A Cost-Benefit Analysis of Hearing Aids, Including the Benefits of Reducing the Symptoms of Dementia

Abstract

We carried out a CBA of hearing aids (HAs) in which we estimated the direct utility benefits, and included the indirect utility benefits working through a reduction in dementia symptoms. The benefits methodology involved using QALYs as the outcome measure and then applying the price of a QALY to convert the outcome measure into monetary terms. The price of a QALY was derived from an age specific VSL estimate. The effects of HAs on utility were estimated from a fixed effects regression on a large national panel data set provided by NACC where we used a negative proxy for the QoL. We also used a fixed effects regression for the estimate of the indirect benefits involving HAs reducing dementia symptoms. We found that the total benefits, mainly coming from the direct benefits, were extremely large relative to the costs, with benefit-cost ratios over 30.

1. Introduction

According to the WHO (2017), an estimated 360 million people around the world have hearing loss (HL). They estimate that the annual cost of unaddressed HL is $750–790 billion globally. This is just for moderate to severe HL (greater than 35 DB in the better ear). $105 billion of this cost is due to a loss of productivity, and a further $573 billion per year involves social costs because of social isolation, communication difficulties and stigma. The cost to the health care sector is in the range $67–107 billion.

Underlying these HL figures, there are strong links between HL and aging, between aging and dementia, and consequentially between HL and dementia. In the US, according to Donohue et al., 18% of adults aged 45–64, 30% of adults aged 65–74, and 47% of adults 75 years and older report HL. Fortunato et al. (2016) state that one fifth of the US population have some form of cognitive loss by the age of 70 years; and Lin et al. (2014) reports that two-thirds of adults 70 years or older have a HL that affects daily living.

Given the size of the HL costs, and the relationships linking HL, aging and dementia, and the fact that the rates of hearing aid (HA) use remain less than 25% in the US (and other industrialized countries)¹ even though potentially they could reduce HL, there are three main research questions that need answering. First, to what extent can HAs reduce dementia? Second, even if HAs can reduce dementia, would HAs be socially worthwhile and pass a CBA test? Lastly, would HAs pass a CBA test just because it lowered dementia?

To answer these questions we are going to carry out a CBA of HAs that estimates both the direct utility benefits of HAs and also the indirect benefits of HAs working through a reduction in dementia. For the CBA, a Quality Adjusted Life Year (QALY) will be used as the outcome measure and this will be converted to a benefit estimate by putting a price on a QALY. Two fixed-effects regression equations using panel data are applied to a large national sample of clients tested for dementia who have also been tested for HL. A subject’s particular visit to an Alzheimer’s Disease Center (ADC) is the unit of observation. Because many characteristics do not vary by visit, in this way we attempt to neutralize the identification problem that unobservable variables may exist in the error term. Estimates of the costs of HAs will come from the literature. We calculate the net-benefits of HAs and, for ease of interpretation, present the results also as a benefit-cost ratio. When we refer to HAs in the main analysis, we are considering only ones that are effective, i.e., provide the wearer with normal hearing. In the final net-benefit calculations, we make adjustments for HAs that are not effective.

In the next section, we give an overview of our data source and explain the specifications of the main variables that will be used in the estimation of the benefits. We then go into details concerning our benefits method and the estimation framework. After highlighting each benefit component, the components are estimated and assembled to form the direct and indirect benefit categories leading to the total benefits. The last piece of the CBA involves providing the costs of HAs. With the costs, the final results can then be determined, which include a sensitivity analysis. The summary and conclusions section mention some policy implications of our results. An appendix presents possible explanations for why HAs are not utilized even by those who have HL.

2. The Data Source and Background for the Key Variables

The data we will be using to estimate the benefits of HAs dementia come from the National Alzheimer’s Coordinating Center (NACC). NACC has constructed a data set that has been operational since 2005. These data consist of demographic, clinical, diagnostic, and neuropsychological information on participants with normal cognition, mild cognitive impairment, and dementia who visited 32 US Alzheimer’s Disease Centers (ADC). The data was collected by trained clinicians using structured interviews and objective test measures. Steps were undertaken to standardize the data across the ADCs and this is why the data set is referred to as the Uniform Data Set (UDS). This data set is fully explained elsewhere (Morris et al., 2006, Beekly et al., 2007 and Weintraub et al., 2009). The UDS has been used by a number of researchers to analyze the progression of dementia, such as by Besser et al. (2014) and by Burke et al. (2016). The UDS was also the data source used for two prior CBAs of dementia interventions related to years of education and Medicare eligibility – see Brent (2017) and Brent (2018).

The UDS has evolved into a panel with 118,341 visit observations, covering up to 12 visits over a thirteen-year period. With an average of around 3.15 visits per patient, there were around 37,544 participants sampled between September 2005 and March 2017. In the previous CBA studies using the UDS, just the data for the initial visit was used. In this CBA, we will be utilizing the full panel, except when variables have missing observations.

