Baseline characteristics of study participants
A total of 15626 (weighted = 15635) women were included in the study. From the respondents one fifth (21.62) were adolescents. Of all, the majority (77.88%) of them were rural in residence. Of married women, 67.37% had more than 5 years of a spousal age difference. Around two-thirds (63%) of women married their first husband before their age of 18 years. Moreover, 26.24% of them married before the age of 15 years (table 1).
Table 1: Socio-demographic and reproductive health-related factors among reproductive age women in Ethiopia, EDHS 2016
Variables categories | Weighted frequency | Weighted Percentage (%) |
Age distribution (N = 156356) | < 20 years | 3,380 | 21.62 |
20–29 years | 5,716 | 36.56 |
> 30 years | 6,539 | 41.82 |
Residence | urban | 3447 | 22.12 |
Rural | 12175 | 77.88 |
Regions | Most urban | 1042 | 6.74 |
| Northern | 4827 | 30.87 |
| Oromia | 5682 | 36.34 |
| SNNp | 3282 | 21.00 |
| Eastern-pasto | 585 | 3.74 |
| Western- Pasto | 204 | 1.30 |
Age at first intercourse (n = 15635) | < 15 years | 3027 | 19.36 |
15–17 years | 5062 | 32.38 |
> 18 years | 7,546 | 48.26 |
Age at first marriage | < 15 years | 3044 | 26.24 |
(n = 11600) | 15–17 years | 4256 | 36.69 |
| > 18 years | 4300 | 37.07 |
Spousal age difference | < 5 years | 3326 | 32.63 |
> 5 years | 6,867 | 67.37 |
Contraceptive | Ever not use | 8895 | 56.95 |
(n = 15635) | Ever use | 6727 | 43.05 |
Religion | orthodox | 6,762 | 43.25 |
Muslim | 4,881 | 31.22 |
protestant | 3,662 | 23.42 |
Others* | 330 | 2.11 |
*Others = catholic, traditional and other |
Regarding socio-economic and information related characteristics of the respondents, 47.77% of them had no education and 49.91% have no formal occupation. More than 34% of the study participants had wealth index status below the middle level and only a quarter (26.37%) had regular media exposure (table 2).
Table 2: socio-economic and information related characteristics among reproductive age women in Ethiopia EDHS, 2016
Predictors | Categories | Weighted Weighted Frequency percentage (%) |
Education | No education | 7469 | 47.77 |
| Primary | 5475 | 35.04 |
| Secondary | 1802 | 11.61 |
| Higher | 868 | 5.57 |
Occupation | Not working | 7799 | 49.91 |
| Agriculture employee | 3248 | 20.77 |
| None agriculture employee | 4576 | 29.32 |
Husband education | No education | 4750 | 46.60 |
| Primary | 3765 | 36.94 |
| Secondary | 971 | 9.53 |
| Higher | 707 | 6.94 |
Husband occupation | Not working | 802 | 7.87 |
| Agriculture employ | 6323 | 61.93 |
| Non-agri-employe | 3078 | 30.20 |
Media exposure | Yes | 4115 | 26.37 |
| No | 11508 | 73.63 |
Wealth index | Poorest | 2630 | 16.82 |
| Poorer | 2803 | 17.93 |
| Middle | 2968 | 18.98 |
| Richer | 3092 | 19.77 |
| Richest | 4143 | 26.49 |
Time to first birth among study participants
Over all 10274 (67.7%) women had given at least first birth. In general the median age of first birth found to be 20 years (IQR = 16–24). The total follow-up period for all 15,626 women was 146,290 person-years of observation. The median, minimum and maximum follow-up period was 8 years one year and 39 years after the age of puberty (10 years from her birth date), respectively. Among women had first birth below 20 years the median age was 18 years (IQR = 15–19), from those women giving first birth in the age bracket of 20–29 years median age was 23 years (IQR = 20–26) and of women celebrate their 30 years before giving birth (n = 533) only 49.5% able to give birth (Fig. 3). The median time to first birth was at lower age for those women enter into sexual intercourse at lower age (< 15 years) 15 years (IQR = 13–17), too early married women (below 15 years) 16 years (IQR = 14–17) and women had no education 18 years (IQR = 15–21) years (table 3). The median age was relatively higher among women those had higher education level 27 years (IQR = 21- -).
Predictors of time to first birth among reproductive-age women in Ethiopia, 2016 EDHS
Differences in all predictor variables at baseline were determined using the Kaplan Meier failure function and the log-rank (χ2) test. The Kaplan Meier failure function with 95% confidence interval was constructed for age at first marriage and women education level (Fig. 4) and annex-1 (Fig. 9). In general, the pattern of the failure function lying below right side to other categories indicated that the group defined by the lower curve had a better survival before giving first birth than the group defined by the above curves. Therefore women married at the age of 18 and above years and women with secondary and higher education level able to delay their first birth in the later age than married below 18 years and below secondary education level respectively as Kaplan Meier failure graph and a log-rank test at (p-value < 0.001) showed (Fig. 4). The log-rank test showed that all predictor variables had a significant survival difference at p-value < 0.001 (Table 3).
Table 3: Kaplan-Meier failure estimate and log rank test comparison of time to first birth among reproductive age women in Ethiopia, 2016 EDHS.
