University Teaching and Referral Hospital, Kenya, and Aga Khan University, Kenya.

In addition to these ethics reviews, the Ministries of Public Health and Sanitation and Ministry of Medical Services (now both under Ministry of Health) in Kenya and the Institutional Review Board of the Guttmacher Institute also reviewed and approved the study. During the collection of field data, verbal consent was obtained from all women presenting for care prior to data collection, while written consents were obtained from all facility managers who were interviewed for the facility component. As per the requirements of the ethics boards, all verbal consents were recorded in the data collection tool by reading the consent statement and allowing the respondent to confirm their consent to participate. The interviewer then signed on the data collection tool that consent had been obtained. In this study, minors were considered as emancipated by virtue of having been pregnant, as per the Kenya adolescent research guidelines. Data collectors and service providers were all taken through the research ethics in human participant surveys, with attention to the key elements of respect, beneficence, and justice in research on human subjects. All participants were assured of strict confidentiality.

Data management and analysis

All data were obtained for analysis in the form of Stata datasets. Initial consistency checks and data re-coding were conducted in Stata 13 [23]. All new variables were generated, tested for consistency with original variable, and stored as new variables while maintaining the original variables. Descriptive statistics of the facility and service provider characteristics were computed and are presented in Table 1 (below). All analysis conducted to produce descriptive statistics were weighted using the survey weights in order to account for the survey design.

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Table 1. Description of healthcare facilities according to facility and service provider characteristics, 2012.

https://doi.org/10.1371/journal.pone.0214049.t001

Statistical modeling was first conducted in Stata 15 using bivariate and multivariable mixed-effects ordered logit models in the Bayesian framework using Stata and OpenBUGS software [24]. Bayesian statistics have in the recent past demonstrated critical advantages over maximum likelihood estimation procedures [25]. This includes Bayesian ability to assign prior information to data, without overreliance on available data alone.

The outcome variable is ordinal, and use of ordered logit models extends the logistic regression models to allow for modeling data which assumes an underlying sequentially incremental nature of a rather categorical outcome. We further considered the use of mixed effects models because theoretically, women treated in one facility (women nested in facilities), as well as those treated in facilities that are in the same county (facilities nested in counties) have more similar treatment experiences than women treated elsewhere. In this analysis, the second level of nesting of facilities in counties was ignored because there were too few facilities in some counties to provide any meaningful structural variability at that level. The final models therefore considered only two levels of women nested in counties, while assuming constant variability between and within facilities.

To account for the multilevel nature of these data, we introduced unstructured random effects in order to capture unobserved non-spatial heterogeneity [25]. Subsequently, we fitted an ordered logit model with structured random effects, using a conditional autoregressive (CAR) model to account for the spatial dependency between counties that are close to each other than those that are far apart [26,27]. Finally, we fitted a convoluted model, combining both the above unstructured and structured spatial random effects in our final model, a special flexibility provided within the framework of Bayesian estimation models [28]. All covariates were first tested for inclusion at 85.0% credibility interval, where initial bivariate models were fitted and all variables that were significant at this more relaxed credibility interval (85%) were considered for inclusion in the final model. Only facility ownership (public/private) failed to meet this inclusion criterion, but we still included this due to its contextual importance to this study.

Within each model, deviance information criterion (DIC) was used to compare models based on goodness of fit, with models with the lowest DIC value having the best fit. Posterior estimates from these models were plotted on county maps in ArcGIS software [29] to visualize the geographical or regional variability in the adoption of highly effective contraceptive methods by PAC patients in health care facilities.

Conclusion

Improving the reproductive health of PAC patients requires considerable efforts at policy, service delivery, and individual levels. These efforts must aim to empower patients to make an informed choice of whether to use contraception and to choose the type of contraception which best suits their reproductive needs. At the policy level, there is a need to focus on service provider skills that are sensitive to patients’ needs and ability to make decisions, and on barriers that influence choice. Widespread service provider empowerment through capacity building for PAC, infrastructural improvement, and contraceptive commodity options, and their secured availability, are paramount in ensuring that they can interact better with patients and can deliver quality PAC services. Together with their availability to offer PAC, service providers can achieve these desirable contraceptive outcomes through effective counseling and contraception to reduce the risks of method failure. This can be attained by opting for methods whose effectiveness are less dependent on patient compliance, such as pills, condoms and injectable contraceptives, and focusing on methods with guaranteed effectiveness soon after a PAC procedure. At the patient level, effective counseling of PAC patients requires understanding the patient’s past experience with contraception and future fertility intentions and desires, in order to meet their needs more specifically. Finally, family planning integration with PAC will ultimately reduce missed opportunities, while promising improved reproductive health outcomes of post-abortion care patients. The potential relationship between the spatial effects on uptake of effective contraception, showing a higher uptake in regions with more health interventions in HIV/AIDS treatment and prevention presents an opportunity for further investigation.