2.1. The Measure of Dementia

A magnetic resonance image (MRI) of the brain can detect whether a person has the pathology of dementia (which may include plaques and fibers for Alzheimer’s disease, if the main type of dementia is involved, and include lesions if vascular dementia is applicable). Although there are currently no treatments that can alter the pathology of the brain, if the criterion for an effective dementia intervention is whether a person can follow a useful and productive lifestyle, then focusing on finding a reduction of symptoms can be a feasible dementia outcome that any intervention can seek to achieve. Hence, we will employ a measure of dementia that focuses on cognitive functioning rather than pathology.

The instrument that we will be using to measure dementia is the Clinical Dementia Rating (CDR) scale. The CDR is a measure of dementia severity used globally based primarily on a neurological exam and informant reporting, see Morris (1997). A CDR was administered to each NACC participant at each visit by a clinician. There are six domains in the CDR: memory, orientation, judgment and problem solving, community affairs, home and hobbies, and personal care. Each domain is assessed using a 0 to 3 interval (none, mild, moderate and severe) with a questionable response being scored as 0.5. The CDR-SB (the CDR sum of boxes) is the aggregate score across all six domains and this has a range of 0 to 18².

2.2. The Hearing Variables

The benchmark for HL that we will be using is the absence of functionally normal hearing. In an interview with the client, a clinician would assess HL if there were any functional impairment, on the basis of there being a reduced ability to do everyday activities, such as listening to the radio or television, or talking with family or friends. There were two ways that hearing could be normal – with and without a HA. We distinguish the two cases of normal hearing in order to test the extent to which the restorative power of HAs brings a subject up to par with regular hearing. H0 is designated as the dummy variable for normal hearing without a hearing aid, and HA is the dummy variable for normal hearing with a hearing aid.

2.3. The Measure of Quality of Life

The Quality of Life (QoL) measure that is in the NACC data set that we will be using as a negative proxy for utility is the Geriatric Depression Scale (GDS), short form. This measure has 15 ingredients and we take the sum of the ingredients. Although the GDS was originally conceived to be a measure of psychological status, it has become accepted to be a valid measure of QoL among older adults with and without cognitive impairment. For example, Vagetti et al. (2014) used the GDS as a measure of QoL to see how it was affected by the extent of physical activity undertaken by the elderly. Brent (2018) also used the GDS as the QoL measure in the CBA of Medicare eligibility.

The GDS is on scale of 0 to 15. It needs to be rescaled (and inverted) to correspond with the QoL that is in the unit interval that we will be using to value expected life years, which is going to be used as our outcome measure. The conversion of GDS to Qol is carried out by:³

$$\text{QoL}=-\frac{\text{GDS}-\text{GDS Min }}{\text{GDS Max}-\text{GDS Min }}$$ (1)

With GDS Max = 15 and GDS Min = 0, the rescaling simplifies to: QoL = – GDS/15.

3. The Method for Estimating the Benefits of Hearing Aids

A HA provides utility (U) directly and also indirectly through the dementia symptoms (D) they reduce. The utility function is specified as:

$$U=U\left(HA,D\left(HA\right),Z\right)$$ (2)

where Z is a vector of all the variables determining an individual’s utility other than hearing aids and dementia (including normal hearing). The direct and indirect utility effects of HAs (holding Z constant) are given by:

$$\frac{dU}{dHA}=\frac{\partial U}{\partial HA}+ \frac{\partial U}{\partial D} \frac{\partial D}{\partial HA}$$ (3)

where $\frac{\partial U}{\partial HA}>0$, $\frac{\partial U}{\partial D}<0$ and $\frac{\partial D}{\partial HA}<0$, which means that both of the utility effects of HAs are expected to be positive.

A common outcome measure used for economic evaluations in the health care field is the quality adjusted life year (QALY) which combines the number of life years (LY) in a health state with the utility (i.e., quality of life) in that health state: QALY = LY × U. When life years are fixed, as in our application, QALYs only change when utility changes:⁴

$$\mathit{\text{dQALY}}=\mathit{\text{LY dU}}$$ (4)

To carry out a CBA, it is necessary that all outcomes be expressed in monetary terms to form the benefits (B). When QALYs are the outcome measure, this effectively means putting a price (P) on the QALYs: B = P × QALY. The change in benefits from HAs is then, using equations (3) and (4):

$$\frac{dB}{dHA}=\frac{P \mathit{\text{dQALY}}}{dHA}=P\left(LY\frac{dU}{dHA}\right)=PLY\left(\frac{\partial U}{\partial HA}+ \frac{\partial U}{\partial D} \frac{\partial D}{\partial HA}\right)$$ (5)

The method for estimating the benefits therefore involves estimating the direct and indirect effects of HAs on utility and valuing this by the price of a life year attached to the number of life years that an individual has remaining in a particular health state. Decomposing equation (5), we define the two categories of benefits:

$$\text{Direct Benefits:\hspace{0.17em}}PLY\left(\frac{\partial U}{\partial HA}\right)$$ (5a)

$$\text{Indirect Benefits:\hspace{0.17em}}PLY\left(\frac{\partial U}{\partial D} \frac{\partial D}{\partial HA}\right)$$ (5b)

4. Estimation Framework.

To enable the utility components of equations (5a) and (5b) to be estimated, we need to specify two equations, one for the effects of hearing on dementia, and another for the effects of hearing and dementia on utility.

