Why Do Women Delay in Seeking Prenatal Care? A Discrete-Time Survival Analysis

This paper evaluates the effect of access to the Ghana national health insurance on the timing of the first prenatal care visit for pregnant women after controlling for other factors. Due to the voluntary nature of the national health insurance program, insurance status is likely endogenous, this paper therefore uses the Multilevel Multiprocess (MLMP) model and the Mixed Proportional Hazard (MPH) model estimation techniques, which controls for endogeneity in survival data analysis. Results from the estimation shows that access to insurance reduces the delays in receiving prenatal care, and increases the probability of seeking prenatal care.


Multiprocess (MLMP) model and the Mixed Proportional Hazard (MPH) model which addresses
endogeneity (unobserved heterogeneity) in survival analysis and duration models. The multilevel multiprocess model is used to analyze the impact of social health insurance on the gestational age at which women receive their first prenatal visit while the mixed proportional hazard model addresses the impact of social health insurance on the probability of seeking prenatal care.
In a developing country context, there have been several studies regarding prenatal care and health insurance. Simkhada et al. (2008) studied the factors affecting the utilization of prenatal care in developing countries and found maternal education, marital status, cost of care, household income, and having a history of obstetric complications as the most significant factors affecting prenatal care. In Ghana, Abrokwah et al. (2014), studied how Ghana's National Health Insurance (NHIS) program affects prenatal care usage and out-of-pocket expenditures using a two-part model and found that access to the national health insurance increases the number of prenatal care visits, and lowers out-of-pocket expenditures. Smith et al. (2006), studied the Community-Based Health Insurance (CBHI) and access to maternal health services for Ghana, Mali, and Senegal and found that CBHI increases maternal health care access.
There is scant economic literature in the area of applying survival analysis and duration models in studying health care seeking behavior-for example how people's behavior changes over time when they are sick, injured or become pregnant, with and without the presence of social intervention programs. There are a few studies that have researched different aspects of timing of prenatal care usage including Essex et al., (1992), Kenney et al., (1995), Currie et al., (1996) and Rowe et al., (2003). Quick et al., (1981), studied the effect of delayed prenatal care on maternal and infant health outcomes and found that women who delay seeking prenatal care have a higher risk of neonatal mortality, higher infant mortality and babies with lower birthweights. Alderliesten et al., (2007) is the only paper to the best of our knowledge that studies delays in prenatal care using survival analysis. They studied the difference in timing of the first prenatal visit between ethnic groups in the Netherlands and the effect of some risk factors on this timing using the Kaplan Meier survival curve and Cox Proportional Hazard Model. They found that in comparison to caucasian Dutch women, there is delay by all ethnic groups in the timing of their first prenatal visit and these differences were explained by risk factors such as poor language proficiency in Dutch, lower maternal education and teenage pregnancies in women born in non-Dutch-speaking, non-Western countries.
To the best of our knowledge, this is the first paper to evaluate the impact of social health insurance on the timing of the first prenatal visit by pregnant women using a survival model which controls for endogeneity and unobserved heterogeneity. The literature on developing countries focuses mostly on prenatal care usage and insurance but not the timing of first prenatal care. Delay in starting prenatal care can lead to higher infant mortality and babies with lower birthweights (Quick et al., 1981;and Kenney et al., 1995). Since most developing countries are plagued with a high incidence of maternal and infant www.scholink.org/ojs/index.php/rem Research in Economics and Management Vol. 6, No. 2, 2021 4 Published by SCHOLINK INC. mortality, this paper identifies insurance as a factor that reduces delays in seeking prenatal care which can help policy makers in their fight against maternal and infant mortality

The Ghana National Health Insurance Scheme
The Ghana National Health Insurance Scheme (NHIS) is a social health insurance program established by the government of Ghana in 2003 to provide affordable healthcare, ensure equity in health coverage and also improve access to health care services for all Ghanaians. The NHIS replaced the "cash and carry (Note 1)" system where user fees were charged for health services.
Informal sector workers who make up the majority of the population could enroll voluntarily into the NHIS. Formal sector workers however, are mandated to enroll and receive a payroll deduction of 2.5 percent of income, unless they are able to prove that they have private health insurance. Informal sector workers who enroll in the NHIS pay a flat premium payment of 7.2 GhC ($1.82) for the poor and 48GhC ($12.11) for the rich. There is also the payment of an annual registration fee, which ranges from 7 to 50GhC ($1.77 to $12.61). Groups such as pensioners, people above the age of 70, children under age 18, the "core poor (Note 2)" and pregnant women (as of 2008) are exempted from paying premiums.
Statistics by the National Health Insurance Authority (NHIA) on NHIS registration show that enrolment has increased since operations began in late 2005. Figure

Nelson-Aalen Estimator Graphs
The Nelson-Aalen estimator is mostly applied to survival data analysis to estimate the cumulative number of expected events over time. This technique is used to estimate the cumulative hazard rate (H(t)) function from censored survival data as an increasing right step function with increments at the observed failure times. H(t) is the sum of the hazards at all event times up to t and it also records the number of times we would expect to observe the hazard over a given period if it were repeatable. The Nelson-Aalen curve shows the relationship between the cumulative hazard rate and time. The hazard rate in this paper is the cumulative probability of receiving prenatal care or the proportion of women who receive prenatal care over time. The time variable is the gestational age at first prenatal visit which is measured in weeks.