Characteristics | N (%) | Ever given Birth | Median (IQR) years | Log-rank | p-value |
Region | Northern | 4827 (30.87) | 3224 (66.8) | 19 [16–24] | 570.2 | <0.001 |
Oromia | 5682 (36.34) | 4130 (72.7) | 19 [16–22] |
SNNPR | 3282 (21.00) | 2192 (66.8) | 20 [16–24] |
Most-urban | 1042 (6.74) | 474 (45.5) | 26 [19–34] |
Eastern-pasto | 585 (3.74) | 424 (72.4) | 19 [16–22] |
Western-semi Pasto | 204 (1.30) | 144 (70.7) | 19 [16–22] |
residence | Urban | 3447 (22.12) | 1769 (51.3) | 23 [18–30] | 916.7 | < 0.001 |
Rural | 12175 (77.88) | 8818 (72.4) | 19 [16–22] |
Education | No education | 7469 (47.77) | 6785 (90.9) | 18 [15–21] | 2545.8 | <0.001 |
Primary | 5475 (35.04) | 2865 (52.3) | 20 [17–24] |
Secondary | 1802 (11.61) | 593 (32.8) | 26 [20–37] |
Higher | 868 (5.57) | 344 (39.6) | 27 [21–49] |
occupation | Not working | 7799 (49.91) | 5243 (67.2) | 19 [16–23] | 461.0 | < 0.001 |
Agriculture | 3248 (20.77) | 2522 (77.6) | 19 [15–21] |
Non agricul- | 4576 (29.32) | 2822 (61.8) | 21 [17–27] |
Wealth index | Poorest | 2630 (16.82) | 2060 (78.3) | 19 [16–22] | 903.9 | < 0.001 |
Poorer | 2803 (17.93) | 2122 (75.7) | 19 [16–21] |
Middle | 2968 (18.98) | 2128 (71.7) | 19 [16–22] |
Richer | 3090 (19.76) | 2089 (67.6) | 19 [16–23] |
Richest | 4131 (26.49) | 2190 (53.0) | 22 [17–30] |
Contraceptive | Ever not use | 8895 (56.95) | 4617 (51.9) | 21 [17–26] | 844.2 | < 0001 |
Ever use | 6727 (43.05) | 5970 (88.7) | 19 [16–22] |
Media exposure | No | 11508 (73.63) | 8342 (72.5) | 19 [16–22] | 576.6 | < 0.001 |
Yes | 4115 (26.37) | 2245 (54.6) | 22 [17–28] |
Ever married | No | 4022 (25.81) | 93 (2.3) | - | 3974.7 | < 0.001 |
Yes | 11600 (74.19) | 10494 (90.5) | 19 [15–21] |
Spousal age gap | < 5 years | 3326 (32.63) | 2984 (89.7) | 19 [16–22] | 129.2 | < 0.001 |
≥ 5 years | 6,867 (67.37) | 6366 (92.7) | 18 [15–21] |
Age at first marriage | Below age 15 | 3044 (26.24) | 2915 (95.8) | 16 [14–17] | 5582.3 | < 0.001 |
15–17 | 4256 (36.69) | 3890 (91.4) | 18 [16–19] |
18 and above | 4300 (37.07) | 3689 (85.8) | 22 [19–25] |
Age at first sex | < 15 years | 3027 (19.36) | 2,860 (94.47) | 15 [13–18] | | |
15–17 years | 5062 (32.38) | 4,576 (90.4) | 18 [16–20] | | |
≥ 18 years | 7,546 (48.26) | 3,151 (41.75) | 22 [19–26] | | |
Husband-education | no education | 4750 (46.60) | 4516 (95.1) | 18 [15–21] | 396.1 | < 0.001 |
Primary | 3765 (36.94) | 3454 (91.7) | 18 [15–21] |
Secondary | 971 (9.53) | 808 (83.2) | 20 [16–23] |
Higher | 707 (6.94) | 573 (81.1) | 21 [17–25] |
Husband occupation | not working | 802 (7.87) | 740 (92.3) | 18 | 256.1 | 0.001 |
agriculture employee | 6323 (61.93) | 5930 (93.9) | 18 |
Nonagricultur | 3078 (30.20) | 2681 (87.1) | 19 |
religion | Orthodox | 6762 (43.25) | 4371 (64.6) | 20 | 178.6 | < 0.001 |
Muslim | 4881 (31.22) | 3593 (73.6) | 19 |
Protestant | 3662 (23.42) | 2367 (64.7) | 20 |
Others | 330 (2.11) | 255 (77.1) | 19 |
Total | | 15,635 | 10635 (67.7) | 20 [16,24] | | |
*N=weighted value, IQR=interquartile |
Parsimonious Model Selection
Cox proportional hazard model
All fourteen predictor variables that were significant at 0.2 p value in bivariable analysis were entered into the multivariable Cox model and ever married reduced from the model due to collinearity effect with age at first marriage. Then the Schoenfeld test for proportional hazard assumption of the time to first birth data was evaluated. The proportional hazard assumption violated in both global test and at each variable level due to significant correlation of time to first birth and all predictor variables (Table 4), as a result, the Cox model was excluded for this data.
