## Abstract

Three mechanisms related to household living standards might affect early-age mortality: the absolute level of deprivation, its level relative to the average of the community, and the inequality in the distribution of deprivation within communities. A large body of literature has explored the effect of the absolute level of deprivation, but little research has examined the association between relative deprivation and early-age mortality, and findings related to deprivation inequality are inconsistent. Using 2008 Bolivian Demographic and Health Survey data, this study explores patterns of association between the three factors and mortality occurring in the neonatal and postneonatal periods. Because household-level deprivation might capture some unmeasured characteristics at the community level, such as area-specific investments, this study decomposes household-level deprivation into its between- and within-community components. The results show that after possible confounders are controlled for, community-level absolute deprivation is a significant predictor of neonatal and postneonatal mortality. Relative deprivation and deprivation inequality are not associated with early-age mortality. These findings are specific to a context of widespread deprivation and low inequality within communities; the role of the distribution of deprivation might be more important in countries in which basic needs are met within a bigger proportion of the population. This study helps identify crucial sectors of development related to living standards and deprivation inequality in order to tackle neonatal and postneonatal mortality.

## Introduction

In many studies on neonatal and infant mortality, traditional biodemographic determinants account for only a limited proportion of household-level variation in mortality (Bengtsson and Dribe 2010; Edvinsson and Janssens 2012). Socioeconomic determinants of infant and child mortality have been extensively analyzed in the literature, but neonatal and postneonatal mortality require further investigation (Neal 2009). The determinant of primary interest in this article is deprivation, interpreted as a lack of basic needs related to housing conditions and living standards. Deprivation can be considered as a concept underlying certain characteristics of living standards and can be derived from a set of observable indicators related to the living environment and the possession of assets. Indeed, focusing only on low income can be an unreliable indicator of poverty, failing to identify those experiencing deprivation and exclusion (Nolan and Whelan 2010).

The literature suggests that deprivation might affect mortality through three mechanisms, leading to the absolute deprivation, relative deprivation, and deprivation inequality hypotheses (Johannesson 2004). The absolute deprivation hypothesis states that the absolute manifestation of deprivation is a determinant of mortality. This hypothesis has found broad support in explaining postneonatal mortality (Bruce et al. 2000), although the picture is unclear for neonatal mortality (Bobak and Leon 1992; Rahman et al. 2010). The relative deprivation hypothesis considers the level of deprivation relative to the average level of the group of reference as a determinant of mortality via social comparisons generating stress and corrosion of social cohesion, which can lead to negative health outcomes (Wilkinson 1997). There is some evidence of an association between unfavorable social comparisons and negative early-age health outcomes, but previous studies were conducted in high-income countries (Lhila and Simon 2010; Olson et al. 2010; Reagan et al. 2007; Tacke and Waldmann 2013). Finally, the deprivation inequality hypothesis considers the contextual effect of the variation in deprivation within communities as a determinant of mortality, for which inequality can be a hazard for the whole population rather than for only the households with less favorable social comparisons. To date, most of the literature on deprivation inequality and relative deprivation and health has focused on adults (Balsa et al. 2014). Here, I simultaneously assess the significance of each of the mechanisms linking deprivation to early-age mortality, in both the neonatal and postneonatal periods. The findings of this work complement the ongoing discussion on the mechanisms linking income to mortality. By considering poverty as a multidimensional condition (Sen 1989), my aim is to assess the net effect of housing conditions and living standards on neonatal and postneonatal mortality while accounting for the effect of the other dimensions of poverty that are left as control variables in the models.

This study focuses on the determinants of neonatal and postneonatal mortality in Bolivia in 2008, when the country had among the highest neonatal and postneonatal mortality rates in the continent (Coa and Ochoa 2009). Marked inequality in early-age mortality indicators existed across the country, with a strong urban-rural gap (Pooley et al. 2008) and a higher incidence of mortality among indigenous newborns (Castellanos 2007). Furthermore, in 2008, I can assess the first results of the Bolivian health reform, which started in 1996 and was further developed in 2002. Bolivia also experienced widespread poverty (Coa and Ochoa 2009) and had one of the highest levels of economic inequality in Latin America (World Bank 2014).

The research question I aim to answer is, How important are absolute deprivation, relative deprivation, and deprivation inequality in determining neonatal and postneonatal mortality at the micro level for the case of Bolivia?

A multilevel structural equation modeling (SEM) approach, combining a three-level discrete-time event-history model for mortality with a latent variable model for deprivation measured at the household level, is applied to data from the 2008 Bolivian Demographic and Health Survey (DHS). Separate models are fitted to estimate the effects of the covariates of interest on mortality occurring in the neonatal and in the postneonatal periods. SEM allows the creation of a latent variable for household deprivation, its decomposition into between-community and within-community between-household components, and their inclusion in the model as predictors of mortality.