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. In addition, patients treated in a particular facility are more likely to have more similar characteristics compared to patients treated in other facilities. Similarly, facilities in one county are likely to have certain characteristics that make them more similar than facilities in other counties while counties close by are likely to exhibit similar characteristics compared to counties that are far apart. We use hierarchical ordered logit models in our analysis, with two levels of random variation by facility and county. 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 . In general, the probability that a patient response will fall in a category higher than is; (3) Where are the counties consisting of patient observations in county . The cut points are labelled for possible outcomes. are the fixed predictors in the model with regression coefficients . These predictors do not contain the constant term since the cut-off points absorb the effects of the constant term. The random effects are assumed to have a multivariate normal distribution.

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 in terms of the binomial distribution and logit model can be written as; (6) Where is defined as and is defined as .

Within the counties, the outcome variable has a conditional distribution of given the county random effects , which is defined as; (7)

And taking the natural logarithms and replacing with its likelihood is expressed as follows’ (8)

Where;

The full log-likelihood function is defined as; (9)

The prior distribution of is multivariate normal with mean zero and a 47 by 47 variance matrix . 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. It can therefore be approximated for the maximum likelihood estimation using mean–variance adaptive Gauss–Hermite quadrature and Laplacian approximation crossed random-effects models.

The initial Bayesian models were fitted within Stata 14, but Stata does not cater for spatial random effects. 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 . The CAR prior is given as and a conjugate hyper prior of was assumed. 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. The approximation of the parameters was done using Markov Chain Monte-Carlo (MCMC) with Metropolis-Hastings algorithms approach. For the bivariate models in Stata, a burnin and thinning of 1000 and 10 respectively were used, while the multivariable model as well as the structured and spatial models were fitted in WINBUGS. In this algorithm, burnin removes unstable values while thinning reduces the autocorrelation.

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. The model that produced the smallest DIC value was considered to be better than its comparators with higher DIC.

Appendix B1:- STATA Bayesian MEOLOGIT models

Appendix B2:- Unstructured random effects model

model {

for (i in 1:N) {# open the loop

       contra_n[i] ~ dcat (p[i,])

      p[i, 1] <- 1/ (1 + exp (-cA[1] + mu[i]))

      p[i, 2] <- 1/ (1 + exp (-cA[2] + mu[i])) - 1/ (1 + exp (-cA[1] + mu[i]))

      p[i, 3] <- 1–1/ (1 + exp (-cA[2] + mu[i]))

D[i] <- m[1]*equals(education[i],1) + m[2]*equals(education[i],2) + m[3]*equals(education[i],3) +m[4]*equals(occupation[i],2) + m[5]*equals(occupation[i],3) + m[6]*equals(occupation[i],4) +

m[7]*equals(severity[i],2) + m[8]*equals(severity[i],3) + m[9]*equals(gestation[i],2) + m[0]*(referred[i]) + m[11]*(public[i]) + m[2]*(obygyn[i])

E[i] <- q[1]*(problem[i]) + q[2]*(strained[i]) + q[3]*(lnpacstafftrained[i]) + q[4]*(qual_index[i]) + q[5]*(unmetneedfp[i]) + q[6]*(fpradio3months[i]) + q[7]*(ancskillprov[i]) + q[8]*(tt2[i]) + q[9]*(lackf7days[i])