Table 4: Schoenfeld residual test for proportionality assumption of the Cox model
Predictors | Rho | Chi2 | df | Prob > Chi2 |
Geo-regions | 0.056 | 91.18 | 1 | < 0.001 |
Residence | -0.078 | 174.81 | 1 | < 0.001 |
Religion | -0.061 | 82.37 | 1 | < 0.001 |
Education level | 0.071 | 107.88 | 1 | < 0.001 |
Occupation | -0.055 | 80.36 | 1 | < 0.001 |
Wealth index | -0.095 | 235.12 | 1 | < 0.001 |
Spousal age difference | -0.108 | 231.14 | 1 | < 0.001 |
Contraceptive use | 0.193 | 1009.79 | 1 | < 0.001 |
Media exposure | 0.030 | 20.33 | 1 | < 0.001 |
Age first marriage | 0.220 | 1589.96 | 1 | < 0.001 |
Age first sex | 0.138 | 463.55 | 1 | < 0.001 |
Husband education | -0.066 | 118.00 | 1 | < 0.001 |
Husband occupation | 0.019 | 13.02 | 1 | < 0.001 |
Global test | | 6191.37 | 13 | < 0.001 |
<0.001 means significant at 5% significance level; proportionality assumption is violated |
Then stratified Cox model also inappropriate for this data because there is no predictor variable that fulfills proportional hazard assumption to be in the model. Another alternative extended Cox (time-varying Cox model) also faces the challenge of choosing the appropriate function of survival time to include in the model. For example, if we create covariate log-survival time interaction term, this interaction term could be appropriate if the hazard ratio comparing any two levels of covariate monotonically increases (or decreases) over time. But in the case of our data, the time distribution is unimodal rather than monotonic (Fig. 4). So those parametric models are considered to the data due to these constraints. |
Appropriate Parametric Survival Model Selection
Exploratory analysis
Baseline hazard plot
The shape of the baseline hazard function (Fig. 5) of time to first birth data looks closer to the hazard function of the classical shape of unimodal hazard curve models. It seems reasonable that first birth starts to happen at puberty (age 10–13 years) and increased to maximum (at the age of 18–22 years), the period at which most girls became married and sexually active. Then, it changes its direction and decreased gradually as those who did not married and sexually inactive or those who planned to delay their first birth in the later age of their life by different reasons. This theoretical concept is similar to the baseline hazard plot of time to first birth data (Fig. 5). Therefore, the shape of hazard function indicated that time to first birth data might be modeled by Log-Logistic, Lognormal or Generalized gamma or inverse Weibull survival models. These are complex "inverted bathtub" shaped functions that might be appropriate for modeling human life over a long period of time (47).
Appropriately transformed survival function plot against the natural log of survival time
A more informative way of assessing whether a particular distribution for the survival times is plausible is to compare the survivor function for the data with that of a chosen model. This technique is through the plot of appropriately transformed survival function with the log of survival time and produce a plot that should give a straight line if the assumed model is appropriate (48).
On the basis of the appropriately transformed survival function plot against the natural log of survival time, the time to first birth data may suitably be explained by Log-Logistic, Lognormal or inverse Weibull survival models as their transformed survival function over log survival time is reasonably straight line (Fig. 6). The final choice of the model was made by fitting model with covariates and through likelihood ratio test for nested models, and Akaike’s information criterion for none nested models, Cox-Snell residuals plot and R2 type statistic for goodness of fit of the model for the given data.
Identifying nested distribution in generalized gamma for the data
Since lognormal, Weibull, exponential, gamma and inverse Weibull can be nested in generalized gamma after multivariable generalized gamma model fitted, Wald test and likelihood ratio tests were applied to identify presence of nesting for this data (Table 5).
Table 5: Identifying the nested model in generalized gamma for time to first birth data
| coefficient | Standard error (Se) | z-value | P value | 95% CI |
Kappa(K) | -0.98 | 0.028 | -38.01 | < 0.001 | (-1.13 ,-0.88) |
Sigma (σ) | 0.11 | 0.002 | | | (0.10 0.11) |
Hypothesis | Likelihood ratio test | Wald test | Decision |
Chi2 | p-value | Chi2 | p-value |
HO: k = 0 lognormal | 1776.84 | < 0.001 | 1444.68 | < 0.001 | Ho rejected |
HO: k = 1 Weibull | | | 5385.27 | < 0.001 | Ho rejected |
HO: k = 1,σ = 1 Exponential | | | 53014.06 | < 0.001 | Ho rejected |
HO: k = σ Gamma | From k and σ CI | | | Ho rejected |
K= -1 Inverse Weibull | | | 0.14 | 0.709 | Ho failed to reject |
Ho: assumption the model is nested in saturated generalized gamma |
When k=-1 inverse Weibull is nested in the Generalized gamma distribution |
Then none nested models were compared using AIC to select best-fitted model and R2 type statistics applied to identify in which model variables best predict the outcome (Table-6).
The inverse Weibull is preferred parametric model for the given data with the highest log likelihood, smallest AIC and higher R2 type statistics prediction of the outcome 58% using variables in the model as shown in (Table 6).
Table 6: None nested parametric survival model comparison of time to first birth data with AIC and R2 type statistics
Model | N | Null model(L0) | Full model(Lp) | df | AIC | R2p | LR chi2(34) | P-value LLF |
Exponential | 9788 | -3467.52 | -2807.93 | 35 | 5685.86 | 12.6% | 1319.18 | < 0.0001 |
Gombertz | 9788 | -1962.20 | 355.51 | 36 | -639.018 | 37.8% | 4635.42 | < 0.0001 |
Weibull | 9788 | -185.63 | 2616.31 | 36 | -5160.62 | 43.6% | 5603.89 | < 0.0001 |
Log normal | 9788 | -32.42 | 3841.78 | 36 | -7611.57 | 54.7% | 7748.42 | < 0.0001 |
Log logistic | 9788 | 43.62 | 4296.98 | 36 | -8521.97 | 58.1% | 8506.74 | < 0.0001 |
Generalized gamma | 9788 | 1387.47 | 5745.62 | 37 | -11417.23 | 59.0% | 8716.29 | < 0.0001 |
Inverse Weibull | 9788 | 2302.55 | 6521.81 | 36 | -12970.98 | 58.0% | 8422.65 | < 0.0001 |
* N number of observations, df =degree of freedom, AIC=Akaike's information criterion, BIC=Bayesian information criterion LLF= full model log likelihood |
Where LP is the log likelihood for the full model with p covariates and L0 is the log-likelihood for the null model, the model with no covariates.