4.1. Effects of Hearing on Dementia.

The first estimation equation starts off in a regression framework with a dependent variable (the extent of dementia symptoms D) that is related to the set of hearing variables H (normal hearing without a hearing aid, H0, normal hearing with a hearing aid, HA, and age A), a set of controls Z that are observed, and an error term u. Although we are here only interested in estimating the effects of the hearing variables on dementia, we need to recognize the heterogeneity problem, that there could also exist a set of unobserved variables that are correlated with both the hearing variables and the random error term, which would cause the hearing coefficient estimates to be biased.

To neutralize the effects of these unobserved variables, a fixed effects framework takes advantage of the fact that we will be using panel data for the estimation, where the observations for all variables x for clients i (1, …, n) are recorded over a number of years t (1, …, T) and so take the form x_it. In our panel, a subject’s particular visit is the unit of observation. However, because in our sample a subject may have visited an ADC more than once in any particular year, to ensure uniqueness, we interpret the panel variables to be represented by x_iv, where visit numbers are v(1, …, V). A fixed effects model can be one-way, focusing on either i or v, or two-way where both i and v are subject to fixed effects. For our man results, we are going to apply a one-way fixed effects model to v, and leave to the sensitivity analysis the application of two-way models.

Our fixed effects model assumes that, for each of the visits, many of the unobserved influences will be unchanged. So, for example, the trained clinicians undertaking the interviews for any particular visit number are the same persons, making the same clinical judgments; or the time taken to undertake, say, the first visit interviews all take uniformly longer. This means that the unobserved variables can be represented by a set of intercepts α_v that varies by visit number, but not by individual. In principle, α_v is subtracted from the error term u_iv, which previously could have been correlated with the unobserved variables, to form a new error term ε_iv The new error term can safely now be assumed randomly and independently distributed with a mean of zero. This is the way that the fixed effects model neutralizes the influence of unobserved variables on estimation. The fixed effects regression equation for our panel data study is:

$$D_{\text{iv}}={\alpha }_0+{\alpha }_{1}H{0}_{\text{iv}}+{\alpha }_{2}H{A}_{\text{iv}}+{\alpha }_3{A}_{\text{iv}}+{\alpha }_Z{Z}_{\text{iv}}+{\alpha }_v+{\text{ε}}_{\text{iv}}$$ (6)

where the α coefficients are the regression parameters to be estimated.

There are twelve visits in our data set. With the set of intercept dummy variables for visits included in equation (6),⁵ the estimation technique is called a least squares dummy variable regression (LSDV).

Using LSDV is equivalent to subtracting the visit specific averages from both dependent and independent variables. So equation (6) can be estimated as a de-meaned approach without actually including all the visit number dummies into the regressions, see Murray (2006). This is useful when the estimates of the dummy variables are not of direct interest. The de-meaned approach makes it clear that fixed effects models are about differences within visits and not across visits. With the demeaned approach, we can see clearly how the non-observed variables are eliminated from equation (6). That is, ${\alpha }_v-{\overline{\alpha }}_{\text{v}}=0$, by assumption that the fixed effects are equal to the average for all v.

The fixed effects model is most appropriate when all clients make the same visit number at the time when a sample is collected. Nevertheless, when different visit numbers appear at the same time a sample is collected, as in our data, there may not be distinct visit intercepts. The intercepts are constant for some visit numbers, but random across samples when persons with different visit numbers with different constant intercepts are included. So, for example, someone making a particular visit number is interviewed by one set of trained clinicians, while others making the same visit number are interviewed by a different set of trained clinicians. Or the first visit duration is not the same amount longer in different samples. In this case, the random effects model could apply, which involves u_v being left in the error term. If the u_v are correlated with the hearing variables and the controls, then one returns to the original biased estimates problem that the fixed effects model was designed to minimize. On the other hand, if the u_v are uncorrelated with the independent variables, then the random effects model has the advantage over the fixed effects model in that the estimated standard errors will be smaller. This is because the random effects model relies on all the variation in the independent variables, both within the observations on visit numbers and across the means of the independent variables, see Murray (2006).

To see whether one can rely on the fixed effects model or the random effects model, Hausman (1978) proposed a test based on the difference in the two sets of regression coefficient estimates. Since the fixed effects estimates are consistent even when u_v is correlated with the independent variables, but the random effect is inconsistent with such a correlation, a statistically significant difference is interpreted as evidence against the use of the random effects model, which implies that our fixed effects regression equation (6) can be used for estimation purposes, see Wooldridge (2002). In the estimation results in tables 3 and 4 we report the Hausman test results, confirming the need to rely on the fixed effects coefficients.