A[i] <- s[1]*(lev46[i]) + s[2]*(evacuation[i]) + s[3]*(maternity[i]) +s[4]*(method_count[i]) + s[5]*(calloc2[i])

mu[i] <- b[1]*equals(age4[i],2) + b[2]*equals(age4[i],3) + b[3]*equals(marital[i],2) +b[4]*equals(marital[i],3) +b[5]*equals(religion[i],2) + b[6]*equals(religion[i],3) +b[7]*equals(religion[i],4) +b[8]*equals(gravidity[i],2) + b[9]*equals(gravidity[i],3) + b[10]*(prev_abortion[i]) +b[11]*equals(modern[i],1) + b[12]*equals(wanted[i],2) + b[13]*equals(wanted[i],3) + b[14]*equals(wanted[i],9) + A[i] + D[i] +E[i] +u[county[i]]+ f[facility[i]]

       }

for (k in 1:47) {

u[k] ~ dnorm(0, tau.h)

           }

for (i in 1:14) {

b[i]~dnorm(0,0.001)

              }

for (i in 1:5) {

s[i]~dnorm(0,1.0E-6)

              }

for (i in 1:9) {

q[i]~dnorm(0,1.0E-6)

              }

for (i in 1:12) {

m[i]~dnorm(0,1.0E-6)

              }

tau.b ~ dgamma(0.5, 0.0005)

sigma.b <- sqrt(1/tau.b)

tau.h ~ dgamma(0.5, 0.0005)

sigma.h <- sqrt(1/tau.h)

for (j in 1:281) {

   f[j] ~ dnorm(0.0,tauv)

   }

  cA[1] <- g[1]

   cA[2] <- g[1] + g[2]

   g[1] ~dnorm(0,0.01)

   #g[2] ~dnorm(0,0.01)

   g[2] ~ dgamma(0.001, 0.001)

   tauv ~ dgamma(0.001, 0.001) # prior structured

    }

Appendix B3:- Structured random effects model

model {

for (i in 1:N) {# open the loop

       contra_n[i] ~ dcat (p[i,])

      p[i, 1] <- 1/ (1 + exp (-cA[1] + mu[i]))

      p[i, 2] <- 1/ (1 + exp (-cA[2] + mu[i])) - 1/ (1 + exp (-cA[1] + mu[i]))

      p[i, 3] <- 1–1/ (1 + exp (-cA[2] + mu[i]))

D[i] <- m[1]*equals(education[i],1) + m[2]*equals(education[i],2) + m[3]*equals(education[i],3) +m[4]*equals(occupation[i],2) + m[5]*equals(occupation[i],3) + m[6]*equals(occupation[i],4) +

m[7]*equals(severity[i],2) + m[8]*equals(severity[i],3) + m[9]*equals(gestation[i],2) + m[0]*(referred[i]) + m[11]*(public[i]) + m[12]*(obygyn[i])

E[i] <- q[1]*(problem[i]) + q[2]*(strained[i]) + q[3]*(lnpacstafftrained[i]) + q[4]*(qual_index[i]) + q[5]*(unmetneedfp[i]) + q[6]*(fpradio3months[i]) + q[7]*(ancskillprov[i]) + q[8]*(tt2[i]) + q[9]*(lackf7days[i])

A[i] <- s[1]*(lev46[i]) + s[2]*(evacuation[i]) + s[3]*(maternity[i]) +s[4]*(method_count[i]) + s[5]*(calloc2[i])

mu[i] <- b[1]*equals(age4[i],2) + b[2]*equals(age4[i],3) + b[3]*equals(marital[i],2) +b[4]*equals(marital[i],3) +b[5]*equals(religion[i],2) + b[6]*equals(religion[i],3) +b[7]*equals(religion[i],4) +b[8]*equals(gravidity[i],2) + b[9]*equals(gravidity[i],3) + b[10]*(prev_abortion[i]) +b[11]*equals(modern[i],1) + b[12]*equals(wanted[i],2) + b[13]*equals(wanted[i],3) + b[14]*equals(wanted[i],9) + A[i] + D[i] +E[i] +u[county[i]]+ f[facility[i]] + sp[county[i]]

    }

for (k in 1:47) {

u[k] ~ dnorm(0, tau.h)

            }

sp[1:47] ~ car.normal(adj[], weights[], num[], tau.b)

for (k in 1:sumNumNeigh)

            {

weights[k] <- 1

            }

for (i in 1:14) {

b[i]~dnorm(0,0.001)

            }

for (i in 1:5) {

s[i]~dnorm(0,1.0E-6)