The inverse of the inverse-Weibull (IW) data follows a Weibull distribution. Graphical demonstrations of how the inverse of inverse-Weibull is Weibull distribution in the time to first birth data (Fig. 7). So the parameter estimates of the IW distribution can be easily obtained by applying to its reciprocal data, the same standard procedures implemented in packages for the Weibull model or the Log-Logistic survival model can be fitted with the cumulative distribution function (Cdf) of IW data very well (49).Therefore in this study, the inverse Weibull model was applied to model the time to first birth data.
Shared Frailty Model
A likelihood ratio test for a variance of frailty theta = 0 yields a highly statistically significant p-value of < 0.001 for all baseline hazard function with both inverse Gaussian and gamma shared frailty distribution in the models (Table 7), suggesting that the frailty component contributes to the model and that there is a within-cluster correlation. The value of shared frailty distribution (θ) is 0.028, 0.23 and 0.18 for inverse-Weibull gamma, log-logistic gamma and lognormal gamma shared frailty models respectively and 0.028, 0.84 and 0.25 for inverse-Weibull-inverse Gaussian, log-logistic- inverse Gaussian and lognormal inverse Gaussian shared frailty models respectively. The inverse Weibull gamma shared frailty model is preferred model for the give data due to its lowest AIC.The dependence within clusters (EAS) for the inverse Weibull gamma shared frailty model found to be (τ = 0.0244) before adjusting for predictors and (τ = 0.014) after adjusting for predictors and after addition of interaction term (θ = 0.025 and τ = 0.012).
Table 7: Parametric shared frailty model comparison on time to first birth data of reproductive age women in Ethiopia, 2016 EDHS
Model | Log-likelihood | DF | AIC | Variance Of θ | LR test of θ = 0 |
Lognormal gamma | 4511.66 | 34 | -8955.31 | 0.18 | < 0.001 |
Lognormal inverse Gaussian | 4511.62 | 34 | -8955.24 | 0.25 | < 0.001 |
Log logistic gamma | 4881.54 | 34 | -9695.08 | 0.23 | < 0.001 |
Log logistic inverse Gaussian | 4936.02 | 34 | -9804.03 | 0.87 | < 0.001 |
Inverse Weibull gamma | 5708.19 | 34 | -11348.37 | 0.028 | < 0.001a |
Inverse Weibull inverse Gaussian | 5707.78 | 34 | -11347.55 | 0.028 | < 0.001 |
a = preferred model |
It also interpreted as prior to adjusting for predictor variables the median increase in the hazard of early childbirth when comparing a woman at a cluster with higher risk of early childbirth to a woman at a cluster with lower risk early childbirth was 24% (MHR = 1.24, 95%, CI [1.21–1.27]). After accounting for predictor factors and interaction term the median increase in the hazard of early childbirth when comparing a woman at a cluster with higher risk of early childbirth to a woman at a cluster with lower risk of early childbirth was 16% (MHR = 1.16, 95%, CI [1.13–1.20]) (Table 8).
Table 8
Bivariable and multivariable inverse-Weibull gamma shared frailty model on predictors of time to first birth among reproductive-age women in Ethiopia, EDHS, 2016
Variable | Null model | First birth status | | Full model |
Log-likelihood | -1036.84 | | 5907.45 |
Effect size | | gave | Not gave | CHR | AHR |
Region | Most urban | | 474 | 568 | 1 | 1 |
Northern | | 3224 | 1603 | 1.08(1.01–1.18)** | 1.08 (0.97–1.19) |
Oromia | | 4130 | 1552 | 1.07 (0.98–1.18)* | 1.18 (1.06–1.30)*** |
SNNP | | 2192 | 1090 | 0.98 (0.90–1.18) | 1.19 (1.06–1.33)*** |
Eastern | | 424 | 161 | 1.00 (0.92–1.09) | 1.16 (105 − 1.28)*** |
western | | 144 | 60 | 1.12 (1.03–1.22)** | 1.37 (1.24–1.52)*** |
residence | Urban | | 1769 | 1678 | 1 | 1 |
Rural | | 8818 | 3357 | 0.96 (0.91–1.02 ) | 1.09 (0.98–1.19) |
Education | No_cation | | 6785 | 684 | 1 | 1 |
primary | | 2865 | 2610 | 1.72 (1.64–1.82)*** | 1.12 (1.05–1.19) |
secondary | | 593 | 1209 | 0.83 (0.76–0.87)*** | 0.86 (0.78–0.96)*** |
