Survival Analysis of Duration of exclusive breastfeeding in Ethiopia: Comparison of Proportional Hazard model and Accelerated Failure Time models

Introduction Early cessation of EBF has the short and long term effect for the welfare of infants including the life-long impacts of poor school performance, reduced productivity, and impaired intellectual development. Objective of the study : the main objective of this study was to compare the performance of CPH model and AFT models in analyzing EBF data in Ethiopia, 2016 EDHS. Specifically, the study aimed to identify the major predictor variables of the duration of EBF based on 2016 EDHS data. Methodology: The secondary data is obtained from Ethiopian Demographic and Health Survey (EDHS), 2016. The outcome variable of this study was the duration of EBF in month. To achieve the objective of the study, descriptive survival analysis like the median survival time, Kaplan Meier survival estimate and log-rank test were used to compare the estimated survival probability among different levels of predictor variables at 5 percent significant level. The Cox proportional hazard regression and Accelerated failure time model were fitted and their results were compared using model comparison criterion such as AIC, BIC. Results: of 1092 interviewed mothers, 15.3 % of them were discontinued EBF and 84.7% of them were exclusively breastfed (censored). The estimated median duration of EBF was 3 months. Based on estimated Kaplan Meier survival curve and log-rank test, it was found that there was a statistically significant difference in survivor experience of discontinuing EBF over each duration with respect to place of delivery, maternal education, husband education, mode of delivery and employment status. The fitted CPH and AFT model indicated that mode of delivery, wealth index, and employment status was found as significant predictors of EBF duration. Moreover, comparatively Weibull AFT model performed better in analyzing EBF data. According to the fitted model, mothers who were in poor wealth index category and who gave birth by cesarean shortens the duration of EBF by 16% and 29% respectively. On the other hand, employed mothers were improved the duration of EBF by 26%. Conclusion: Weibull AFT model is performed better in analyzing EBF data. A mother who was unemployed, poor wealth index, and gave birth by cesarean shortens the duration of EBF than their counterparts. Therefore, special emphasis should be given for mothers who are unemployed, who are economically poor, and give birth by cesarean to improve the duration of EBF.


INTRODUCTION
Exclusive breastfeeding is the practice of feeding only breast milk (including expressed breast milk) and allows the baby to receive vitamins, minerals or medicines and water, breast milk substitutes, other liquids and solid foods are excluded [1]. Fatty acids needed for the infant's growing brain, eyes, and blood vessels are the only contents of breast milk that are not available in other types of milk. Moreover, breast milk helps against multiple diseases, such as gastrointestinal and acute respiratory infections [2], thus, reduces infant mortality and helps faster recovery during illness. In recognition of these benefits, WHO and the United Nations Children's' Fund (UNICEF) recommends all mothers should breastfeed exclusively for the first six months of life and continued breastfeeding for two years or more in conjunction with complementary food as human milk alone is no longer sufficient for both nutritional and developmental reasons [3].
Globally approximately 40% of infants and in developing countries 38% of infants were exclusively breastfed respectively [2,5]. Among 96% of all infants' death occur in the world each year non-exclusive breastfeeding share 55% of diarrheal death and 53% of acute respiratory [3] deaths which is much higher in Asia and Africa [6,25]. On the other hand, exclusive breastfeeding practice is the most effective intervention to save the lives of infants and children.
Nearly, 13%-15% of deaths of children aged less than five years could be prevented if universal coverage of EBF were increased to 90% among infants aged less than six months [4] Even though the Ethiopian Health Sector Transformation Plan (HSTP IV) had planned to increase the proportion of exclusive breastfeeding from 52% to 72% by the end of 2020, only 58% of infants exclusively breastfed with a median duration of 3.1 months (EDHS, 2016) and other available studies in different parts of Ethiopia indicated that the prevalence is ranges from 40.6% to 81. Since the age at Early cessation of EBF has the short and long term effect for the welfare of infants including the life-long impacts of poor school performance, reduced productivity, and impaired intellectual development it is very important variable to determine the important factors of EBF duration. Survival analysis is used for this purpose, statistical methods frequently used to analyze time to event data and has an advantage of controlling censoring observation than any other statistical methods. Cox Proportional Hazard model is the popular model in analyzing survival data, which assume constant hazards. However, the assumption of constant hazards in PH model is not always satisfied by the survival data. The misinterpretation of parameter estimation and decreasing the power of statistical tests are associated with violation of the PH assumptions. On the other hand, Accelerated Failure Time models can be used as the alternative to Cox PH model if the constant hazards' assumption is violated, that is why we want to compare [4] the CPH and AFT models for the analysis of current EBF data. To the best our knowledge, no study had been conducted to determine the determinants of EBF duration by comparing CPH regression and AFT model. Therefore, the main objective of this study was to compare the performance of CPH model and AFT models in analyzing EBF data in Ethiopia, 2016 EDHS.
Moreover, the major factors of early cessation of EBF would be identified.

Data Source
The secondary data was obtained from Ethiopian Demographic and Health Survey

Study Design and Source population
The 2007 Ethiopia population and Housing Census (PHS) is used as a sampling frame of 2016 EDHS and in the first stage 202 in urban areas and 443 rural areas within the nine regions and two administrative cities and thereafter as a second stage, 28 households per cluster were selected with equal probability. Finally the sample used for this study is taken from women's data and total number of children included was 1092. Sampling unit of this study was women whose last child is younger than six months and living with their mothers only.

