Demographic changes and ageing

A recent United States (US) Census Bureau (Bernstein and Edwards, Reference Bernstein and Edwards2008) press release states the 65 and older age group will increase from 38.7 million to nearly 88.5 million by 2050. Stated differently, this means nearly one in five US residents will be 65 years or older. Along the same lines, the 85 and older age group (referred to as the oldest-old) will increase nearly 300 per cent from 5.4 million to 19 million. Census projections also show the national median age continues to increase and if this is examined by race, the projection is striking. For Whites, the median age increases slightly from 38.4 to 39.4; but for Blacks, it increases from 31.7 to 38.9 (see Bernstein and Edwards, Reference Bernstein and Edwards2008).

A final demographic characteristic to note is life expectancy, which has been steadily increasing in the US at a rate of two years per decade (White Reference White2002). Census projections show life expectancy for Whites will increase from 78.9 in 2010 to 83.3 by 2050. Once again, this is striking for Blacks, with life expectancy increasing from 73.8 to 81.8 years. As Cohen (Reference Cohen, Anderson, Bulatao and Cohen2004: 1) highlights, ‘life expectancy [between 1950 and 2000] at age 65 rose 31 percent for men and 28 percent for women’ due to advances in medicine, healthier lifestyles and greater access to care. Clearly, the USA is steadily progressing in median age and life expectancy for both Whites and Blacks. This upcoming demographic shift provides an excellent opportunity to address a wide range of ageing issues.

Background on disparities in health services utilisation: economic access, usual source of care, individual beliefs

Dunlop et al. (Reference Dunlop, Manheim, Song and Chang2002) provide a solid contribution in the area of health disparities and utilisation for older adults. Employing data from the Asset and Health Dynamics of the Oldest Old (AHEAD) survey, these scholars examine ethnic/racial differences in utilisation due to economic access. The logistic regressions show older African American males are significantly less likely to engage in any contact with a physician even after controlling for demographic characteristics, chronic conditions and functional limitations when compared to White males (the reference group). These scholars suggest that economic access ‘continues to influence the use of some health services’ and their findings also ‘indirectly suggest that geographic barriers do not play a significant role in the observed utilization disparities [due to the significant gender/ethnic interactions in medical care utilisation], except perhaps in outpatient surgery’ (Dunlop et al. Reference Dunlop, Manheim, Song and Chang2002: 231). To a large extent, other scholars have corroborated these findings (see Bernstein Reference Bernstein2004; Chen et al. Reference Chen, Diamant, Pourat and Kagawa-Singer2005; Walker et al. Reference Walker, Steers, Liang, Morales, Forge, Jones and Brown2010).

Usual source of care (USC) has also been considered a factor in explaining health disparities and utilisation (see Corbie-Smith et al. Reference Corbie-Smith, Flagg, Doyle and O'Brien2002; DeVoe et al. Reference DeVoe, Fryer, Phillips and Green2003; Escarce and Mcguire Reference Escarce and Mcguire2004; Escarce et al. Reference Escarce, Epstein, Colby and Schwartz1993; Lambrew et al. Reference Lambrew, DeFreise, Carey, Ricketts and Biddle1996). In this context, USC refers to a particular health-care provider an individual seeks for medical advice and treatment. This is analogous to registering with a primary care clinic or general/family practice (GP/FP) office in the case of the United Kingdom, the Netherlands and New Zealand (see Schoen et al. Reference Schoen, Osborn, Doty, Bishop, Peugh and Murukutla2007). Scholars have found individuals with a regular physician are more apt to use preventive services and, in turn, maintain better health. In fact, Sox et al. (Reference Sox, Swartz, Burstin and Brennan1998) suggest USC may be a stronger predictor of health access when compared against health insurance. This is an important consideration because Blanchard and Lurie's (Reference Blanchard and Lurie2005) analysis of data from the Commonwealth Fund 2001 Health Care Quality Survey shows over 80 per cent of Whites list a doctor's office as USC while less than 66 per cent of Blacks do so. Another noteworthy study examines the impact of USC on the utilisation of preventive services after controlling for endogeneity (Xu Reference Xu2002). More specifically, this study recognises ‘individuals who are likely to use more preventive services may choose to have a regular doctor or site’ and this is ‘driven by unobservable preferences’ (Xu Reference Xu2002: 1513). Results suggest the impact of USC decreases after controlling for unobserved characteristics. Nevertheless, the presence of a USC is beneficial for blood pressure and cholesterol screenings, and important preventive services for coronary artery disease, kidney damage, stroke and atrial fibrillation. These findings are important for they also show having a regular site can be as effective as a regular doctor for other preventive screenings.