The main contribution of this study is the use of multilevel models to simultaneously assess the significance of each of the mechanisms linking deprivation to the components of infant mortality, in both the neonatal and postneonatal periods. Wilkinson (1994) theorized that the distribution of wealth might play a role in only those countries where basic needs are met, but its effect on health outcomes in low- and middle-income countries has rarely been explored. Moreover, to my knowledge, no prior research exists involving the decomposition of household deprivation into its household- and community-level components and the assessment of their effect on mortality. Finally, a lack of studies related to the effects of living standards and housing conditions on neonatal and postneonatal health outcomes is evident in the literature. Adding evidence on the association between deprivation and the components of infant mortality might shed light on the reasons for the differential trends in neonatal and postneonatal mortality observed over the last decades, given that the pace of the decline of neonatal mortality rate has been slower than that of postneonatal mortality (UNICEF et al. 2015).

## Hypotheses Linking Deprivation and Early-Age Mortality

### Absolute Deprivation

Deprivation, defined as a lack of basic needs related to housing conditions and living standards, can be considered to be an underlying cause of many infant deaths because of its effect on several risk factors during the antenatal and neonatal periods (Wagstaff 2002). Unfavorable economic conditions have been found to be positively associated with risk factors, acting through environmental aspects (Jain 1985; Rutstein 2000); nutritional deprivation, in both mothers and children (World Health Organization 1999); maternal education (Neal 2009); and reduced access to health care (Lawn et al. 2005).

When deprivation is defined as a lack of basic needs related to the housing environment, the effects of environmental factors on health in the neonatal period are inconsistent. The quality of sanitation, water, and indoor air are strongly associated with infant mortality (Bruce et al. 2000; Esrey 1996), but evidence of different impacts on mortality at specific ages within the first year of life is limited. The association between neonatal mortality and environmental factors is found to be weaker than for postneonatal mortality (Bobak and Leon 1992) or even nonsignificant (Rahman et al. 2010). The smaller influence of environmental factors on neonatal mortality could be due to the fact that in the first month of life, mortality is more strongly associated with endogenous determinants, such as preterm birth complications or congenital diseases (Black et al. 2010; Taskaya and Demirkiran 2016). Another factor might be the reduced time of exposure to environmental factors of only 28 days.

### Relative Deprivation

It has been argued in the literature that the relative level of deprivation might be a better predictor of health outcomes than its absolute level (Marmot et al. 1991). According to this hypothesis, the level of a household’s wealth should be compared with the level of the reference group when assessing its effect on health (Wilkinson 1997). In general, poorer health among more disadvantaged people may be due to the lack of material and social resources (Lynch et al. 2001) and to negative upward social comparisons (Kawachi et al. 2002). Few studies have focused on the relationship between relative deprivation and early-age health outcomes (Lhila and Simon 2010), and these studies are all set in high-income countries; a gap in the literature on the effects of relative deprivation in the context of low- and middle-income countries is evident. Although it is reasonable to think that children are unaware of social comparisons (Turley 2002), relative deprivation could affect their parents (Reagan et al. 2007). In two studies based in the United States, higher relative deprivation was significantly associated with higher probabilities of low birth weight, preterm birth (Lhila and Simon 2010), and intrauterine growth restriction (Reagan et al. 2007). On the other hand, a U.S. study found a stronger effect of absolute income, rather than its relative level, on infant health outcomes (Olson et al. 2010). Reagan et al. (2007) and Lhila and Simon (2010) identified maternal stress as the pathway through which infant health is affected.

### Deprivation Inequality

In addition to the absolute and relative level of deprivation, the distribution of deprivation might have a contextual effect on health outcomes (Johannesson 2004). The overall quality of public services could be worsened by the segregation of the rich into their own communities, with access to private education and health care (Stiglitz 2013). Deprivation inequality fosters the erosion of social cohesion, generating shame, depression, anxiety, crime, and violence (Wilkinson 1997). It is worth highlighting the difference between the deprivation inequality and the relative deprivation hypotheses: whereas the former states that inequality in the distribution of deprivation can be a hazard for the whole population and does not affect only people who care about social comparisons, the latter affirms that better-off households may even benefit from living in an unequal society. Inequality is calculated at the community level, assigning the same value to all the households within the same community; comparatively, relative deprivation involves different values for each household given that it compares their deprivation with the average level of deprivation of their community.

Studies assessing the effects of inequality on health have produced inconsistent findings. This debate can be summarized by two systematic reviews about the relationship between inequality and health by Lynch et al. (2004) and Wilkinson and Pickett (2006), who drew opposite conclusions. Although Lynch et al. (2004:5) stated that there is “little support for the idea that income inequality is a major, generalizable determinant of population health differences,” Wilkinson et al. (Wilkinson and Pickett 2006:1768) argued that “[the majority of the studies] suggest that health is less good in societies where income differences are bigger.” This difference might be due to the fact that inequality could have an effect on health only in countries where the condition of absolute deprivation is overcome, whereas absolute material standards could still be the major determinants of mortality in less developed countries (Marmot 2005; Wilkinson 1997).

Finally, it might be argued that studying the deprivation inequality hypothesis is irrelevant in countries with very low levels of inequality within communities. However, in Bolivia, the within-community variance component was estimated to account for one-fifth of the total variance (Temporin 2019), thus presenting nonignorable differences across households. In such a context, the effect of inequality might be significantly associated with neonatal and postneonatal mortality.