Table 3:

LSDV Estimates for Fixed and Random Effects Models of Hearing Variables on Dementia (p-values in parentheses)^†

	Without Controls		With Controls
Variable	Fixed Effects	Random Effects	Fixed Effects	Random Effects
H0: α1	−0.4804*** (0.000)	−0.4083*** (0.000)	−0.3630*** (0.000)	−0.3144*** (0.002)
HA: α2	−0.7937*** (0.000)	−0.7896*** (0.000)	−0.7251*** (0.000)	−0.7230*** (0.000)
Age A: α3	0.0302*** (0.000)	0.0199*** (0.000)	0.0337*** (0.000)	0.0260*** (0.000)
Medicare			−0.7583*** (0.000)	−0.7205*** (0.000)
APOE (1 Copy)			0.9493*** (0.000)	0.9720*** (0.000)
APOE (2 Copies)			2.2881*** (0.000)	2.3323*** (0.000)
Height			−0.0536*** (0.000)	−0.0570*** (0.000)
Female			−1.028*** (0.000)	−1.0780*** (0.000)
Ln Education			−1.7409*** (0.000)	−1.8329*** (0.000)
Constant	0.4496 (0.101)*	1.2711 (0.000)***	9.0354*** (0.000)	10.1009*** (0.000)
Number of Obs.	16,596	16,596	13,894	13,894
R2 Within	0.0151		0.0773
F††	21.59*** (0.021)		11.45*** (0.000)
Chi-Square†††	276.08*** (0.000)		92.32*** (0.000)

^†All equations include eleven of the twelve visits variables.

^††Significance levels on coefficients:

^*10%;

^**5%;

^***1%.

^†††The F-test is for the null that all the α_v are equal to zero.

^††††The Chi-square is the Hausman test for the null that that the difference between the fixed and the random coefficients estimates are not systematic.

Table 4:

LSDV Estimates for Fixed and Random Effects Models of Hearing Variables on the GDS (p-values in parentheses)^†

	Without Controls		With Controls
Variable	Fixed Effects	Random Effects	Fixed Effects	Random Effects
H0: β1	−0.0623 (0.396)	−0.0295 (0.686)	−0.0541 (0.455)	−0.0294 (0.684)
HA: β2	−0.4519*** (0.000)	−0.4531*** (0.000)	−0.4078*** (0.000)	−0.4097*** (0.000)
Age A: β3	0.0039* (0.087)	0.0014 (0.529)	0.0046* (0.080)	0.0029 (0.267)
CDR-SB: βD	0.1427*** (0.000)	0.1456*** (0.000)	0.0468*** (0.000)	0.0469*** (0.000)
Medicare			−0.8573*** (0.000)	−0.8476*** (0.000)
Ln Education			−0.6444*** (0.000)	−0.6724*** (0.000)
Married			−0.1367*** (0.000)	−0.1346*** (0.001)
Independent Level L1			−0.9072*** (0.000)	−0.9186*** (0.000)
Constant	1.7817*** (0.000)	1.9758*** (0.000)	5.1691*** (0.000)	5.3851*** (0.000)
Number of Obs.	16,033	16,033	15,914	15,914
R2 Within	0.0396		0.0675
F††	4.12*** (0.000)		2.90*** (0.001)
Chi-Square†††	80.58*** (0.000)		41.25*** (0.000)

^†Significance levels on coefficients:

^*10%;

^**5%;

^***1%.

^††The F-test is for the null that all the β_v are equal to zero.

^†††The Chi-square is the Hausman test for the null that that the difference between the fixed and the random coefficients estimates are not systematic.

4.2. The Effects of Hearing and Dementia on Utility.

The second estimation equation has utility U as the dependent variable, and dementia symptoms D and the set of hearing variables H as the independent variables, again with the vector Z as controls. We will also express the second regression as a fixed effects model and leave it to the Hausman test to confirm that this is preferable to the random effects model.

The regression equation for U in a panel data format is, with β_v as the set of visit dummy variables and the other β coefficients are the regression parameters to be estimated:

$$\underset{\_}{U_{\text{i}v}}={\beta }_0+{\beta }_{1}H{0}_{\text{i}v}+{\beta }_{2}H{A}_{iv}+{\beta }_3{A}_{iv}+{\beta }_D{D}_{iv}+{\beta }_Z{Z}_{iv}+{\beta }_{\text{v}}+{\gamma }_{\text{i}v}$$ (7)