Ayalon and King-Kallimanis (Reference Ayalon and King-Kallimanis2010) provide another important contribution in understanding health disparities and utilisation for older adults. Instead of focusing on access to care, socio-economic characteristics (socio-economic status (SES)), insurance or USC, these researchers examine time and value preference. Employing the time-tradeoff module of the 2002 Health and Retirement Study, these researchers show Blacks are ‘more willing to live longer in imperfect health [and] relative to Whites, Blacks are more likely to report a longer time-tradeoff’ (Ayalon and King-Kallimanis Reference Ayalon and King-Kallimanis2010: 1184). In other words, Blacks are willing to trade more years of life at worse health as compared to fewer years of life in perfect health. Equally important, this work suggests ‘in this sample of community dwelling older adults, it is the subjective perception of one's health that is associated with one's preferences, rather than one's objective medical or cognitive states' (Ayalon and King-Kallimanis Reference Ayalon and King-Kallimanis2010: 1194). If this is the case, then racial disparities in health utilisation may originate due to relative differences. Perhaps, some of this could be reconciled by controlling for individual attitudes regarding health insurance and health intervention. More recent work by Bibb, Padden and Ferguson (Reference Bibb, Padden and Ferguson2012) encourages researchers to investigate such factors. Based on a homogenous convenience sample of 202 older adults from data collected using questions from the Behavioral Risk Factor Surveillance System Survey (BRFSS 2007–2009), these scholars find that both social determinants of health (i.e. race, income, education) and moderators (i.e. perceived health status, obesity) impact health utilisation but variation still exists. They conclude by suggesting future research should explore the association between non-social determinants and utilisation.

Discrete data: Negative Binomial, Poisson and Quantile Regression

The paper contributes to the existing body of literature by adding important health behaviour/belief measures lacking in previous studies and modelling health utilisation employing Quantile Regression (QR). With this approach, the researcher can compare how Blacks/Whites differ across the entire distribution and this is demonstrated in Table 2 with Negative Binomial (NB) estimates presented along with QR estimates at the 25th, 50th, 75th and 90th percentiles (see Hao and Naiman Reference Hao and Naiman2007; Koenker Reference Koenker2004, Reference Koenker2005; Winkelmann Reference Winkelmann2008). Although a large body of literature exists on health utilisation, few researchers have undertaken such an analysis for older adults. Some of this can be attributed to issues involving small sample size and limitations of statistical packages. Previously, much of health utilisation research employed count models, such as Poisson or NB, to examine medical visits. The Poisson model takes the following form:

(2)$${\rm Prob[}Y = y_i |x_i {\rm ]} = \displaystyle{{\exp ( - \lambda _i )\lambda _i^{yi}} \over {\Gamma (1 + y_i )}}$$

where λ _i=exp(α+x _i′β), y _i=0, 1, …, i=1,…,N.

Table 2.

Quantile Regression and Negative Binomial (NB) comparison

Notes: Modal categories: white, female, married, south, overweight. Age 1 is spline with 65–74 years and Age 2 is spline with 75+. Q: quantile. MSA: Metropolitan Statistical Area. PCS: Physical Component Summary. MCS: Mental Component Summary.

Significance levels: * p<0.10, ** p<0.05, *** p<0.01.

With the Poisson, the log-linear conditional function equals the variance, which is E[y _i|x _i]=Var[y_i|x_i]=λ _i. Since this fails to account for over-dispersion, researchers opt to use the more flexible NB model, which takes the following form:

(3)$${\rm Prob[}Y = y_i {\rm |}x_i {\rm ]} = \displaystyle{{{\rm \Gamma (}\theta \lambda _i + y_i {\rm )}q^{\theta \lambda _i} (1 - q)^{yi}} \over {{\rm \Gamma (}1 + y_i {\rm )\Gamma} (\theta \lambda _i )}}$$

where y _i=0,1,…, q=1/(1+θ).

With NB, the conditional mean remains E[y _i|x _i]=λ _i; however, the Var[y _i|x _i]=λ _i [1+(1/θ)λ _i^P−1]. An early paper by Winkelmann (Reference Winkelmann2004) shows the NB and the Probit-Poisson-log-normal are considerably superior to Poisson based on the log-likelihood. The Schwartz Information Criterion, which accounts for a difference in the number of estimated parameters, yields a similar conclusion. In other words, models that take unobserved heterogeneity into account perform much better. Winkelmann's (Reference Winkelmann2004) study is among a small group that examines utilisation across the entire distribution function and his findings suggest varying effects for the lower and upper part. Greene (Reference Greene2008) also examines doctor visits using the German Socio-economic Panel and finds different functional forms of NB outperform Poisson based on the likelihood ratio test.