### The Hypotheses in the Context of Peripheral Countries

When categorizing countries by trading patterns and world-system roles rather than income, one can expect the effects of the mechanisms linking deprivation to early-age mortality to be different between peripheral and nonperipheral countries than they are between high- and low-income countries. For instance, Moore (2006) found a significant difference in the relationship between income inequality and life expectancy in nonperipheral and peripheral countries but not when the countries were stratified according to their GDP per capita. Inequality might be an important health hazard factor in peripheral countries, even if they are considered middle- or even high-income countries: their populations are more vulnerable because of, among other things, neoliberal philosophies and international trade agreements (Coburn 2000). This article therefore adds evidence to the literature about the relationship between inequality and health outcomes by setting the analyses in Bolivia, which has been categorized as a middle-income (World Bank 2014) and peripheral country (Moore 2006).

## The Bolivian Context

In 2008, Bolivia was among the most delayed countries in the demographic transition in South America, although positive trends in each mortality-related indicator were converging with the rest of the continent. Bolivian neonatal, infant, and child mortality rates were among the highest in the continent—at, respectively, 27, 50, and 14 deaths per 1,000 live births (Coa and Ochoa 2009). Moreover, in 2008, Bolivia was one of the most unequal (World Bank 2014) and poorest countries in South America, having among the worst performances with respect to the poverty headcount ratio at national poverty lines (45% of the population) and chronic malnutrition (22% of children) (Coa and Ochoa 2009). There was marked urban-rural inequality in the distribution of wealth (Castellanos 2007) as well as in the demographic indicators concerning early-age mortality (Pooley et al. 2008).

The Bolivian health system has undergone major changes in recent decades. The Bolivian health reform, launched in 1996, had an important development in 2002, when a package of free services covering 547 health issues was implemented (Ledo and Soria 2011). Bolivian indicators concerning prenatal and childbirth care, and neonatal and infant mortality showed a steady improvement after the health program began (Coa and Ochoa 2009).

Finally, indigenous ethnicity is an important characteristic of the Bolivian population: more than 61% of Bolivian people were estimated to have native origins (Instutito Nacional de Estadística (INE) 2002). The indigenous population suffers from social exclusion in terms of poverty, education, and health (Castellanos 2007), and social norms and cultural beliefs shape behaviors affecting early-age mortality (Kitts and Roberts 1996).

## Data and Measures

### The 2008 Bolivian Demographic and Health Survey

The 2008 Bolivian DHS is the data source for this micro-level study (Coa and Ochoa 2009). DHS data sets have a three-level structure, with children nested within households, nested within primary sample units (PSUs). In the sampling process, clusters of a standard size of 100 households were identified and mapped in the territory of the country under investigation, and a further selection within each of these clusters was made. Each of these areal units served as a PSU, which broadly corresponds to villages in rural areas and neighborhoods in urban areas (Ackerson and Subramanian 2008). For this study, PSUs are considered proxies for the respondents’ communities, as in previous studies (Robson et al. 2012; Uthman et al. 2011). *Communities* are therefore defined as clusters of households within a geographical living environment. PSUs are a consistent measure of community in DHS surveys (Griffiths et al. 2004), and their sample size has been demonstrated to meet the optimum size with a tolerable precision loss (Kravdal 2006).

Only births occurring within 10 years of the survey were included in the analysis in order to minimize changes in the values of time-varying covariates and in mortality patterns over time and to minimize recall error (Eisenhower et al. 1991). Models that include births occurring within five years of the survey were also fitted, and results are shown in section 2 of the online appendix. Surviving children born within a year of the date of the interview, having therefore incomplete exposure to the risk of postneonatal mortality, were excluded from the analysis to avoid issues related to different lengths of exposure. The analyses considered only those children in households with complete data on the ownership of the indicators related to housing conditions and predictors of mortality, giving a total of 18,302 children belonging to 5,849 households and to 988 communities. The exclusions had little impact on the distribution of the DHS wealth index in the sample.

### Mortality Outcome

Separate models were fitted for the neonatal and postneonatal periods. The dependent variable of the structural model for mortality is based on the child’s age at death, or for surviving children (with censored durations), on the age at the end of the observation period. The postneonatal period was divided into 112-day subperiods, and a categorical independent variable was included in the models to indicate the subperiod during which the death took place. There were 983 deaths within the first year of life in the sample, corresponding to 5.4% of the total (SD = 0.25), 527 of which happened within the neonatal period. The number of neonatal deaths per community ranges from 0 to 9, and the number of postneonatal deaths per community ranges from 0 to 6.

### Indicators of Deprivation

The full set of indicators related to housing conditions, living standards, and owned assets available in the DHS data set include availability of electricity; availability of clean water; type of sanitation; material of the floor; type of cooking fuels; and ownership of refrigerator, radio, television, motorbike, car, telephone, or bicycle. These are the indicators used in the construction of the DHS wealth index (Rutstein and Johnson 2004).

All the observed variables were dichotomized in order to simplify the interpretation of the parameters of the models, reflecting the categorizations used in previous research (World Health Organization (WHO) and UNICEF 2014). Section 1 of the online appendix provides a description of the dichotomization of the indicators, and upcoming Table 1 shows descriptive statistics of these indicators.

### Other Socioeconomic Determinants

A set of seven socioeconomic determinants, listed in Table 1, were included in the models as control variables.