4.3. The Utility Effects of Hearing Aids

From equation (7), we derive the direct effect of HAs on utility: $\frac{\partial U}{\partial HA}={\beta }_2$; and from equations (6) and (7) we obtain the indirect effect of HAs on utility: $\frac{\partial U}{\partial D} \frac{\partial D}{\partial HA}={\beta }_D{\alpha }_2$. As explained in connection with equation (1), our measure of U in regression equation (7) will use data specified in GDS units, which needs to be inverted and rescaled to be converted to positive and unit interval QoL units. Consequently, the benefits of HAs presented in equations (5a) and (5b) will be estimated by:

$$\text{Direct Benefits:\hspace{0.17em}}P\times LY\left(-{\beta }_2/15\right)$$ (8a)

$$\text{Indirect\hspace{0.17em}Benefits:\hspace{0.17em}}P\times LY\left(-{\beta }_D/15\right){\alpha }_2$$ (8b)

4.4. The Selection of the Controls

We will use for the Z variables the two interventions that were shown to causally effect dementia symptoms (years of education and Medicare eligibility) and all the other controls included in the dementia CBAs using the UDS, Brent (2017, 2018). These other controls were: hereditary factors (height and family dementia variables which include one and two copies of the gene apolipoprotein E, APOE e4); demographic characteristics (race and gender); and independent living levels (living independently or with assistance). Other factors that are known to be associated with dementia symptoms (such as alcohol, smoking, depression, blood pressure, and obesity) are excluded from our analysis. This is because these variables are behavioral, and as such, are likely to result from dementia and not just cause it. They are therefore excluded to avoid any possible reverse causation.

5. The Description of all the Variables used in the Study and the Data Summary.

All the variables to be used in the two estimation equations are listed in table 1 together with their definitions. The definitions come from NACC’s “Description of NACC Derived Variables to be Used in Data Analysis” (August 2014) and NACC’s Uniform Data Set (UDS) “Coding Guidebook for Initial Visit Packet” (last modified January 14, 2014). When there was no missing information, there were 17,341 observations. Actual sample sizes for the estimation equations were dependent on the number of missing observations for variables included in the particular regression equation.

Table 1:

Definitions of all the Variables

Variable	Description
D: CDR-SB	Clinical Dementia Rating (CDR) Sum of Boxes (SB). Total CDR score based on Memory, Orientation, Judgement & Problem Solving, Community Affairs, Home & Hobbies, Personal Care, each of the six categories on a scale of 0 to 3.
Geriatric Depression Scale (GDS)	Total GDS score. Sum of the 1s for the 15 ingredients of the GDS scale, short form.
H0	Without a hearing aid, is the subject’s hearing functionally normal? 1 = Yes; 0 = No if any functional impairment exists (reduced ability to do everyday activities such as listening to the radio or television, talking with family and friends).
HA	If the subject is wearing a hearing aid, is the subject’s hearing functionally normally? 1 = Yes; 0 = No if any functional impairment exists (reduced ability to do everyday activities such as listening to the radio or television, talking with family and friends).
AID	Does the subject usually wear a hearing aid? 1 = Yes if the subject wears a hearing aid to perform everyday activities (such as listening to the radio or television, talking with family and friends); 0 = No.
Age A	Subjects age at time of visit.
Medicare	Is the subject eligible for Medicare? Age ≥ 65 = 1; Age < 65 = 0.
APOE (1 copy)	Number of Apolipoprotein E (APOE e4) 1 copy. 1 = 1 copy of e4 allele; 0 = No e4 allele copy or 2 e4 allele copies
APOE (2copies)	Number of Apolipoprotein E (APOE e4) 2 copies. 1 = 2 copies of e4 allele; 0 = No e4 allele copy or 1 e4 allele copy
Height	Subject’s height in inches.
Female	Subject’s sex. Female = 1; Male = 0
Ln Education	Subject’s years of education in natural logs.
Married	Subject’s marital status is married. Yes = 1; All other statuses = 0.
Independence Living Level L	The subject’s level of independence. L1 = Able to live independently, L2 = Requires some assistance with complex activities, L3 = Requires some assistance with basic activities, L4 = Completely dependent.
White	NIH race definition. 1 = White; 0 = Non-White.
Visits	Number of UDS visits at NACCs.

Table 2 gives the data summary in terms of the number of observations, mean values, standard deviations and minimum and maximum values. We can see that, on average, subjects had 15 years of education, scored a 3 on the CDR-SB dementia scale, and the QoL was “good” (had a 1.96 value for the GDS). The average age was 72 years. In our sample, 38% were males, 81% were white, 35% had 1 copy of APOE e4, 7% had two copies, and 63% lived completely independently (living level 1).