Higher | | 344 | 524 | 0.72 (0.65-.80)*** | 0.75 (0.65–0.85)*** |
occupation | not working | | 5243 | 2556 | 1.18 (1.13–1.24)*** | 0.98 (0.92–1.04) |
agriculture | | 2522 | 726 | 0.98 (0.93–1.04) | 0.94 (0.88–1.02) |
Nonagriculture | | 2822 | 1754 | 1 | 1 |
Wealth index | poorest | | 2060 | 570 | 1 | 1 |
Poorer | | 2122 | 681 | 1.03 (0.96–1.10) | 0.98 (0.91–1.05) |
Middle | | 2128 | 840 | 1.12 (1.05–1.21)*** | 1.00 (0.93–1.09) |
Richer | | 2089 | 1001 | 1.12 (1.05–1.21)*** | 1.10 (1.01–1.19)* |
Richest | | 2190 | 1941 | 1.12 (1.05–1.21)*** | 1.08 (0.97–1.15) |
Spousal age gap | < 5 years | | 2984 | 342 | 1 | 1 |
≥ 5 years | | 6366 | 501 | 1.26 (1.21–1.33)*** | 1.11 (1.05–1.16)*** |
Contraceptive | Ever not use | | 4617 | 4278 | 1 | 1 |
Ever use | | 5970 | 757 | 0.50 (0.48–0.52)*** | 0.91 (0.86–0.97)*** |
Media exposure | No | | 8342 | 3166 | 1 | 1 |
Yes | | 2245 | 1870 | 1.10 (1.04–1.15)*** | 1.01 (0.94–1.08) |
Age at first marriage | < 15 years | | 2915 | 129 | 9.10 (8.83–9.86)*** | 1.26 (0.87–1.82) |
15–17 years | | 3890 | 366 | 3.47 (3.30–3.64)*** | 2.33 (2.08–2.63)*** |
≥ 18 years | | 3689 | 611 | 1 | 1 |
Age at first sex | < 15 years | | 2,860 | 167 | 1.89 (1.78–1.99))*** | 27.78 (23.26–32.26)*** |
15–17 years | | 4,576 | 486 | 0.68 (0.65–0.71)*** | 2.60 (2.07–2.63)*** |
≥ 18 years | | 3,151 | 4395 | 1 | 1 |
Husband educati | No Edu- | | 4516 | 234 | 1 | 1 |
primary | | 3454 | 311 | 0.99 (0.94–104) | 1.03 (0.97–1.09) |
secondary | | 808 | 163 | 0.88 (0.81–0.95)*** | 1.05 (0.96–1.15) |
Higher | | 573 | 134 | 0.68 (0.63–0.74)*** | 1.03 (0.93–1.14) |
Husband occupation | not working | | 740 | 62 | 1.14 (1.05–1.23)*** | 0.98 (0.91-1.o6) |
agriculture | | 5930 | 393 | 1.13 (1.08–1.19)*** | 0.96 (0.91–1.02) |
Non agriculture | | 2681 | 397 | 1 | 1 |
religion | orthodox | | 4371 | 2391 | 1 | 1 |
Muslim | | 3593 | 1288 | 1.02(0.97–108) | 1.10 (1.03–1.19)*** |
protestant | | 2367 | 1295 | 0.99(0.92–1.05) | 1.01 (0.92–1.10) |
Others | | 255 | 75 | 0.90 (0.77–1.06) | 1.03 (0.87–1.22) |
theta | | 0.05 (0.04–0.06) | | | | 0.028 (0.027–0.04)*** 0.025 (0.016–0.039)†*** |
MHR | | 1.24 (1.21–1.27) | | | | 1.17 (1.17–1.21)*** 1.16 (1.13–1.20) † *** |
LR test of theta = 0 | Chibar2(1) | 126.23 | | | | 35.40 |
Prob-hibar2 | < 0.001 | | | | < 0.001 |
* Significant at 95% CI, ** Significant at 99% CI |
MHR = median hazard ratio, † from interaction model |
Annex 2: Table 10: Interaction involving inverse Weibull gamma shared frailty model (effect modification) |
Variable | unadjusted | adjusted | Interaction model |
Log likelihood | | 5907.45 | 5802.68 |
Effect size | CHR | AHR | AHR |
Region | Most urban | 1 | 1 | 1 |
Northern | 1.08(1.01–1.18)** | 1.05(0.95–1.16) | 1.08(0.97–1.19) |
Oromia | 1.07 (0.98–1.18)* | 1.18(1.06–1.30)** | 1.18(1.06–1.30)*** |
SNNP | 0.98 (0.90–1.18) | 1.22(1.09–1.37)** | 1.19(1.06–1.33)*** |
Eastern | 1.00 (0.92–1.09) | 1.11(1.01–1.24)* | 1.16(105 − 1.28)*** |
Western | 1.12 (1.03–1.22)** | 1.35(1.22–1.49)** | 1.37(1.24–1.52)*** |
Residence | Urban | 1 | 1 | 1 |
Rural | 0.96 (0.91–1.02 ) | 1.03(0.93–1.14) | 1.09 (0.98–1.19) |
Education | No_educ | 1 | 1 | 1 |
Primary | 1.72 (1.64–1.82)*** | 0.95(0.89–1.01) | 1.12 (1.05–1.19) |
Secondary | 0.83 (0.76–0.87)*** | 0.85(0.77–0.94)*** | 0.86 (0.78–0.96)*** |
Higher | 0.72 (0.65-.80)*** | 0.66(0.58–0.75)*** | 0.75 (0.65–0.85)*** |
Occupation | not working | 1.18 (1.13–1.24)*** | 0.98(0.92–1.04) | 1.01(0.95–1.06) |
| Agriculture | 0.98 (0.93–1.04) | 0.94(0.88–1.02) | 0.93(0.86–1.01) |
| Non agriculture | 1 | 1 | 1 |
Wealth index | Poorest | 1 | 1 | 1 |
Poorer | 1.03 (0.96–1.10) | 0.98(0.91–1.05) | 0.98(0.91–1.05) |
Middle | 1.12 (1.05–1.21)*** | 1.00(0.93–1.09) | 0.98(0.92–1.06) |
Richer | 1.12 (1.05–1.21)*** | 1.10(1.01–1.19)* | 1.04(0.96–1.12) |
Richest | 1.12 (1.05–1.21)*** | 1.08(0.97–1.15) | 1.01(0.91–1.12) |