Paternal occupation is a strong determinant of the socioeconomic status of a household (Cornia 2014; Thomas 1990). Maternal education is associated with infant mortality due to higher knowledge about complications, adequate access to health services, quality of feeding, and household sanitation (Neal 2009). Indigenous groups account for more than one-half of the Bolivian population and had worse health indicators, including infant mortality (Bello and Rangel 2000). Many low- and middle-income countries present urban-rural differences in early-age mortality (Van de Poel et al. 2009): rural places might be affected by issues of accessibility and a lack of infrastructure (Andersen 2002), which are also captured by the variable for the distance to health facilities. Moreover, in relation to the distance to health facilities, the DHS provided a binary variable, with categories “Not a big problem” and “Big problem,” for women’s reported difficulty in getting medical help. A more informative variable would have been the real distance to health facilities, but the only available data set was related to main roads (GeoBolivia 2013), and this was not sufficiently detailed to include all the walking trails that women might use. Finally, because the health system reform may have reduced the impact of deprivation on mortality by smoothing disparity levels in the access to the health system among different households, models including the interactions between the dummy variable for pre-/post-2002 and the three socioeconomic determinants of interest were fitted in section 3 of the online appendix.

All the variables were provided by DHS, apart from the distance to the closest municipal capital, which was obtained by linking the geographic information system (GIS) location of the centroid of the DHS clusters with other GIS data sets (GeoBolivia 2012, 2013, 2017a, 2017b). The GPS coordinates of each PSU were randomly displaced by DHS because of confidentiality issues (Perez-Heydrich et al. 2013). Although cluster displacement might induce large misclassification errors when the distance between clusters’ centroids and health facilities or other specific locations is calculated (Skiles et al. 2013), the random displacement of the centroid of the PSUs is unlikely to affect the results of this study.

### Biodemographic Determinants

Four biodemographic determinants were included in the models (Table 1). Child’s sex has been found to be associated with infant mortality: death rates are higher among boys than girls because of a more marked male biological weakness (Naeye et al. 1971). On the other hand, differences based on the gender of the newborn might arise from different behaviors among parents in terms of seeking neonatal care and spending on health care (Willis et al. 2009). Birth order has been found to be correlated with neonatal mortality because the firstborn child has less experienced parents, and fourth or higher-order children have higher risks of infection given that they have to compete for resources with their siblings (Edvinsson and Janssens 2012). A maternal age higher than 30 can lead to a higher risk of neonatal mortality (Arokiasamy and Gautam 2008). Finally, in relation to birth spacing, intervals between consecutive deliveries that are too short or too long can lead to a mother’s depletion (Winikoff 1983). The variable for preceding birth interval was categorized as first birth, less than 24 months, and 24 or more months.

## Statistical Methods

### Critique of the DHS Wealth Index

Monetary measures of deprivation (such as income) are often unavailable or unreliable in low- or middle-income countries (Filmer and Scott 2012). Composite indices of deprivation help overcome this issue because they are calculated from a set of observable indicators. Many approaches to the choice of weights for the indicators exist (Vandemoortele 2014). Among these, principal component analysis (PCA) uses an orthogonal transformation to convert a set of observed correlated indicators into a set of linearly uncorrelated principal components (Jolliffe 1986: chapter 7). This method is used in the construction of the DHS wealth index, probably the most widespread index measuring deprivation (Rutstein and Johnson 2004). However, many limitations affect PCA. First, no investigation of the correlation among the indicators is carried out before the index is constructed, leading to the potential inclusion of indicators with a strong linear dependence (Kolenikov and Angeles 2004). Second, only the first principal component is used to derive the scores of the wealth index, ignoring a high proportion of the total variation in the observed indicators (Kolenikov and Angeles 2004). Third, PCA treats all indicators as continuous, even if they are binary or categorical variables (Howe et al. 2008). Finally, constructing an index from a set of indicators leads to measurement error, which can bias the estimates of the association between the DHS wealth index and other variables.

### Rationale for the Construction of a Latent Variable for Household Deprivation

Here, deprivation is conceptualized as a variable underlying certain characteristics of a household’s living standards. A latent variable for household deprivation was constructed from a set of observed indicators associated with housing conditions and living standards by using structural equation modeling (SEM).

In general, an SEM is composed of a measurement model and a structural model, which are estimated simultaneously. The measurement model describes the relationship between the latent variable and the observed indicators. The structural model is a regression of the latent variable on a set of covariates (Bartholomew et al. 2011). SEM is a model-based method, allowing for the estimation of standard errors and the testing of hypotheses on the parameters of the model (Bartholomew et al. 2011).

SEM allows for addressing the issues associated with the use of the DHS wealth index. First, I inspected of the correlation matrix of all indicators before creating the index in order to avoid multicollinearity and to have a coherent set of indicators measuring household deprivation. Second, the indicators included in the measurement model of SEM can be binary or polytomous variables (Muthén et al. 2010). Finally, because latent variables were not directly measured, they are not associated with measurement error, and therefore no bias was introduced in the estimation of their association with other covariates (Muthén et al. 2010).

### Multilevel Structural Equation Model

Here, the structural model included latent variables for household and community deprivation as predictors in a multilevel logistic model for mortality. The SEM involved a single-level measurement model for household deprivation and a three-level model for mortality, with children nested within households nested within communities.