Table 2:

Descriptive Statistics for all the Variables

Variable	Number	Mean	Standard Deviation	Minimum	Maximum
CDR-SB	118,341	3.10	4.74	0	18
GDS	103,164	1.96	2.48	0	15
H0	108,090	0.75	0.43	0	1
HA	16,907	0.86	0.34	0	1
AID	108,343	0.16	0.37	0	1
Age A	118,341	74.78	10.26	18	110
Medicare	118,341	0.85	0.36	0	1
APOE (1 copy)	99,870	0.33	0.47	0	1
APOE (2 copies)	99,870	0.06	0.24	0	1
Height	102,087	65.48	4.03	37	84
Female	118,341	0.58	0.49	0	1
Ln Education	117,508	2.69	0.28	0	3.4
Married	117,725	0.60	0.49	0	1
Independence Level L1	118,100	0.64	0.48	0	1
Independence Level L2	118,100	0.18	0.39	0	1
Independence Level L3	118,100	0.11	0.31	0	1
Independence Level L4	118,100	0.06	0.24	0	1
White	118,341	0.81	0.39	0	1
Visits	118,341	3.15	2.24	1	12

6. Estimation Results

6.1. Estimating the Effects of the Hearing Variables on Dementia Symptoms

The estimates for equation (6) are in table 3. All variables are statistically significant at well below the 1% level. The results with the controls are the more meaningful ones and these are the ones that will be discussed in detail. As the Hausman test rejects that the null that the difference between the fixed effects and the random effects are not systematic, the fixed effects with controls results are the relevant ones.

As expected, hearing normally with and without a HA has a negative impact on dementia symptoms. Interestingly, HAs reduce CDR-SB twice as strongly as does hearing normally without HAs (the difference between α₁ and α₂ is highly statistically significant). Note that on the CDR-SB scale, 0.5 is the difference between a unit change in a domain being detected by the evaluator and a “don’t know” verdict. So in this sense, the – 0.7251 reduction that HAs produce has economic significance and not just statistical significance. The third hearing variable, age, has a small, yearly, positive impact on dementia symptoms. It would take about 11 years of aging to offset the hearing advantages of normal hearing without a HA, and nearly 22 year of aging to offset the hearing advantages provided by wearing a HA.

Of the controls that were interventions in their own right in prior CBAs, i.e., Medicare eligibility and years of education, the results from the panel data analysis confirms the fact that they significantly lower dementia symptoms. Hereditary factors played a strong role in explaining dementia symptoms, as one copy of APOE e4 increased the CDR-SB by one point and two copies increased the CDR-SB by two points. Height had a significantly, small negative effect.

Being female had a negative one-point effect on the CDR-SB. Although, females are more likely to have dementia, one of the main reasons for this is that women live longer than men do. Once one controls for age, and hereditary factors, it may be that the fact that females are generally healthier than men are helps to explain the negative female dementia effect in our results. In particular, HL among the elderly (presbycusis) is higher for males than females.⁶ Thus, as equation (6) contains HL, we are also effectively controlling for this positive male influence on dementia symptoms helping to render the female effect on dementia negative.

6.2. Estimating the Effects of the Hearing Variables on Utility

The estimates for equation (7) are in table 4. For interpretation purposes, it is important to recall that the dependent variable GDS was an inverse proxy for QoL. Therefore, a negative sign means that the variable concerned improves QoL and a positive sign indicates an adverse utility effect. Again, the fixed effects with controls results are the relevant ones. All the variables (but two of the hearing variables) were significant at least the 1% level.

The only one of the hearing variables that was significant was HA and this raised utility (lowered the GDS) as expected. It would seem that recovering the capacity to hear after HL affects utility more than having normal hearing in the first place. Being elderly, by itself, did not lower utility. Having dementia symptoms decreased utility (raised the GDS) and this was the necessary second step for HAs to have positive indirect benefits, given that HAs had previously been found to lower CDR-SB. All four controls (Medicare eligibility, years of education, being married and living independently) raised utility levels.

7. The Benefit Components and the Resulting Benefits Estimates.

There are five components that make up the direct and indirect benefits of HAs expressed in equations (8a) and (8b): β₂, β_D, α₂, P and LY. We take estimates for the three utility components β₂, β_D, α₂, from tables 3 and 4. What remains to be explained is our methods for estimating P and LY.

7.1. The Price of a QALY

Our estimate of P builds on the method first developed by Hirth et al. (2000), see Brent (2014). Their method was based on the idea that, if one could obtain an independent estimate of the lifetime benefits B from being in a particular health state, then one can back out the implied value of P for an annual QALY. Hirth et al. consider a number of alternative measures for B. We are going to concentrate solely on a willingness to pay measure based on revealed preferences between occupation risk and wages in the labor market, in which case B will be given by the value of a statistical life (VSL). Since our sample consists of mainly the elderly, it is the VSL of older adults when they were working that is relevant for our purposes. By reversing B = P × QALY we obtain:

$$P=\frac{B}{\mathit{\text{QALY}}}=\frac{VSL}{LY\times U}$$ (9)

The P in equation (9) will be calculated in two steps. In the first, there will be no quality of life adjustment and U will be set equal to 1. In this context, P reduces to VSL/LY, which is simply the value of a statistical life year (VSLY). The second step entails applying the quality of life adjustment to the VSLY obtained in the first step.