Spousal age difference | < 5 years | 1 | 1 | 1 |
≥ 5 years | 1.26 (1.21–1.33)*** | 1.09(1.04–1.14)** | 1.11(1.05–1.16)*** |
Contraceptive use | Ever not | 1 | 1 | 1 |
Ever use | 0.50 (0.48–0.52)*** | 0.94 (0.89–0.99)* | 0.91(0.86–0.97)*** |
Media exposure | No | 1 | 1 | 1 |
Yes | 1.10 (1.04–1.15)*** | 1.01(0.94–1.08) | 0.99(0.94–1.06) |
Age at first marriage | < 15 years | 9.10 (8.83–9.86)*** | 2.82 (2.60–3.03)** | 1.26 (0.87–1.82) |
15–17 years | 3.50 (3.30–3.64)*** | 1.98 (1.85–2.13)** | 2.33 (2.08–2.63)*** |
≥ 18 years | 1 | 1 | |
Age at first sex | < 15 years | 1.89 (1.78–1.99))*** | 13.60 (12.50-14.93)** | 27.78 (23.26–32.26)*** |
15–17 years | 0.68 (0.65–0.71)*** | 3.23 (3.03–3.52)** | 2.60(2.07–2.63)*** |
≥ 18 years | 1 | 1 | |
Husband education | No _educ | 1.47 (1.34–1.59)*** | 0.94(0.85–1.05) | 0.94(0.85–1.05) |
primary | 1.45(1.32–1.59)*** | 1.00(0.91–1.11) | 1.00(0.91–1.11) |
secondary | 1.28(1.16–1.41)*** | 1.03(0.93–1.14) | 1.03(0.93–1.14) |
Higher | 1 | 1 | 1 |
Husband occupation | not working | 1.14(1.05–1.23)*** | 0.98(0.91-1.o6) | 0.97 (0.90–1.05) |
agriculture | 1.13(1.08–1.19)*** | 0.96(0.91–1.02) | 0.97 (0.92–1.03) |
Non agriculture | 1 | 1 | 1 |
Religion | orthodox | 1 | 1 | 1 |
Muslim | 1.02(0.97–108) | 1.07(0.99–1.15) | 1.10 (1.02–1.18)** |
protestant | 0.99(0.92–1.05) | 1.01(0.92–1.10) | 1.00 (0.92–1.09) |
Others | 0.90 (0.77–1.06) | 1.03(0.87–1.22) | 1.05(0.89–1.25) |
> 18intercourse and marriage | | 1 |
< 15marriege < 15 intercourse | | 1.32 (0.62–2.89) |
< 15 marriage 15-17intercourse | | 0.86(0.62–1.23) |
15–17 intercourse < 15marriage | | 4.55 (2.13–10.02)*** |
15–17 intercourse 15–17 marriage | | 2.63 (2.01–3.45)*** |
Theta | | | | 0.025 (0.016–0.039) |
P | | | 10.11(9.97–10.25) | |
1/p | | | 0.099(0.098-0.10) | |
Theta | | | 0.028 [0.027–0.04] | |
LR test of theta = 0 | Chibar2(1) | | 35.40 | |
Prob-hibar2 | | < 0.001 | |
*** p value < 0.01 ** p value < 0.05 * p value < 0.25 |
Annex 3: Table 11: Output comparison from shared frailty models of inverse Weibull gamma frailty and log logistic frailty inverse Gaussian survival models. |
variable | Log-logistic inverse-Gaussian shared frailty | Log-logistic-gamma shared frailty | Inverse Weibull gamma shared frailty | |
Log likelihood | 4942.16 | 4890.75 | 5907.45 | |
Effect size | TR (CI) | TR (CI) | HR | TR (CI) |
Region | Most urban | 1 | 1 | | 1 |
Northern | 1.01 (0.98–1.02) | 1.01 (1.00-1.02) | 1.05(0.95–1.16) | 1.00(0.99–1.01) |
Oromia | 0.99 (0.95–1.01) | 0.99 (0.98-1.00) | 1.18(1.06–1.30)** | 0.98(0.97–0.99)** |
SNNP | 1.00 (0.99–1.02) | 1.00 (0.99–1.01) | 1.22(1.09–1.37)** | 0.98(0.97–0.99)** |
eastern | 0.99(0.98–1.01) | 1.00(0.98–1.01) | 1.11(1.01–1.24)* | 0.99(0.98–0.99)* |
western | 0.98 (0.96–0.99)** | 0.98 (0.96–0.98)** | 1.35(1.22–1.49)** | 0.97(0.96–0.98)** |
residence | urban | 1 | 1 | 1 | 1 |
rural | 1.00 (0.99–1.02) | 1.00 (0.99–1.01) | 1.03(0.93–1.14) | 1.00(0.99–1.01) |
Education | No education | 1 | 1 | 1 | 1 |
primary | 1.01(1.01-.02)* | 1.01(1.01–1.01)* | 0.95(0.89–1.01) | 1.01(0.99–1.01) |
secondary | 1.03(1.01–1.04)** | 1.03(1.01–1.04)** | 0.85 (0.77–0.94)** | 1.02(1.01–1.03)** |
higher | 1.07(1.05–1.08)** | 1.08(1.06–1.09)** | 0.75 (0.65–0.85)** | 1.04(1.03–1.05)** |
occupation | not working | 1.00 (0.99–1.01) | 1.00 (0.99–1.01) | 0.98(0.92–1.04) | 1.00(0.99–1.01) |
| agriculture | 1.01 (1.00-1.02) | 1.00 (1.00-1.02) | 0.94(0.88–1.02) | 1.01(0.99–1.01) |
| Non agriculture | 1 | 1 | 1 | 1 |
Wealth index | poorest | 1 | 1 | 1 | 1 |
poorer | 1.00 (0.99–1.01) | 1.00 (0.99–1.01) | 0.98(0.91–1.05) | 1.00(0.99–1.01) |
Middle | 1.01 (1.00-1.01) | 1.00 (1.00-1.01) | 1.00(0.93–1.09) | 1.00(0.99–1.01) |
richer | 0.99 (0.98–0.99)* | 0.99 (0.98–0.99)* | 1.10(1.01–1.19)* | 0.99(0.98–0.99)* |
richest | 1.00 (0.99–1.01) | 1.00 (0.99–1.01) | 1.08(0.97–1.15) | 0.99(0.98–1.01) |
Spousal age difference | Less than 5 years | 1 | 1 | 1 | 1 |
