Time to first antenatal care visit among pregnant women in Ethiopia: secondary analysis of EDHS 2016; application of AFT shared frailty models

Background: The survival of pregnant women is one of great interest of the world and especially to a developing country like Ethiopia which had the highest maternal mortality ratios in the world due to low utilization of maternal health services including antenatal care (ANC). Survival analysis is a statistical method for data analysis where the outcome variable of interest is the time to occurrence of an event. This study demonstrates the applications of the Accelerated Failure Time (AFT) model with gamma and inverse Gaussian frailty distributions to estimate the effect of different factors on time to first ANC visit of pregnant women in Ethiopia. Methods: This study was conducted by using 2016 EDHS data about factors associated with the time to first ANC visit of pregnant women in Ethiopia. A total of 4328 women from nine regions and two city administrations whose age group between 15 and 49 years were included in the study AFT models with gamma and inverse Gaussian frailty distributions have been compared using Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) to select the best model. Results: The factors residence, media exposure, wealth index, education level of women, education level of husband and husband occupation are found to be statistically significant (P-value < 0.05) for the survival time of time to first ANC visit of pregnant women in Ethiopia. Inverse Gaussian shared frailty model with Weibull as baseline distribution is found to be the best model for the time to first ANC visit of pregnant women in Ethiopia. The model also reflected there is strong evidence of the high degree of heterogeneity between regions of pregnant women for the time to first ANC visit. Conclusion: The median time of the first ANC visit for pregnant women was 5 months. From different candidate models, Inverse Gaussian shared frailty model with Weibull baseline is an appropriate approach for analyzing time to first ANC visit of pregnant women data than without frailty model. It is essential that maternal and child health policies and strategies better target women’s development and design and implement interventions aimed at increasing the timely activation of prenatal care by pregnant women. The researchers also recommend using more powerful designs (such as cohorts) for the research to establish timeliness and reduce death. This study was carried out in Ethiopia, and Ethiopia was the second-most populous country in Africa next to Nigeria and found in the horn of Africa. The administrative structure of Ethiopia consists of nine regional states (Tigray, Afar, Amhara, Oromiya, Somali, Benishangul Gumuz, Southern Nations Nationalities and People (SNNP), Gambela, and Harari) and two city administrations (Addis Ababa and Dire Dawa) [16]. We have used 2016 EDHS data. This is the fourth national representative survey done at the country level. The main goal of this dataset was to provide up-to-date information about the key demographic and health indicators. The 2016 EDHS used a two-stage stratified sampling design to select households. In the first stage, there were 645 enumeration areas (202 urban and 443 rural) based on the 2007 Ethiopia Population and Housing Census. A total of 18,008 households were considered, of which 16,650 households and 15,683 women were eligible. The women were interviewed by trained lay interviewers. All women of reproductive age (15 to 49 years) who were either permanent residents of the selected households or visitors who stayed in the selected household the night before the survey, were eligible for the study. A total of 15,683 women aged 15–49 years were interviewed with a response rate of 95% [17]. For the current study 4328 pregnant women from nine regions and two city administrations were included (Fig. 1). Sample size and sampling procedure to reach the final sample size in 2016 EDHS This study was conducted on pregnant women ages 15–49 years from nine regions and two city administrations in Ethiopia by a survey done obtained from EDHS 2016. A secondary data source from 2016 EDHS was used. Pregnant women of age 15–49 years and whose gestational age (duration of pregnancy in weeks) was known at first ANC visit were included in the study (event). In addition, women who did not access ANC throughout pregnancy and the duration of pregnancy were recorded at delivery, or termination of pregnancy recorded was also included as censored observation. However, women who had ANC visit but their gestational at ANC visits was unknown (unrecorded) were excluded from this study. The dependent variable is time-to-first ANC receipt among pregnant women which is measured in months. The survival time was the duration of pregnancy (in months) measured from the time of conception to the first ANC visit (event) and others who did not attend ANC throughout of pregnancy period regardless of the outcome of pregnancy were considered as (censored). Different covariates were considered in this study to determine factors associated with time to first ANC visit. The region was considered as a clustering effect in all frailty models (Table 1). List of predictor variables for the assessment of time to first ANC visit in Ethiopia Time was measured in a month(s) from date of pregnancy to first ANC booking for women’s having at least one ANC visit and their current gestational age otherwise. The event was considered to happen if the pregnant women had at least one ANC ad considered censored otherwise. Survival analysis is a collection of statistical procedures for data analysis for which the outcome variable of interest is time until an event occurs. The Cox Proportional Hazard Model is a multiple regression method used to evaluate the effect of multiple covariates on survival time. The accelerated failure time model is an alternative to Cox PH and parametric models for the analysis of survival time data. Unlike the proportional hazards model, it is used to measure the direct effect of the explanatory variables on the survival time instead of a hazard. frailty is an unobserved random factor that modifies multiplicatively the hazard function of an individual or cluster of individuals in time to