For the first step, it is important to recognize that the VSL is accumulated over a lifetime and thus requires discounting to be reduced to an annual value. If the social discount rate is r, and the age specific years of life expectancy is L, the relation between the VSLY and the VSL is given by Aldy and Viscusi (2008) as:⁷

$$\text{VSLY}=\frac{r VSL}{1-{\left(1+r\right)}^{-L}}$$ (10)

Aldy and Viscusi (as well as Hirth et al.) used the standard discount rate used in health care evaluations of r = 3% as recommended by Gold et al. (1996). The oldest age cohort covered by Aldy and Viscusi in their VSL estimates was 55 to 62 years, and the VSL at 62 years was found to be $5.09 million in 2000 dollars. Using this discount rate and VSL figure, and taking the life expectancy at 62 years to be L = 23,⁸ equation (10) produces a VSLY estimate of $310,000.⁹

For the second step, which involves adjusting the VSLY for U, we follow Hirth et al. and use the age-specific quality of life estimates that come from the Beaver Dam Health Outcomes Study, see Fryback et al. (1993). We take the U estimate based on the Quality of Well-Being index (QWB) developed by Kaplan and Anderson (1988). The average QWB for males and females over the two age ranges 65 to 74 and 75 to 84 was 0.70.¹⁰ With U = 0.70 in equation (9), and a VSLY of $310,000, the estimate of P is $442,857.

7.2. The Number of Life Years

The LY in the direct benefits equation (8a) will not be the same duration as the LY in the indirect benefits equation (8b). The HAs provide direct utility benefits throughout the remaining life of the subject and not just for the period when dementia sets in. So, for the direct benefits, the life expectancy is 23 years as this was used in the calculation of P. For the indirect benefits, the utility comes from the reduction in dementia symptoms that HAs provide and this occurs just when the client has dementia. We take the median life expectancy for a subject first diagnosed with dementia as 11 years (see Aneshensel et al., 1995) and this is our estimate for the LY for the indirect benefits.¹¹

7.3. The Resulting Estimates of the Benefits of Hearing Aids

We take the coefficient estimates for β₂, β_D and α₂ from the fixed effects with controls regression equations in the results section. This is because, as explained earlier, the Hausman test indicates that one can reject the null that there is no systematic difference between the fixed and the random effects estimates, and one knows in advance that the fixed effects estimates are consistent. From table 3, α₂ = – 0.7251, and from table 4, β₂ = – 0.4078 and β_D = 0.0468. Consequently, we obtain as our estimates of (8a) and (8b):

$$\text{Direct Benefits:\hspace{0.17em}}=\$442,857\times 23\left(0.0272\right)=\$276,916.$$

$$\text{Indirect\hspace{0.17em}Benefits:\hspace{0.17em}}=\$442,857\times 11\left(0.0023\right)=\$11,021.$$

A final adjustment to the benefits estimates just derived is necessary because of the fact that all of our analysis so far has been in terms of wearing HAs that result in normal hearing, and not all HAs are effective. Of the 16,907 visits by clients wearing HAs, 14,587 had normal hearing, an effectiveness rate of 86.28%. Multiplying the two categories of benefits of normal hearing from HAs by 0.8628 produces adjusted indirect benefits of $238,917 and adjusted indirect benefits of $9,508. This makes the lifetime total benefits of purchasing, and wearing, HAs $248,425.

8. The Costs of Hearing Aids

The costs of HAs come from the Cost-Utility Analysis carried out by Abrams et al. (2002). They costed separately the HAs and the post fitting support services, which were called audiologic rehabilitation (AR). Since our data on HAs relates to subjects whose hearing is restored to being normal, we will assume that the HAs we are costing do work reasonably effectively and so include the AR costs in addition to the costs of the HAs.

The costs for HAs included: labor, supplies and materials, equipment and other costs (administration and building maintenance, etc.). These costs were itemized under four headings and listed as: audiological assessment $64.01, HA evaluation $941.65, HA orientation $26.11 and post-fitting follow-up $24.96. The AR costs covered the transport costs of attending four support group sessions and averaged $62.70. The total costs per person were $1,119. The data were collected between 1999 and 2001, so we assume they were in 2000 prices and so approximately contemporaneous with the benefits figures presented earlier.

Since Donohue et al. (2010) report that most individuals (77%) with HL require two devices, we will use double the $1,119 price of one HA, i.e., $2,238, to be our estimate of the one-time cost of wearing HAs. Donohue et al. also indicate that the average life of hearing instruments is four to six years. To simplify, we will assume that corresponding to the direct benefits period that last 23 years, five sets of HAs would be required. Discounted at 3%, this makes the present value of the lifetime HA costs $8,498.¹²

9. The Net Benefits and Sensitivity Analyses

Subtracting the costs of $8,498 from the $248,425 total benefits figure produces a net-benefits amount of $239,927, with a benefit-cost ratio of 29.23. Clearly, HAs are very socially worthwhile.

