A Study on Self-Assessed Life Expectancy Among Older Adults in Côte d’Ivoire

Background: The purpose of this study was to estimate individuals’ expected longevity based on self-assessed survival probabilities and determine the predictors of such subjective life expectancy in a sample of elderly people in Côte d’Ivoire. Methods: Paper-based questionnaires were administered to a sample (n=267) of older adults residing in the city of Dabou, Côte d’Ivoire in May 2017. Information on subjective expectations regarding health, comorbidities, and self-assessed survival probabilities were collected. The subjective expectations were related to sociodemographic, health and lifestyle indicators. A spline-based approach was used to estimate the overall distribution of life expectancy for each individual using two to four points of self-assessed survival probabilities. A finite mixture of regression models was used to identify clusters/components of the overall subjective life expectancy distribution of the study participants. Results: The mean subjective life expectancy in older people varied according to four components/clusters. The average subjective life expectancy among the elderly was 79.51, 78.89, 80.02 and 77.79 years in the first, second, third and fourth component of the subjects' overall subjective life expectancy, respectively. The effect of sociodemographic characteristics, comorbidities, and lifestyle on subjective life expectancy varied across components. For instance, a U-shape relationship between household per capita income and subjective life expectancy was found for individuals classified into the third component, and an inverse U-shape relationship was found for individuals classified into the fourth component. Conclusion: We extended the estimation of subjective life expectancy by accounting for heterogeneity in the distribution of the estimated subjective life expectancy. This approach improved the usual methods for estimating individual subjective life expectancies and may provide insight into the elderly’s perception of aging, which could be used to forecast the demand for health services and long-term care needs.

3 Studies using subjective life expectancy (SLE) as a measure of longevity have stressed that SLE is an important determinant of changes in labor supply, health, and consumption behaviors [1][2][3].
Subjective life expectancy determines the intended retirement age [1] and the way older workers prepare for their retirement [2]. There is evidence that older workers take into consideration subjective life expectancy in their decision to postpone retirement [2]. Even among retirees, subjective life expectancy affects the decision to return to paid work [2]. Furthermore, subjective life expectancy has been shown to affect health self-regulation [3]. Individuals with low subjective life expectancy have a weak intention to perform physical exercises, and when they do, they are less likely to plan for those exercises. Subjective life expectancy has also been shown to affect bequest, consumption, and savings [4]. Although important, given its social and economic implications, research on subjective life expectancy in developing nations is lacking, particularly for the elderly.
This paper focuses on the case of a Sub-Saharan African country, Côte d'Ivoire. Côte d'Ivoire is a developing country with a low life expectancy (55.7 years on average at the national level, based on the Population and Housing Census of 2014). The poverty rate is relatively high (46.3% in 2015), with 30% of the overall population living in slums [5]. Several non-communicable and communicable illnesses that include Human Immunodeficiency Virus/Acquired Immune Deficiency Syndrome (HIV/AIDS), tuberculosis, blood pressure, are highly prevalent, and unhealthy behaviors like smoking or alcohol consumption are also developing. All these factors tend to affect individuals' health conditions, and thus, their subjective life expectancy. An individual's subjective life expectancy is key for understanding individual consumption choices and behaviors, especially for older individuals [6,7], and can potentially lead to the development of specific policies to address aging. However, measuring SLE is not a straightforward task.
Several studies use the self-assessed survival probabilities (SSPs), i.e. assessment of the probability of surviving to a certain predefined age [4], to determine the time until the end of life. Previous studies have established that the SSP is a good predictor of real life expectancy and mortality [6][7][8][9].
Interestingly, the variance of the SSP declines with age [10], thus, the SSP gives an accurate measure of life expectancy as age increases. Thus, it has been recommended that studies dealing with the end of life behaviors should use SLE instead of actuarial tables [5]. However, critics argue that the traditional approach for measuring the SLE using only one SSP fails to fully capture the expectations formation process of individuals who are subject to that exercise.
In this paper, we aim to (i) estimate older adults' SLE using the two to four SSPs, and (ii) identify the determinants of such SLE in Côte d'Ivoire. The rest of the paper is organized as follows. Section 1 presents the methods used to address the above aims. Section 2 presents the dataset used herein and is followed by a description of the methodological approach. Section 3 is devoted to the presentation and discussion of the results and is followed by a conclusion in Sect. 4.