event data [18]. The data set was downloaded from the website https://dhsprogram.com after an approval letter for use had been obtained from the measure DHS. Variables were extracted from the EDHS 2016 kids and individual women’s data set using a data extraction tool. After data management, cleaning and weighting descriptive measures such as median, percentage, graphs, and frequency tables were used to characterize the study population. Time to first ANC visit was estimated using the Kaplan-Meier (K-M) method. The log-rank test was applied to compare the survival time difference between groups of categorical variables with the outcome of interest. In any applied set, survival data can be fitted using Cox Proportional Hazard [19], Accelerated Failure Time [19], and parametric shared frailty models [20]. Univariate and multivariate analyses were performed and all significant variables in univariate analyses (p < 0.05) were included in all multivariable analyses of the AFT shared frailty model and the best model was selected using AIC and BIC criteria. Data were entered and cleaned using SPSS-22 and analyzed using STATA-14. The Cox proportional model is proposed by [19] which is a semi-parametric model for the hazard function that allows the addition of covariates while keeping the baseline hazards unspecified and can take only positive values. This model gives an expression for the hazard at time t for an individual with a given specification of a set of explanatory variables denoted by X and it is generally given by: Where h0(t) is the baseline hazard function at time t, X is the vector of values of the explanatory variables and β = (β1, β2, …, βk) is the vector of unknown regression parameters that are assumed to be the same for all individuals in the study, which measures the influence of the covariate on the survival experience. In accelerated failure time models we assume that the effect of the covariates will be a multiplication of the expected survival time. A general formulation for the AFT hazard for an individual I with covariates P is summarized in vector 푿 [21]. Where ηi = a ' X = a1x1i + a2x2i + ……. .  + apxpi is the linear component of the model in which 푥ji is the value of 푗th explanatory variable 푿j for the ith individual and exp − (a1x1i + a2x2i + ……. .  + apxpi) is acceleration factor. Where a1, a2, …… . , ap are the unknown regression coefficients of the explanatory variables x1, x2, …… . , xp. The corresponding survivor function will be Where so(t) the baseline survival function. Multivariate or shared frailty model is a conditional independence model in which frailty is common to all subjects in a cluster. The concept of frailty provides a suitable way to introduce random effects in the model to account for association and unobserved heterogeneity. In its simplest form, frailty is an unobserved random factor that modifies multiplicatively the hazard function of an individual or cluster of individuals [18]. introduced the term frailty and [22] promoted the model by its application to the multivariate situation on chronic disease incidence in families. The multivariate frailty model is an extension of the univariate frailty model which allows the individuals in the same cluster to share the same frailty value. When frailty is shared, dependence between individuals who share frailties is generated. Let us have j observations and i subgroups. Each subgroup consists of ni observations and ∑i=1rni=n, where n is the total sample size. The hazard rate for the jth individual in the ith subgroup is given by: Here frailty Z is the random variable varying over the population decreases (Z < 1) or increases (Z > 1) the individual risk. If the proportional hazards assumption does not satisfy, the accelerated failure time frailty model can be used. The AFT shared frailty model is an appropriate choice for multivariate clustered survival time data, especially when observations within a cluster share common unobservable frailty. It explicitly takes into account the possible correlation among failure times. Suppose logTij be the logarithm of the survival time of the jth pregnant woman in the ith region, (j = 1, 2, …, ni and i = 1, 2, …., 11), and Xij be the vector of covariates associated with this individual. Then the shared AFT frailty model is given by: Where β is the vector of unknown regression coefficients μ is the intercept parameter, σ is the scale parameter, the ∈ij’s are independent identically distributed random errors, and the Zi’s are the cluster-specific random effects which are assumed to be i.i.d random variable with density function f (zi). Here we have assumed that the shared frailty (random) effect Zi following gamma and inverse Gaussian distribution with mean zero and variance θ, as defined in the density function in Eqs. (4) and (5) respectively. One important problem in the area of frailty models is the choice of the frailty distribution. Various studies have been done on the choice of distribution of frailty random variables. While some authors use continuous distributions such as Gamma [18, 22], inverse Gaussian [23, 24], log-normal [25] and positive stable [26]. However, the Gamma and Inverse Gaussian distribution are the most common and widely used in literature for determining the frailty effect, which acts multiplicatively on the baseline hazard [27] and [23]. Where θ > 0, indicates the presence of heterogeneity. So, the large values of θ reflect a greater degree of heterogeneity among regions of pregnant women and a stronger association within regions. In these models, frailty could be considered as an unobserved covariate that is additive on the log failure time scale and describes some reduced or increased event times for different clusters. All observations within a cluster share a common unobserved random effect. Now the conditional survivor function and hazard function for the jth individual of ith cluster is written as: From equation [9], we have ∈ij=logtij−μ−X′ijβ−Ziσ. Where S0(.) and h0(.) are the survivor and hazard function of ∈ij respectively, and β is a vector of fixed effects associated with a vector of covariates Xij measured on the jih individual in the ith cluster. The associations within group members (regions) are measured by Kendall’s, for gamma frailty distribution is given by: –