The latent variable for household deprivation was decomposed into between- and within-community components because it might include some unmeasured characteristics of the community, such as availability of utilities at the community level or area-specific investments. The effects of both components on mortality are of interest. The between-community effect represents the influence of community-level deprivation on mortality, and the within-community effect allows an assessment of the relative-deprivation hypothesis, as explained in the upcoming section Testing the Relative-Deprivation Hypothesis. Such decomposition is common in multilevel models (Curran and Bauer 2011; Steele et al. 2016).

The analyses were carried out using the MPlus software version 7 (Muthén et al. 2010). Bayesian estimation is the only method available for three-level SEM in MPlus (Muthén et al. 2010). Markov chain Monte Carlo (MCMC) methods provided an approximation of the posterior distributions of the parameters. The results of this study are based on two parallel chains. The length of the chains depends on the convergence criterion given that the convergence is reached when the proportional scale reduction factor is close enough to 1 for each parameter (Gelman et al. 2004) and is shown below each model in upcoming Tables 4 and 5 (as well as Tables A1 and A2 in the online appendix).

The first half of each chain was discarded as burn-in. Default noninformative priors were used: *N*(0, ∞) for intercepts; regression slopes; parameters of the measurement model; inverse gamma *IG*(0, −1) for variance covariance blocks of size 1; and inverse Wishart *IW*(0, −*p* − 1) for variance covariance blocks, where *p* > 1 is the size of the blocks (Asparouhov and Muthén 2010). The parameter estimates were computed as the mean of the chain values for each parameter from the MCMC estimation, and the standard errors were the standard deviations of the chain values. The fitted models are compared with the same models with an increased chain length of 100,000 iterations in section 4 of the online appendix.

### Measurement Model for Deprivation

The measurement model specifies the relationship between the latent variable for household deprivation and its manifestations (the observed indicators). The form of the measurement model is the same for all models considered in the study.

*x*

_{rjk}the response on the

*r*th (

*r*= 1, …,

*p*) binary item for household

*j*(

*j*= 1, …,

*n*

_{k}), nested within community

*k*(

*k*= 1, …,

*K*). Then the logit of the probability of household

*j*in community

*k*to own item

*r*can be expressed as

_{r0}and α

_{r1}are, respectively, the difficulty and the discrimination parameters. The difficulty parameter α

_{r0}indicates how difficult is it to own an item, and the discrimination parameter α

_{r1}indicates how well the

*r*th item discriminates between households with different scores of household deprivation.

In order to identify the model, one of the α_{r1}s was constrained to 1. Thus, the scale of the latent variable and the scale of the chosen item were set to be the same.

### Structural Model for Mortality

*d*

_{ijk}the binary response for neonatal death of child

*i*in household

*j*in community

*k*, coded 1 for a death and 0 for survival, and let

*p*

_{ijk}= Pr(

*d*

_{ijk}= 1). The structural model for the effect of household deprivation on neonatal mortality is

**x**

_{ijk}is a vector of covariates, η

_{jk}is the latent variable for household deprivation as in Eq. (1), $vjkhh~N0\sigma v2hh$ is the household random effect, and $vkPSU~N0\sigma v2PSU$is the community-level random effect.

However, the effect of the latent variable for household deprivation of Eq. (2) also captures the effects of any community-level component of deprivation. It is therefore desirable to decompose the effect of the latent variable into its within- and between-community components (Steele et al. 2016). As explained earlier, the within-community effect is the effect of the level of a household’s deprivation relative to the mean deprivation in the community, and it allows a test of the relative-deprivation hypothesis.

The structural model specifying such a decomposition of η_{jk} is

The within-effect λ_{W} represents the effect of the departures of each household’s score in deprivation from their community mean, and the between-effect λ_{B} represents the effect of the between community-level mean of deprivation. For postneonatal mortality, three binary responses, *d*_{tijk}, indicate whether a child died during interval *t*, (*t* = 1, 2, 3). The structural models for postneonatal mortality have the same form as Eqs. (2) and (4) but include two changes. The left sides of the models become logit(*p*_{tijk}), where *p*_{tijk} = Pr(*d*_{tijk} = 1) is the probability of death in each subperiod; and on the right side, two dummy variables indicating the second and the third subperiods within the postneonatal period allow the hazard of mortality to change over the three intervals.

Because the latent variables have no natural scale, standardized coefficients λ^{∗} = σ_{u}^{(hh)}λ, $\lambda W\u2217=\sigma u2hh\lambda W$, and $\lambda B\u2217=\sigma u2PSU\lambda B$ were calculated. The odds ratios (ORs) associated with absolute deprivation, relative deprivation, and community-level deprivation in Tables 4 and 5 as well as Tables A1–A4 in the online appendix were calculated by exponentiating the standardized coefficients and are associated with an increase of 1 standard deviation in the latent variable.

### Testing the Absolute-Deprivation Hypothesis

The absolute deprivation hypothesis states that the absolute level of individual deprivation is a significant determinant of child health (Wagstaff 2002). As mentioned earlier, this study aimed to assess deprivation from a broad perspective as a lack of basic needs related to housing conditions and living standards. The inclusion of household-level deprivation $\eta jkhh$ as a predictor of mortality in the structural model of Eq. (2) allowed an assessment of the absolute deprivation hypothesis. The test of the absolute deprivation hypothesis is the test of λ = 0.