Methods
Sampling strategy, data collection, and outcome measures For this study, data were taken from the health section of a survey developed by students and researchers at the Ecole Nationale Supérieure de Statistique et d'Economie Appliquée (ENSEAnational school of statistics and applied economics in English) and administered to a sample of 15-to 65-year-olds from Dabou and its vicinity, a small town at 60 kilometers from Abidjan, Côte d'Ivoire.
A multistage sampling strategy was used and motivated by the need for economical (limited budget) and practical (limited number of interviewers, restricted time) efficiency. We randomly selected households stratified on 5 levels: 1) group 1: Dabou (1 locality), 2) group 2: 4 villages (Dabou's vicinity) with more than 700 households, 3) group 3: 3 villages with 400 to 700 households, 4) group 4: 8 villages with 150 to 400 households, and 5) group 5: 1 village with less than 150 households. We used the following respective sampling rate: 5%, 20%, 33%, 50% and 100%. This drawing allowed us to obtain a sample of 2776 households, among which 663 from group 1 (Dabou), 794 from group 2, 427 from group 3, 823 from group 4 and 69 in from group 5. Then, at the level of each household, a simple random draw was used to capture one individual among those 15 and above in age. The number of individuals aged 15 and above retained amounted to 2523, with a refusal rate estimated at 9%. Because our target population was elderly, we extracted information from this dataset regarding individuals aged 50 to 65.
Two questionnaires, validated through a pre-test procedure, were used in the survey. Informed consent was obtained from all subjects (for participants under 18 from a parent and/or legal guardian) before administration of the survey. The first questionnaire was administered to the head of the household to gather information on the members of the household, including demographic characteristics, education and employment status, and dwelling/living conditions. The second questionnaire gathered information about the participants' health, including overall self-assessed health, conditions, physical functioning, health behaviors (e.g. smoking, alcohol, diet, exercise), and self-assessed survival probabilities for four target ages (70, 75, 80 and 85). The dataset also contains some socioeconomic variables that include gender, age, employment status, and living conditions (Appendix A). From this dataset, we extracted information about all individuals aged 50 to 65 to target elderly populations.

Approach
The methodological approach used in this paper is twofold: (i) using the approach developed by Bellemare et al. (2012) to calculate the life expectancy using the SSPs as an input [11], and (ii) using a finite mixture of regression models to investigate the determinants of the estimated life expectancy. A technical note on the methodological approach is presented in Appendix B.
The approach by Bellemare et al. is based on a cubic spline smoothing around each SSP value. This smoothing helps to estimate the cumulative distribution function of the subjective life expectancy for each individual. Given that the cumulative distribution function is strictly monotonic, the function can be approximated by a cubic polynomial around each SSP. Subsequently, the cumulative distribution function of the subjective life expectancy is estimated by connecting these local polynomials. Finally, the average life expectancy for each individual is calculated from the estimated cumulative distribution function. As an example, suppose that a person reports 100 as its SSP for the target age of 70, 60 as its SSP for the target age of 75, 30 as its SSP for the target age of 80, and 0 as its SSP for For comparison purposes, we plotted the distribution of the estimated subjective life expectancy for both males and females (stratified by age groups) using kernel density estimation.
In the second step of our methodological approach, we used a finite mixture model to assess the

Descriptive Statistics
The dataset used consists of 267 individuals with an average age of 56.4 and predominantly males (55.4%). We found that 60% of the individuals had a low education level. Table 1 provides additional statistics on the dataset. From these average values in Table 1, we found that the obesity rate grows slightly with age (12% on average for individuals aged 50-55, 13% for individuals aged 55-60 and 19% for individuals aged 60-65). Moreover, alcohol consumption declines slightly with age, while the smoking rate only declines after the age of 60. In addition, the employment rate decreases with age (from 71% for those aged 50-55 to 36% for those aged 60-65). It is also notable that only a relatively small proportion of older people perform physical activity (only 21% of those aged 50-65 perform physical activity). Furthermore, for each age group the SSP declines with the target age. However, for the same target age, the average SSP increases with age groups. At the target age of 75, for example, the average SSP is 60% for individuals aged 50-55, 66% for those aged 55-60, and 71% for those aged 60-65.

The self-assessed life expectancy function
We plotted the kernel densities per gender and age group and we added the national life expectancies trend line (red dashes) for comparison purposes and for each graph in order to better describe the estimated life expectancy. Figure 1 shows that the distribution of estimated life expectancy is not the same among the genders and age groups. Individuals in Dabou estimate their survival to be higher than the national average, and this situation is pronounced for males. However, for both males and females, and for the three age groups considered herein, the distribution of estimated life expectancies appears to be a combination of at least two probability distributions. In each group, there is a proportion of individuals who had a low estimation of their life expectancy, and those with medium or high estimations of their life expectancy. The same holds for the estimated global life expectancy distribution (Figure 2 in Appendix A). Several reasons, like changes in selfreported health [2] or perceived health conditions, might explain these differences.
The red dashes for each sex and age group are the national life expectancy calculated using the actuarial method by the National Statistics Office in Côte d'Ivoire. The blue curve represents the kernel density of the estimated subjective life expectancy. For males aged 50-55, the national life expectancy is 73.5 (red dashes, by actuarial method), while the kernel density shows that the major part of the male aged 50-55 has an estimated subjective life expectancy higher than 73.5 (the density distribution is primarily located at the right side of the red dashes).