More than 5 years | 0.99 (0.98–0.99)** | 0.99 (0.98–0.99)** | 1.09(1.04–1.14)** | 0.99(0.99–0.99)** |
Contraceptive use | Ever not use | 1 | 1 | 1 | 1 |
Ever use | 1.00 (0.99–1.01) | 0.99 (0.99–0.99)* | 0.94(0.89–0.99)* | 1.01(1.01–1.02)* |
Media exposure | Had no access | 1 | 1 | 1 | 1 |
Had access | 1.00(0.99–1.01) | 1.00 (1.00-1.01) | 1.01(0.94–1.08) | 1.00(0.99–1.01) |
Age at first marriage | less than 15 years | 0.85 (0.84–0.86)** | 0.84 (0.83–0.85)** | 2.82(2.60–3.03)** | 0.90(0.89–0.91)** |
15 to 17 years | 0.90 (0.89–0.91)** | 0.89(0.88–0.90)** | 1.98(1.85–2.13)** | 0.94(0.93–0.95)** |
18 and above | 1 | 1 | 1 | 1 |
Age at first sex | < 15 years | 0.83(0.81–0.84)** | 0.82(0.81–0.83)** | 13.60(12.50-14.93)** | 0.77(0.76–0.78)** |
15 to 17 years | 0.91 (.90-0.92)** | 0.91 (0.90–0.92)** | 3.23(3.03–3.52)** | 0.89(0.88–0.90)** |
≥ 18 years | 1 | 1 | 1 | 1 |
Husband education | No education | 1 | 1 | 1 | 1 |
primary | 1.00 (0.99-1.00) | 1.00(0.99–1.01) | 1.03(0.97–1.09) | 1.00 (0.99-1.00) |
secondary | 1.00 (0.99–1.01) | 1.00(0.99–1.01) | 1.05(0.96–1.15) | 1.00 (0.99–1.01) |
higher | 0.99 (0.97–1.01) | 1.00(0.99–1.01) | 1.03(0.93–1.14) | 0.99 (0.97–1.01) |
Husband occupation | not working | 1.00 (0.99–1.02) | 1.00(0.99–1.01) | 0.98(0.91-1.o6) | 1.00 (0.99–1.02) |
agriculture | 1.01 (1.00-1.01) | 1.00(1.00-1.01) | 0.96(0.91–1.02) | 1.01 (1.00-1.01) |
Non agriculture | 1 | 1 | 1 | 1 |
Religion | orthodox | 1 | 1 | 1 | 1 |
Muslim | 0.99 (0.98–0.99)!* | 0.99(0.98–0.99)** | 1.10(1.03–1.19)** | 0.99 (0.98–0.99)** |
protestant | 0.99 (0.98–0.99)!* | 0.99(0.98–0.99)** | 1.01(0.93–1.10) | 0.99(0.99–1.01) |
others | 0.99 (0.97-1.00) | 0.98(.97- 1.01) | 1.06(0.89–1.27) | 0.99(0.98.1.01) |
ln_gam/p | | -3.09(-3.07, -2.95) | -2.82(-2.85,-2.79) | 2.31(2.30–2.33) | 2.31(2.30–2.33) |
ln_theta | | -0.17 (-0.42-0.08) | -1.47(-1.66,-1.28) | -3.58(-4.00, -3.17) | -3.58(-4.00, -3.17) |
Gamma/p | | 0.05(0.04–0.05) | 0.06(.06-0.062) | 10.11(9.97–10.25) | 10.11(9.97–10.25) |
Theta | | 0.84 (0.65–1.09) | 0.23 (0.19–0.28) | 0.03 (0.03–0.04) | 0.03 (0.03–0.04) |
LR test of theta = 0 | Chibar2(1) | 702.10 | 599.27 | 35.40 | |
Prob-hibar2 | < 0.001 | < 0.001 | < 0.001 | < 0.001 |
! Significant beyond two decimal points |
* Significant at 95% CI, ** Significant at 99% CI |
Multivariable analysis of Inverse Weibull gamma shared frailty model
In the inverse Weibull gamma shared frailty model, the null model, only with the cluster effect and the full model, with predictor factors were compared to visualize reduction of frailty variance on the addition of predictor variables which revealed that in the full model variance theta reduced from null model 0.05 to 0.028 (Table 8) and 0.025 in the interaction model significantly (annex 2, table 10) (table part) (Interaction involving inverse Weibull gamma shared frailty model) respectively. In this model predictor variables geographical regions, women education level, contraceptive use, spousal age difference, age at first marriage, age at first sexual intercourse, religion and age at first sexual intercourse interaction with age at first marriage, were significant predictor variables at 95% confidence level. This shows that they were significant factors for determining the time to first birth for Ethiopian reproductive age women.
Having the same frailty or cluster effect living in Oromia increased the hazard of early childbirth by 18% (AHR = 1.18, 95%, CI: 1.06–1.30); living in SNNP increased the hazard of early childbirth by 19% (AHR = 1.19, 95, CI:1.06–1.30); living in Eastern pastoralist region increased the hazard of early childbirth by 16% (AHR = 1.16, 95%, CI:1.05–1.28) and living in western semi pastoralist regions increased the hazard of early childbirth by 37% (AHR = 1.37, 95%, CI:1.24–1.52) than living in most urban regions controlling for other factors (Table 8).