### Testing the Relative-Deprivation Hypothesis

The relative deprivation hypothesis states that the relative level of deprivation is a better predictor of health outcomes than absolute deprivation (Marmot et al. 1991; Wilkinson 1997). The relative deprivation is defined as a comparison of an individual’s deprivation score with the mean level of deprivation in some reference group: in this case, other households in the community. By decomposing the latent variable for household deprivation into its between- and within-community components, Eqs. (3) and (4) allowed for an assessment of the relative deprivation hypothesis: the within-community component of deprivation represents the difference between the score of the latent variable of each household and the average of their community. According to the relative deprivation hypothesis, the larger the negative departure of a household’s score in deprivation from the community mean, the higher the mortality due to less favorable social comparisons. In the case of better-off households, the hypothesis is that the larger the positive departure, the lower the mortality. The test of the relative deprivation hypothesis is the test of λ_{W} = 0.

### Testing the Deprivation Inequality Hypothesis

The third hypothesis is the deprivation inequality hypothesis: the distribution of deprivation within a community has an effect on mortality (Johannesson 2004). Inequality results from nonrandom sorting of households into communities, which leads to the concentration of households of similar characteristics within areas. The community-level standard deviation of the scores of the latent variable for household deprivation was used as a measure of inequality within communities.

The design of the Bolivian DHS survey involved no more than 20 households per community, making the use of the most widespread measures for inequality, such as the Gini coefficient (Dorfman 1979), Kaplan’s measure (Daly et al. 1998), or Theil index (Weich et al. 2002), inappropriate. For instance, the Gini coefficient would underestimate the extent of inequality with such a small sample size (Ghosh 1975). Therefore, the within-community standard deviation of the scores of the latent variable for deprivation was chosen as a measure of inequality because it may suffer less than other measures from small-sample bias and does not require a sample as large as measures based on the quintiles or deciles of the distribution.

Because no SEM software allows simultaneous modeling of a latent variable and the inclusion of its standard deviation in the structural model, a two-stage estimation process was used. First, the factor scores of the latent variable for household deprivation were obtained from the measurement model without the within-between decomposition of Eq. (1), and the within-community standard deviations were calculated from the scores. In the second stage, the standard deviation was included as a predictor in the SEM where the measurement model was estimated simultaneously with the mortality model.

Equation (4) includes $SD\u0302k\eta \u0302jkhh$ as a predictor of mortality in the structural model. The test of the deprivation-inequality hypothesis is the test of λ_{ineq} = 0.

### Stepwise Approach in the Inclusion of the Variables

For both neonatal and postneonatal periods, four models were fitted. Models (a) and (b) include, respectively, the latent variable for household deprivation defined at the household level shown in Eq. (2), and the latent variable for household deprivation decomposed into its between- and within-PSU components as in Eqs. (3) and (4), and do not include any control variables. Model (c) includes the decomposed latent variable and the variable for deprivation inequality with no controls, and Model (d) includes these variables and controlled for the set of socioeconomic and biodemographic variables described earlier, allowing the simultaneous assessment of the hypotheses linking deprivation and early-age mortality.

## Results

### Measurement Models for Deprivation

Before the models were fit, investigation of the associations between the covariates revealed that all the covariates were weakly correlated, so no issue of multicollinearity arose when they were included in the SEM.^{1}

The measurement models related to the neonatal and postneonatal periods (Table 2) present very similar discrimination and difficulty parameters. This result was expected because the sample in the postneonatal period corresponds to the sample in the neonatal period, except for the children who experienced neonatal death and those born less than a year from the date of the interview. Cooking fuel, electricity, and material of the floor are the indicators that best discriminate between households with different scores of deprivation: they have the highest values of the discrimination parameter α_{r1}.

Table 3 shows the results of the variance partitioning of Eqs. (3) and (4). For a logit model, the child-level residual variance is $\sigma v2child=\pi 2/3\u22453.29$ (Snijders and Bosker 2012). Intraclass correlation coefficients (ICCs) can be calculated to assess the degree of homogeneity within a given cluster. In the three-level model for mortality, the household ICC—that is, the correlation between the mortality risks of two siblings—was calculated as $ICCvhh=\sigma v2hh+\sigma v2PSU/$($3.29+\sigma v2hh+\sigma v2PSU)$. In all models, the great majority of the variance in both neonatal and postneonatal mortality lies within households. Moreover, a great proportion of variation in the latent variable for household deprivation is explained by the grouping of households within a community.

### Models for Neonatal and Postneonatal Periods

The estimates of Models (a) and (b) are shown in Table 4. To simplify the interpretation, the sign of the latent variable for household deprivation was reversed so that higher scores are associated with higher deprivation. Therefore, an OR higher than 1 means that higher deprivation is associated with higher mortality.