Although NB is a superior modelling framework for health utilisation, it does not uncover how this utilisation varies across the distribution function. Moreover, this approach does not work well if the underlying process for the outcome variable contains many outliers (see Figures 1 and 2). In other words, NB may not be the best approximation for a skewed-location distribution (see Koenker and Geling Reference Koenker and Geling2001). In contrast, QR is robust to outliers and scale effects since the estimation minimises least absolute deviation. This is represented as:

(4)$$\beta (\tau ) = {\rm argim}1/n\sum\nolimits{\rho_\tau} (Y_i - Xi'b).$$

QR transforms the conditional distribution function into segments (or quantiles). This transformation, denoted T(z _i, α), and the conditional α-quantile of z, denoted Qz(α|x _i), provides estimates for the entire conditional distribution function where 0<α<1 (Koenker and Bassett Reference Koenker and Bassett1978; Miranda Reference Miranda2006). For this to work, a sufficient precondition is the conditional distribution function, f(Y|x), is both continuous and positive. Since this cannot be satisfied with count data, Machado and Santos Silva (Reference Machado and Santos Silva2005: 1227) devised an alternative by ‘constructing a continuous random variable whose quantiles have a one-to-one relation with the quantiles of Y′. Building upon earlier work by Stevens (Reference Stevens1950) and Pearson (Reference Pearson1950), Machado and Santos Silva (Reference Machado and Santos Silva2005) propose adding a uniformly distributed random variable, denoted Z, to the dependent variable, Y, thereby artificially imposing continuity (see Figure 3). This is achieved by jittering with the following transformation, z=y+u where u~U(0,1) and then substituting this equation in the conditional quantile for counts, Qz(α|xi)=α+exp[x_i′β(α)]. The end result is the following equation:

(5)$$Q_Z [\alpha {\rm |}{\bi x}] = Q_Y [\alpha {\bf |}{\bi x}] + \displaystyle{{\alpha - \mathop \sum \nolimits_{y = 0}^{QY(\alpha |{x})} {\rm Prob}(Y = y|{\bf x})} \over {{\rm Prob}(Y = Q_Y (\alpha |{\bf x})|{\bf x})}}$$

Figure 1.

Boxplot of total visits. This plot shows a high degree of positive skewness.

Note: Vertical line signifies mean visits.

Figure 2.

Boxplot of total visits by race. This plot shows positive skewness for both Whites and Blacks.

Note: Vertical line signifies mean visits.

Figure 3.

(A) Without transformation (total visits as discrete data). (B) With transformation (total visits after transforming (or jittering) the discrete data to achieve a smooth, continuous function).

This process of ‘jittering’ can be implemented with any continuous distribution with support on [0,1) and can be employed to fully uncover a discrete distribution for empirical research (see Winkelmann's Reference Winkelmann2006 follow-up study). Such an iterative process employs linear programming rather than least squares or maximum likelihood estimation methods. As such, results cannot be interpreted in the same manner as ordinary least squares. Due to this, marginal effects are typically presented along with the direct estimates (see Tables 3 and 4).

Table 3.

Entire quantile distribution for selected coefficients

Notes: Model includes all variables as in Table 2. However, only selected ones are shown for this nine quantile distribution. Q: quantile.

Significance levels: * p<0.10, ** p<0.05, *** p<0.01.

In non-technical and simplified terms, consider a situation with only two outcomes: no/yes or failure/success or zero/one (i.e. Bernoulli distribution). How does one convert this discrete data into continuous? By transforming the data where continuity is artificially constructed with a uniform random variable (i.e. process of jittering). Now, the distribution can be cut into various segments or, in technical terms, quantiles. Although there is no specific rule, scholars typically use either 10 or 25 per cent cut-offs and this has become the convention (see Trevidi and Munkin Reference Trivedi and Munkin2010). This analysis presents both series of cut-offs (see Tables 2 and 3). In terms of a formal model, this analysis can be depicted as:

(6)$$\eqalign{ & Total\,Visits = \alpha + \beta ({\rm Black}) + \delta ({\rm Demographic}) + \eta ({\rm Economic}\,{\rm Factors}) \cr & + \rho ({\rm Health}\,{\rm Attributes}) + \tau ({\rm Health}\,{\rm Beliefs}) + v({\rm Geography}) + \varepsilon} $$

Table 4.

Marginal effects (ME) for selected coefficients with 95 per cent confidence interval (95% CI)

Notes: Model includes all variables as in Table 2, however, only selected ones are shown for this distribution. Q: quantile.

Equation (6) shows Total Visits (health services utilisation) is explained by race, matrix of demographic characteristics, economic factors, health attributes, health beliefs and Census region. Since the main independent variable of interest is a dummy variable for race (i.e. Black/White), the Results section provides interpretations based on marginal effects. This provides a comparison of how total visits (or utilisation rates) vary as race changes from White=0 to Black=1. All of the analysis is conducted using STATA 11 (StataCorp LP, College Station, Texas, USA; see the Appendix for step-wise procedures).