Average Time at First Prenatal Visit
Uninsured Insured

Multilevel Multiprocess Model (MLMP)
The multilevel multiprocess models (MLMP) are used to control for selection biases which arise from unobserved personality traits. The MLMP model consists of multilevel proportional hazards equations which include correlated heterogeneity components, with normally distributed random effects and are used to control for endogeneity and selection effects. Including jointly normally distributed random effects allows one to adjust estimates for the correlation of the total underlying residuals, and it allows one to estimate the covariance matrix of residuals and, hence, the selection effects (Lillard, 1993).
In controlling for endogeneity in survival analysis, the MLMP models estimate lognormal survival models jointly with probit models. If the hazard of the event under study is affected by an endogenous dummy, the hazard in question and the occurrence of the endogenous dummy are modeled jointly: Where ℎ is the log of the hazard, * is the endogenous dummy variable, i indexes individuals and j indexes the recurrent observations. Vector X is a vector of explanatory variables in the equations. The lognormal model is further reformulated as an accelerated failure-time (AFT) model which measures the direct effect of the explanatory variables on the survival time. The log failure times (τ) model can be represented as: (1) = (1) + (1) + (2) = (2) + (2) + (2) These equations are seemingly unrelated because the error terms can be correlated. The AFT model assumes that the distribution of the duration of an individual with covariate vector X and the transformed duration of are the same since the covariates affect the duration proportionally (Bijwaard, 2008).
When the coefficient β is greater than zero, the covariate accelerates the duration, and decelerates the duration when the coefficient is smaller than zero.

Mixed Proportional Hazard (MPH) Model
The Mixed proportional hazard (MPH) model estimates discrete time proportional hazards models using maximum likelihood estimation by specifying the hazard rate as the product of a regression function that captures the effect of observed explanatory variables, a base-line hazard that captures variation in the hazard over the spell, and a random variable that accounts for the unobserved heterogeneity. In the mixed proportional hazard model, the hazard is a function of a regressor , unobserved heterogeneity , and a

Multilevel Multiprocess Model Estimation Results
Results from estimation of the 2005 is shown in table 2 below on the effect of social health insurance on the gestational age at first prenatal care visit, controlling for some demographic characteristics using the multilevel multiprocess model to control for endogeneity. The MLMP models measure the direct effect of the explanatory variables on the survival time. If the time ratio is greater than 1, then the gestational age increases as the value of the explanatory variable increases. However, if the time ratio is less than 1, then the gestational age decreases as the value of the explanatory variable increases.
Results of two models are presented in Table 2; model 1 includes the basic characteristics of the woman and household and model 2 adds regional dummy control variables. For the main variable of interest, insurance status, the results from Table 2 shows that the impact of insurance on the gestational age at first visit is negative and statistically significant at the 5% level for both models. The time ratio shows that having insurance decreases the gestational age at which women receive their first prenatal care compared to the uninsured. The value of the time ratio suggests that switching from being uninsured to being insured decreases the time a pregnant woman waits to receive her first prenatal care by 53%. This result is expected because health insurance lowers health care costs for pregnant women and enables them to reduce the delays in receiving their first prenatal care.
In terms of the other factors affecting the timing of prenatal care, a few results are worth pointing out.
Both models show that married women receive prenatal care earlier than unmarried women. Women who travel a longer distance before getting to a health facility delay their first prenatal visits. Most women in the informal sector are traders who are mostly in the lower income quintile. The result shows that women who are in trade delay seeking prenatal care. Table 3 shows results for pooled data using the MLMP model. The results are consistent with the previous results. More specifically, insurance decreases the gestational age at first prenatal visit by 47%.
Women who have experienced still-births in previous pregnancies receive care earlier than women who haven't. The dummy variable for the survey year is not significant.

Mixed Proportional Hazard Model Estimation Results
The proportional hazard model measures the effect of the explanatory variable on the hazard rate, which in the case of this study is the probability of receiving prenatal care. If the hazard ratio is greater than 1, then the probability of receiving prenatal care increases as the value of the explanatory variable increases.
If the hazard ratio is less than 1, then the probability of receiving prenatal care decreases as the value of the explanatory variable increases.
The results from Table 4 shows that having insurance increases the probability of receiving prenatal care compared to the uninsured in the 2005. As insurance becomes more affordable and accessible to pregnant women, even those who would have otherwise not received prenatal care are now more likely to receive care. Insurance is still positive and statistically significant in the pooled data as shown in Table 5. The Published by SCHOLINK INC. statistically significant coefficient for the duration variable in both Tables 4 and 5 suggests that, the further along a woman gets into her pregnancy, the more likely she is to receive prenatal care. Women with primary school education and lower are less likely to receive prenatal care compared to women with higher education. Less educated women may be less likely to realize the benefits of using prenatal care services as compared to educated women (Matsumura & Gubhaju, 2001). Being married also increases the probability of receiving prenatal care.   *, ** and *** indicate statistical significance at 10, 5 and 1% respectively Note. The MPH models measure the effect of the explanatory variables on the probability of receiving prenatal care.

Conclusions and Policy Implications
This paper studies how the introduction of the Ghana National Health Insurance Scheme (NHIS) has changed the gestational age at which pregnant women receive their first prenatal care as well as the probability of women receiving prenatal care. The paper uses survival analysis techniques to model the gestation age at first prenatal visit (time to event). The multilevel multiprocess hazard (MLMP) model and the mixed proportional hazard (MPH) model survival techniques are used to control for unobserved heterogeneity and endogeneity of the insurance status.
The results show that having insurance significantly reduces the gestational age at which a pregnant woman receives her first prenatal care and also increases the probability of a pregnant woman receiving prenatal care.
From a policy perspective this reduction in the timing of the first prenatal visit can help reduce maternal mortality as certain complications can be detected earlier on and prevented or treated and thereby reducing deaths from such complications. The WHO can urge other developing countries to initiate similar social health programs to help produce improved health outcomes.