            }

for (i in 1:9) {

q[i]~dnorm(0,1.0E-6)

            }

for (i in 1:12) {

m[i]~dnorm(0,1.0E-6)

            }

tau.b ~ dgamma(0.5, 0.0005)

sigma.b <- sqrt(1/tau.b)

tau.h ~ dgamma(0.5, 0.0005)

sigma.h <- sqrt(1/tau.h)

for (j in 1:281) {

    f[j] ~ dnorm(0.0,tauv)

    }

    cA[1] <- g[1]

    cA[2] <- g[1] + g[2]

    g[1] ~dnorm(0,0.01)

    g[2] ~ dgamma(0.001, 0.001)

    tauv ~ dgamma(0.001, 0.001)

      }

Appendix B4:- Convolution (Structured and unstructured) random effects model

model {#open the model

for (i in 1:N) {

       contra_n[i] ~ dcat (p[i,])

      p[i, 1] <- 1/ (1 + exp (-cA[1] + mu[i]))

      p[i, 2] <- 1/ (1 + exp (-cA[2] + mu[i])) - 1/ (1 + exp (-cA[1] + mu[i]))

      p[i, 3] <- 1–1/ (1 + exp (-cA[2] + mu[i]))

D[i] <- m[1]*equals(education[i],1) + m[2]*equals(education[i],2) + m[3]*equals(education[i],3) +m[4]*equals(occupation[i],2) + m[5]*equals(occupation[i],3) + m[6]*equals(occupation[i],4) +

m[7]*equals(severity[i],2) + m[8]*equals(severity[i],3) + m[9]*equals(gestation[i],2) + m[10]*(referred[i]) + m[11]*(public[i]) + m[12]*(obygyn[i])

E[i] <- q[1]*(problem[i]) + q[2]*(strained[i]) + q[3]*(lnpacstafftrained[i]) + q[4]*(qual_index[i]) + q[5]*(unmetneedfp[i]) + q[6]*(fpradio3months[i]) + q[7]*(ancskillprov[i]) + q[8]*(tt2[i]) + q[9]*(lackf7days[i])

A[i] <- s[1]*(lev46[i]) + s[2]*(evacuation[i]) + s[3]*(maternity[i]) +s[4]*(method_count[i]) + s[5]*(calloc2[i])

mu[i] <- b[1]*equals(age4[i],2) + b[2]*equals(age4[i],3) + b[3]*equals(marital[i],2) +b[4]*equals(marital[i],3) +b[5]*equals(religion[i],2) + b[6]*equals(religion[i],3) +b[7]*equals(religion[i],4) +b[8]*equals(gravidity[i],2) + b[9]*equals(gravidity[i],3) + b[10]*(prev_abortion[i]) +b[11]*equals(modern[i],1) + b[12]*equals(wanted[i],2) + b[13]*equals(wanted[i],3) + b[14]*equals(wanted[i],9) + A[i] + D[i] +E[i] +u[county[i]]+ f[facility[i]] + sp[county[i]]

    }

for (k in 1:47) {

u[k] ~ dnorm(0, tau.h)

            }

sp[1:47] ~ car.normal(adj[], weights[], num[], tau.b)

for (k in 1:sumNumNeigh)

            {

weights[k] <- 1

            }

# All priors and hyperpriors:

#Priors for beta coefficients

for (i in 1:14) {

b[i]~dnorm(0,0.001)

            }

for (i in 1:5) {

s[i]~dnorm(0,1.0E-6)

          }

for (i in 1:9) {

q[i]~dnorm(0,1.0E-6)

            }

for (i in 1:12) {

m[i]~dnorm(0,1.0E-6)

            }

tau.b ~ dgamma(0.5, 0.0005)

sigma.b <- sqrt(1/tau.b)

tau.h ~ dgamma(0.5, 0.0005)

sigma.h <- sqrt(1/tau.h)

for (j in 1:281) {

    f[j] ~ dnorm(0.0,tauv)

    }

    cA[1] <- g[1]

    cA[2] <- g[1] + g[2]

    g[1] ~dnorm(0,0.01)

    #g[2] ~dnorm(0,0.01)

    g[2] ~ dgamma(0.001, 0.001)

    tauv ~ dgamma(0.001, 0.001) # prior structured

      }