The standardized ORs of absolute deprivation (λ^{∗}) in Model (a) are positive and significant for both periods: a 1 standard deviation increase in household deprivation is associated with a 15% increase in the odds of death within the neonatal period and a 17% increase within the postneonatal period (both *p* values < .01). In the models without control variables, absolute deprivation is associated with early-age mortality, with a slightly stronger association with postneonatal mortality than with neonatal mortality. The same pattern was found after controlling for the other confounding variables (OR = 1.07 in the neonatal period, OR = 1.08 in the postneonatal period; full results not shown).

However, the latent variable for household deprivation might capture some unmeasured characteristics at the community level. The decomposition of the latent variable into its between- and within-community between-household components allows the role of the two components of deprivation to be disentangled (Curran and Bauer 2011; Steele et al. 2016). Tables 4 and 5 show estimates of the standardized ORs of relative deprivation and community-level deprivation of Models (b), (c), and (d). In the models controlling for the set of socioeconomic and biodemographic variables, the ORs associated with the community mean level of deprivation ($\lambda B\u2217$) are both significant at the .10 level (*p* value = .02 in the neonatal period and *p* value = .07 in the postneonatal period): a 1 standard deviation increase in community-level deprivation is associated with a 8% increase in the odds of neonatal death and a 4% increase in the odds of postneonatal death. The decomposition suggests that the association found in the first model is mainly driven by the between-community component of deprivation rather than a household’s deprivation relative to the level of deprivation within its community. After the effects of the confounding variables are accounted for, neither of the ORs for relative deprivation ($\lambda W\u2217$) (*p* value = .48 in the neonatal period and *p* value = .32 in the postneonatal period) and deprivation inequality (λ_{ineq}) (*p* value = .27 in the neonatal period and *p* value = .21 in the postneonatal period) are significant.

Section 2 of the online appendix shows the results of the models including only births occurring within five years of the survey. The main difference is related to the fact that community-level deprivation is not significant for the postneonatal period, but this is probably due to the reduced sample size: 52.0% of the observations were excluded. No substantial difference is observed for the neonatal period. Models using only births in the last year were also fitted, but none of the covariates of interest are significant, probably because of the very reduced sample size: 88.9% of the observations were excluded (results not shown). Section 3 of the online appendix shows the results of the models including the interaction between the three variables of interest and the binary variable for pre-/post-2002. As in the previous models, community-level deprivation is the only significant socioeconomic determinant for both periods. None of the interaction terms are significant for the postneonatal period, but the interaction terms involving relative deprivation and deprivation inequality in the neonatal period are significant, indicating a crossover interaction that deserves further investigation. Section 4 of the online appendix shows the results for Model (d) after the number of MCMC iterations was increased to 100,000. The coefficients are very similar to those of Table 5. Models including the DHS wealth index instead of the latent variable for household deprivation were fitted, and the results are shown in section 5 of the online appendix. Many differences in the significance of the ORs can be found, among which the main difference is related to the fact that the effect of community-level deprivation on postneonatal mortality is not significant.

## Discussion

In this study, absolute deprivation was found to be significantly associated with both outcomes, with a slightly stronger association with postneonatal mortality than with neonatal mortality (Table 4). Evidence in the literature suggests that the association between air pollution and mortality is weaker in the neonatal period than in the postneonatal period (Bobak and Leon 1992, 1999). Although overall infant mortality is strongly correlated with the quality of sanitation, water, and indoor air (Bruce et al. 2000; Esrey 1996), environmental factors might have a smaller association with neonatal mortality given that mortality in the first month of life is more strongly associated with endogenous factors arising during the delivery or in the antenatal and postpartum periods, such as congenital diseases (Black et al. 2010; Taskaya and Demirkiran 2016). Another reason could be the shorter time of exposure to environmental factors of only 28 days. If early-age mortality is considered to be the result of a “cumulative series of biological insults” (Mosley and Chen 1984), the effects of inadequate housing conditions might need a time span of longer than four weeks to be totally expressed.

Community-level deprivation was found to be a significant predictor of both neonatal and postneonatal mortality (Table 5). Several studies assessed environmental deprivation to be a risk factor for a set of birth outcomes; in particular, a low neighborhood socioeconomic level is associated with perinatal mortality (De Graaf et al. 2013), preterm birth (O’Campo et al. 2007), postneonatal mortality (Guildea et al. 2001), and malformations (Deguen et al. 2016). Many aspects of community-level deprivation, ranging from housing to safety and social cohesion, might have an effect on birth outcomes. Moreover, especially in low- and middle-income countries, improving environmental factors—such as extending the electric grid and enhancing latrine facilities and sources of domestic water—can have a fundamental effect on birth outcomes (Jaadla and Puur 2016; Patel 1980; Van de Poel et al. 2009).

Relative deprivation was not found to be significantly associated with mortality occurring in the first year of life (Table 5). Little research exists about the association between negative social comparisons and early-age health outcomes. In relation to the mechanisms through which relative deprivation might affect infant mortality, Reagan et al. (2007) focused on the influence on parents: unfavorable social comparisons can affect material resources and the quality of the social life of a household. In particular, maternal stress-induced smoking is addressed as one pathway through which infant health could be affected (Lhila and Simon 2010). However, this pathway is an unlikely explanation in Bolivia because smoking is uncommon, especially in rural areas, where the prevalence of smokers may be low due to the price of cigarettes and the widespread poverty (Albalak et al. 1999). Further, only 6.4% of the interviewed women in this sample declared themselves to be smokers.