Study Variables
The duration of EBF was the outcome variable (survival time) and breastfeeding status was an event indicator dichotomized as 1, if a child is given any type of food or liquid other than breast milk before six months and 0, otherwise. The main independent variables taken from available studies related to duration of EBF and its determinants [8,[26][27][28][29][30][31][32][33][34] are husband educational level, wealth index of household, place of residence, mother educational level, employment status, age at first birth, age of mothers during the last birth, place and mode of delivery, birth order, previous birth interval, sex of a child, infant antenatal check-up (ANC). [5] Kaplan Meier survival estimators, median survival time, log-rank test, were used for analysis of survival data. Kaplan Meier survival estimator is used to compare survivor experience of event among different level of predictor variables and log-rank test is used to evaluate whether there is statistically a significant difference among KM survival curves. At null hypothesis log-rank statistic is approximately distributed as chi-square distribution with k-1 degree of freedom, and we conclude that there is a significant difference among KM survival curves if p-value is less than 5 percent significance level. All data analysis was performed using stata version14.2. Accelerated failure time model [6] AFT model provides an alternative to CPH model for statistical modeling of survival data when the proportional hazard assumption of Cox model is do not satisfied (Wei, 1992). In this model, the logarithm of survival time is response variable and includes an error term which is assumed to follow specific probability distribution such as exponential, Weibull, log-normal, log-logistic, etc.

The Cox proportional hazard (CPH) regression model
The assumption of AFT model is that the effects of covariates act multiplicatively with respect to survival time. The log linear representation of AFT model is given by

Summary of Socio demographic characteristics of Respondents
Among 1092 interviewed mothers used for this study, 15.3% of them discontinued EBF and 84.7% of them were continued EBF (censored).
Almost half (49.3%) of the babies were males, of whom those who exclusively breastfed accounts for 47.8% and 57.8% of them were didn't exclusively breastfed. In contrast, of 545 female babies 52.2% were exclusively breastfed and 42.4% were didn't exclusively breastfed.
The percentage of exclusively breastfed babies was higher (46.7%) for those first born than those born in the 2 nd and 3 rd and 4 th and above. The percentage of EBF was higher (55.3%) for those mothers delivered at home than for those mothers delivered at health facility (44.7%). Regarding the number of births for each pregnancy, almost all single births (99%) were exclusively breastfed and only 1% of multiple births were exclusively breastfed. The percentage of EBF for the employment status was 63% and 37% for unemployed and employed mothers respectively.
The highest percentage of EBF in Mode of birth variable was observed for women who gave birth vaginally than those who gave birth by Cesarean. Regarding the wealth index of mothers the highest (51.2%) and lowest percentage of EBF (13%) was observed for Poor and medium class of mothers respectively. The highest percentage of EBF was observed for those mothers from rural areas (81%) than for those mothers from urban areas (19%). Regarding the proportion of EBF in age group the highest proportion was observed for mothers in the age group <20 years (57.6%) followed by those in the age group of 20 to 29 (41.5%) and 30 and above years (0.9%) [7] respectively. The percentage of EBF for those mothers attended ANC for fewer than four times (80%) was observed as four times higher than those attended ANC for at least four times (20%).
Finally, the proportion of EBF for the number of children ever born was higher for mothers who had one to three children (53.3%) followed by those who had 4 to 6 (31.1%) and 7 and higher (15.6%) respectively (Table1).  The result of log-rank test (  KM survival curve, by number of children [10] delivery, number of children ever born, mother education and employment status comparing with that of null model (−2LL=1688). Equivalently, by using Wald chi-square test, the variables above are significant at 25 percent level and candidate for the inclusion in the multivariate model (Table 3). On the other hand omitting the variables ANC, Sex, Birth interval, husband education, age at birth, residence, birth type, and age of mother does not bring a significant change on the value of -2LL. Once again, the number of children was significant at 5% level at multivariate analysis. Therefore the main effects of the final model were wealth index, mode of delivery, employment status, and number of children ever born (      The present study found that the mode of delivery is a significant predictor of duration of EBF.

Kaplan Meier Survival curve estimates
The estimated coefficient of mothers who gave birth by cesarean is -0.3421:TR= exp(−0.3421) = 0.71 which suggests the mothers who gave birth by cesarean decrease the duration of EBF approximately by 29 percent compared to mothers who gave birth vaginally.
Similar findings obtained by [1,4,22,24] revealed that mothers who gave birth vaginally were more likely to practice EBF than those who gave birth by cesarean section. In contrast, a study by [28] found that children of mothers who experienced cesarean section had 29% lower risk of finishing EBF before six months (HR=0.71, 95% CI:(0.55,0.91)) compared with children whose mothers had vaginal delivery. [14] This study found that the employed mothers increase the duration of EBF approximately by 26 percent ((TR = exp(0.233) = 1.262), 95% : (1.08,1.48)) compared to unemployed mothers.
This might be unemployed mothers early discontinued EBF to search a job for their daily food.
This study agreed with the study done in Goba, and Somali regional state of Ethiopia [23,37]. In contrast, the study found by Hunegnaw (2013) found that Place of delivery was significantly associated with duration of exclusive breastfeeding. In these studies, Mothers who gave birth in health facilities have longer duration in breastfeeding practice compared as mothers who gave birth in other places. In contrast, the present study showed that place of delivery and mother's education level had not significant effect on the duration of exclusive breastfeeding [8,22,36].
According to our study, mothers whose wealth index is in poor level decrease the duration of EBF approximately by 16 percent (TR = exp(−0.1745)=0.84,95% : (0.72,0.98) compared to those in the rich level. This is similar with that found by Chekol et al [16].
Conclusion: being unemployed and gave birth by cesarean shortens the duration of EBF. On the other hand, poor mothers discontinued EBF early than rich mothers. Therefore special emphasis should be given for unemployed and poor mothers and also for those gave birth by cesarean. On the other hand, Weibull accelerated failure time model was better than CPH model to determine the associated factors of EBF duration. Therefore, the study recommends this model as alternative of CPH model.