With the same level of frailty and adjusting for the other factors women having secondary and higher education level have 14% (AHR = 0.86, 95% CI: 0.78–0.96) and 25% (AHR = 0.75,95% CI: 0.65–0.85) hazard reduction of first birth at early age compared to women with no education level respectively. It was also seen that from the accelerated failure time output women who had secondary education able to delay their first birth by a factor of 1.02 (ATR = 1.02, 95% CI: 1.01–1.03) and those who had higher education by a factor of 1.04 (ATR = 1.04, 95%; CI: 1.03–1.05) than those women had no any formal education at any time (table 10).
Women with richer wealth index were had 10% higher hazard of first birth at an early age compared to those women with poorest wealth index keeping other factors constant and in the same frailty level (AHR = 1.10, 95%, CI:1.01–1.19).
Women living in the same cluster and adjusted for other factors women ever using any methods of contraceptive to delay first birth reduces the hazard of first birth at an early age by 0.91 times compared to ever non-users (AHR = 0.91, 95%, CI:0.86–0.97).
Adjusting for other factors and women in the same frailty having spousal age difference greater than 5 years had 11% higher hazard of first birth at an early age compared to women having spousal age difference less than 5 years (AHR = 1.11, 95% CI:1.05–1.16).
At the same level of susceptibility and holding constant other factors women who were married 15–17 years had 2.33 (AHR = 2.33, 95%, CI:2.08–2.63) times higher hazard of first birth at early age compared to women those who were married 18 years and above respectively. It was also interpreted as time to first birth was accelerated by a factor of 0.90 (ATR = 0.90: 95% CI:0.89-91) among women married before 15 years and by factor 0.94 (ATR = 0.94, 95%, CI:0.93–0.95) among married 15 to 17 years compared to women married 18 years and later at any time (Annex 3, Table 11)
The hazard of first birth at an early age was increased by (AHR = 23.81, 95%, CI: 22.22–25.64) times in married stratum and reduced by (AHR = 0.063, 95%, CI: 0.035–0.11) time in not married stratum among women who were started sexual intercourse earlier than 15 years than those women started sexual intercourse at the age of 18 years and later with marriage in the same level frailty level and making constant other factors. The hazard of early childbirth was higher among women who were stated intercourse 15 to 17 years in marriage by (AHR = 5.56, 95%, CI: 5.26–5.88) and it was reduced by (AHR = 0.033: 95%, CI:0.022–0.048) in those started intercourse before marriage than those who were started sexual intercourse in marriage at the age of 18 years and later (Table 9).
Table 9: crude, adjusted and marriage specific strata comparison of effect sizes to identify interaction or confounding
Age at first sex | Crude HR | Adjusted HR | Married stratum | Not married stratum |
< 15 years | 1.89 (1.78–1.99) | 12.26 (11.26–13.33) | 23.81 (22.22–25.64) | 0.063 (0.035–0.11) |
15–17 years | 0.68 (0.65–0.71) | 3.22 (3.03–3.45) | 5.56 (5.26–5.88) | 0.033 (0.022–0.048) |
≥ 18 years | Reference | 1 | 1 | 1 |
LR test for interaction | Degree of freedom | Chi-square statistic | p-value | |
Age at first marriage with age at first sexual intercourse | 4 | 184.33 | < 0.001 | |
The hazard of early childbirth was higher among Muslim religion followers by 10% than orthodox followers given that they were in the same cluster and control for other factors (AHR = 1.10, 95%, CI: 1.03–1.19).
For both below 15 years and 15 to 17 years age at first sexual intercourse the crude, marriage strata specific and adjusted hazard ratio were different. However, the crude hazard ratio was in between marriage strata which indicate marriage is effect modifier of age at first sexual intercourse on time to first birth data (Table 9).
In addition to main effect the interaction term revealed that those married before the age of 15 and enter into sexual intercourse at the age of 15–17 years had an increased hazard of first birth at an early age by (AHR = 4.55, 95%,CI: 2.13–10.02) than who were enter into sexual intercourse with marriage at the age of 18 and later. The hazard of an early childbirth increased by (AHR = 2.63, 95%, CI: 2.01–3.45) times among women had sexual intercourse at marriage 15 to 17 years than who were married 18 years and later.
Model Adequacy
The finding of the bivariable analysis showed that region, respondents education, respondents occupation, household wealth index, spousal age difference, contraceptive use, age at first marriage, age at first sexual intercourse, media exposure, husband education, and occupation were significantly associated with time to the first birth. Residence and religion were included in the multivariable analysis due to previous research significance. However, in the multivariable analysis; region, respondent’s education, age at first sexual intercourse, age at first marriage, spousal age difference, contraceptive use, household wealth index, religion and age at first sexual intercourse and age at first marriage interaction terms are statistically significant predictors of time to first birth among reproductive-age women in Ethiopia (Table 8).
The Cox-Snell residuals versus the Nelson-Aalen cumulative hazard function were obtained by fitting the cox gamma shared frailty, inverse Weibull gamma shared frailty, log-logistic inverse Gaussian frailty and lognormal gamma shared frailty models. The Nelson Aalen cumulative hazard function against the Cox-Snell residuals has a linear pattern making a straight line through the origin of the inverse Weibull gamma shared frailty model when compared to the rest models. This suggests that the inverse Weibull gamma shared frailty model provided the best fit for the time to first birth data analysis (Fig. 8)
Some variability about the 45° line in the right-hand tail is due to reduced effective sample caused by prior gave birth and censoring.