Deprivation inequality was not a significant predictor of infant mortality (Table 5). This finding is consistent with Szwarcwald et al. (2002), who found a nonsignificant association between income inequality, measured by the within-neighborhood Gini coefficient of household income, and neonatal mortality in a micro-level study in Rio de Janeiro. On the other hand, Mayer and Sarin (2005) found income inequality to be a significant predictor of postneonatal mortality at the national level. However, in macro-level studies, the ecological fallacy could lead to an artefactual correlation between inequality and health outcomes: because of the curvilinear relationship between health and income, a one-unit increase in income is associated with a higher increase in health among the poor than among the rich (Gravelle 1998). Therefore, any reduction in inequality generated by transfers from the richer to the poorer leads to a better global health outcome.

Finally, the results of the models including the DHS wealth index were substantially different from those including the latent variable for household deprivation (section 5 of the online appendix). As explained earlier, a latent variable approach offers several advantages over the DHS wealth index (Múthen et al. 2010). Moreover, the observed indicators included in the measurement model for the latent variable were selected based on their correlation, ensuring that only indicators related to the latent concept of deprivation were included in the model.

## Conclusions

This article explored the role of absolute deprivation, relative deprivation, and deprivation inequality as predictors of neonatal and postneonatal mortality in Bolivia, contributing evidence to the field of socioeconomic determinants of early-age mortality in low- and middle-income countries. Although there is a large body of research assessing income as a determinant of mortality, the findings of this article complement the existing literature given that poverty is considered a multidimensional condition (Sen 1989). The determinant of interest is household deprivation, interpreted as a lack of basic needs related to housing conditions, and the other nonmonetary dimensions of poverty are left as control variables. A methodological improvement in the measurement of deprivation is proposed: a latent variable approach allows for addressing issues related to measurement error that could bias the estimates of its association with the mortality outcome. Moreover, to my knowledge, no previous study has proposed a decomposition of household deprivation into its household- and community-level components and assessed their effect on mortality.

This study found support for the absolute deprivation hypothesis for both neonatal and postneonatal mortality, with a slightly higher gradient of association with postneonatal mortality than with neonatal mortality. The relative deprivation hypothesis found no support for any component of early-age mortality. The pathway through which unfavorable social comparisons might foster maternal stress-induced smoking, and therefore affect infant mortality outcomes, was unlikely in Bolivia. Finally, I found little evidence to support the deprivation inequality hypothesis in the neonatal and postneonatal periods in the context of a peripheral country (Moore 2006). Although these findings are consistent with previous literature, the contributions of this work are beyond prior research: to the best of my knowledge, the application of multilevel SEM to the study of the mechanisms linking deprivation to early-age mortality in the context of a middle-income peripheral country such as Bolivia has never been attempted.

Despite differences across households living in the same community that were not very large, Bolivia presented a nonignorable amount of within-community variance (Temporin 2019). However, it remains possible that relative deprivation and deprivation inequality measured within communities could be predictors of early-age mortality in more unequal contexts. Moreover, as highlighted by Wilkinson and Pickett (2006), the relationship between inequality and mortality might depend on the size of the area in which inequality was calculated; a community might be a too small an area to reflect the extent of social class differences in a society. An important limitation of this study is that because the community in which one lives is not randomly assigned, unobserved household characteristics (such as risk aversion) may be correlated with both the level of deprivation in the community and the probability of infant mortality. Unfortunately, the data do not permit the more conservative fixed-effects assumption. In any case, I argue that a household’s residential location can be considered the result of a constrained choice—for instance, by economic resources.

To conclude, I found that in contexts of widespread poverty and deprivation like Bolivia, satisfaction of basic needs related to housing conditions is more important than social comparisons and the overall level of inequality in determining early-age health outcomes. Relative deprivation and inequality in the distribution of deprivation might play a role in determining health only after basic needs are met and the condition of absolute deprivation is overcome (Marmot 2005; Wilkinson 1994). This might not be the case in Bolivia, where the pragmatic consequences of a poor physical environment are still of primary importance for early-age mortality: children living in poor conditions might be more exposed, for example, to infections and respiratory problems. Policies aimed at reducing early-age mortality in countries like Bolivia should therefore focus on satisfying basic needs related to housing conditions and living standards. Moreover, the implementation of programs aimed at improving community-level factors, such as availability of electricity and quality of water and sanitation, can play a role in both neonatal and postneonatal mortality.

## Acknowledgments

The author thanks Professor Arjan Gjonca for his extensive and helpful comments on earlier drafts and Professor Fiona Steele for her advice on statistical methods. The study was funded by the ESRC under Grant No. 201557818/1-23-A000. The funders had no role in study design, data collection, and analysis; decision to publish; or preparation of the article.

## Data Availability

The data sets generated and/or analyzed during the current study are available from the corresponding author on reasonable request.

## Compliance With Ethical Standards

### Ethics and Consent

This research did not involve human participants and/or animals.

### Conflict of Interest

The author declares no conflict of interest.

## Note

^{1}

The strongest association was found between variables Region and Indigenous, with a Cramer’s V of .51.

## References

*Sistema de salud de Bolivia*[The health system of Bolivia]

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