Determinants of the self-assessed life expectancy
The determinants of the estimated life expectancy were modeled through a finite mixture of regression models. Based on the Akaike Information Criterion (AIC) and the log-likelihood, the model with four clusters/components was selected. Table 1 in Appendix A presents the AIC and log-likelihood values for the models with two, three and four clusters/components.
The results of this selected model are presented in Table 2 and illustrate the effects of concomitant variables on the probability of being in each cluster and Table 3 for the determinants of the estimated life expectancy. Some descriptive statistics about the clusters are given in Table 2 in Appendix A. The average probabilities of being appropriately classified into each cluster are all above 80%, indicating that the model has good classification power. The first cluster represents 24.73% of the population, and the average subjective life expectancy in this cluster is 79.51 years. The second cluster contains 20.97% of the sample. The average subjective life expectancy of this cluster is quite similar to that of cluster 1 (78.89 years). That being said, compared to individuals in cluster 1, which reported a poor state of health reduces individual probability while having a mother alive or thinking that health limits the working capability increases the probability to be in cluster 2. The effects of obesity also depend on the clusters. We found no evidence for an effect of obesity on subjective life expectancy for individuals in the lowest cluster. However, for individuals in the highest two clusters of subjective life expectancy, being obese reduces the subjective life expectancy, while for those in cluster 2, obesity seems to increase their subjective life expectancy. In terms of unhealthy behavior, we found that smoking reduces subjective life expectancy for individuals in the highest cluster, but also for those in cluster 2. However, for those in the lowest cluster and those in cluster 1, smoking has a positive effect on the subjective life expectancy. This result has been explained in the literature as the optimism of smokers regarding their own survival [12]. Excessive alcohol consumption also reduces subjective life expectancy in all clusters, apart from individuals in the lowest cluster for whom it increases subjective life expectancy. Rappange et al. also report that excessive alcohol consumption is positively associated with SSPs for some categories of individuals [13]. For individuals with the highest (cluster 3) and lowest (cluster 4) subjective life expectancy, we found that performing physical activities increases individual subjective life expectancy, while for those in the middle clusters (clusters 1 and 2), there is a decrease in subjective life expectancy. Not having a specific diet increases subjective life expectancy for individuals in all clusters, apart from those in the first middle cluster (cluster 1), for whom it reduces the subjective life expectancy.
In terms of employment, we found that being employed reduces an individual's subjective life expectancy in both the highest and lowest subjective life expectancy clusters, while the opposite effect was found for the two middle clusters. Having a low education/school level reduces an individual's subjective life expectancy in all clusters, apart from those in the first middle cluster, for which no significant effect was observed. This finding is consistent with the literature that highlights the heterogeneous effect of education on subjective life expectancy [7,13]. Estimates also show that

Discussion
This manuscript analyzed the subjective life expectancy among elders in Côte d'Ivoire. We propose a novel approach to estimate the subjective life expectancy. This approach builds on the method by Bellemare et al. that is based on splines [11]. It requires at least two points of SSPs to be assessed by individuals. Based on the estimated subjective life expectancy, an analysis of its determinants is proposed. This analysis uses a finite mixture of the regression model to account for the heterogeneous distributions that compose the overall distribution of the subjective life expectancy.
The estimated model allows for the classification of older people into clusters of people that have optimistic, pessimistic and moderate self-assessment of their life expectancy. These clusters are discriminated against by the self-assessed poor state of health, the self-assessed decreasing health, the self-assessed working capacity limitation due to health, an observed chronic condition, and the mother being alive. In terms of determinants of subjective life expectancy, the results suggest that the determinants of subjective life expectancy vary among clusters. The pessimistic cluster is positively associated with poor health behavior (smoking, alcohol consumption, and having no diet).
Results also suggest that low education levels and being employed are negatively associated with subjective life expectancy while having a physical activity is positively associated with subjective life expectancy for both pessimistic and optimistic clusters. Furthermore, a U-shape relationship was found between a household's income per capita and subjective life expectancy for the optimistic while a reverse U-shape relationship was found for the pessimistic. The role of socioeconomic and living condition variables has also been highlighted.
It is worth noting that our results are in line with existing literature dealing with different aspects of subjective life expectancy [7,10,12,13]. These results suggest that promoting good health behaviors, improving health and living conditions, as well as employment status, are key to increasing elders' subjective life expectancy. However, even though the results are promising, they lack generalizability. The dataset used is related to only one region of the country. Furthermore, due to its geographic proximity (under 50 kilometers and accessible by paved road) with the largest urban center of the country (the economic capital, Abidjan), this region benefits from the health facilities provided in the capital. This might affect individuals' perception of their own health and this region could differ from others.

Conclusion
In this paper, we combined a spline-based approach and a finite mixture of regression models to estimate the subjective life expectancy based on the SSPs and identified the determinants of the subjective life expectancy among elders, respectively. Doing so, we improved the estimation of subjective life expectancy by accounting for the heterogeneity of the distribution of the estimated subjective life expectancy. This approach is an improvement of the usual practices for estimating individual subjective life expectancy and may provide insights into the elderly's perception of aging, which could be used to forecast the demand for health services and long-term care needs. It may also provide important information for the development of health policy strategies aimed at addressing 19(1):121-137 (2016).

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