Because the net-benefits amount is so favorable, and the policy implications of the CBA so important, it is necessary to check the robustness of the results to alternative scenarios that would reduce the estimates of the benefits or raise the estimates of the costs. Our CBA methodology used P and QALYs for the benefits and we consider variations for these two ingredients first. Then we consider raising the costs.

9.1. A Lower Price for a QALY

For our main estimate of P, we took the $310,000 which was the VSLY amount and utility adjusted it (that is, divided it by the utility of a LY for an elderly person which was 0.70) to produce the $442,857 figure that we used as our best estimate for P. So one alternative is to stick with a full quality life year and not divide by 0.70. Keeping the $310,000 value for P would lower the net-benefits by about a third. The effectiveness adjusted direct benefits were $167,242; the effectiveness adjusted indirect benefits were $6,656; and the net benefits were $165,400 with a benefit-cost ratio of 20.46.

9.2. A Lower Number of QALYs due to Using Lower Bound Utility Estimates.

The number of QALYs generated corresponded to utility being enhanced from HAs with the number of life years considered fixed. There were three coefficients that formed the utility gains in the estimates of the direct and indirect benefits expressed in equations (8a) and (8b). Instead of the best estimates, we can replace the three coefficient estimates with those that come from the lower bounds of the 95% confidence intervals. In this case we have: α₂ = – 0.5726, β₂ = – 0.3030 and β_D = 0.0308. The new benefits results were:

$$\text{Direct Benefits:\hspace{0.17em}}=\$442,857\times 23\left(0.0202\right)=\$205,751.$$

$$\text{Indirect\hspace{0.17em}Benefits:\hspace{0.17em}}=\$442,857\times 11\left(0.0015\right)=\$7,253.$$

With the effectiveness adjustment, and the deduction of the costs, the net-benefits would again be reduced by about a third. The direct benefits were $177,518; the indirect-benefits were $6,258; the net benefits were $175,278 with a benefit-cost ratio of 21.63. The “switching value” for the effectiveness adjusted indirect net-benefits to be zero was only β₂ = – 0.0145. There was thus an almost zero chance that HAs do not improve QoL and in in this way be socially worthwhile.

9.3. A Lower Number of QALYs due to Using an Alternative Estimation Technique.

This variant also (like in section 9.2) provides different values for the benefits via alternative estimates for the three utility coefficients α₂, β₂ and β_D. For the main results, the three coefficients came from one-way fixed effects models used to estimate equations (6) and (7). As an alternative, we will apply a two-way framework that allows for both visits and individual effects to be used as controls. We take all the independent variables specified in tables 3 and 4, together with the set of twelve visit dummy variables, and add the set of 6,116 individual dummy variables. Since a two-way fixed effects model cannot be applied in this context, a random effects model was used as the estimator.¹³ The estimates from the random effects model were: α₂ = – 0.3073, β₂ = – 0.1738 and β_D = 0.0637. Again using equations (8a) and (8b) we found:

$$\text{Direct Benefits:\hspace{0.17em}}=\$442,857\times 23\left(0.0116\right)=\$118,018.$$

$$\text{Indirect\hspace{0.17em}Benefits:\hspace{0.17em}}=\$442,857\times 11\left(0.0013\right)=\$6,357.$$

With the effectiveness adjustment, and the deduction of the costs, the net-benefits once more are reduced by about a third. The direct benefits were $101,824; the indirect-benefits were $5,485; the net benefits were $101,483 with a benefit-cost ratio of 18.42.

9.4. A Higher Cost Estimate

Turning now from benefit alternatives to cost variations, we consider the special case where HAs are replaced annually rather than every four years as in our base-line estimates. Although this is clearly a worst-case scenario, this is a useful exercise if, for no other reason, it is a very simple way of allowing the effects of technological change to impact the CBA of HAs. De Silva et al. (2013) find that manufacturer prices, and hence HA costs, depend crucially on the technical design of HAs. The smaller the size (at best it is completely-in-the-canal of the ear and largely concealed) and the more advanced the processor type, the higher the premium a firm charges for the HA. The role then of the heroic assumption of the annual replacements of HAs is envisaging individuals taking advantage of an industry with assumed rapidly advancing technologies that annually improve comfort and effectiveness (without lowering prices to the consumers).¹⁴

Purchasing a HA for $2,238 annually for 23 years at a discount rate of 3% had a present value of $37,854. This cost figure is 4.54 times larger than our baseline cost estimate. Nonetheless, the net-benefit at $210,571 is only reduced by 12% by this higher cost with the benefit-cost ratio still being large at 6.31.

10. Summary and Conclusions

We carried out a CBA of HAs in which we estimated the direct utility benefits, and also included the indirect utility benefits working through a reduction in dementia symptoms. The benefits methodology involved using QALYs as the outcome measure, and then applying the price of a QALY to convert the outcome measure into monetary terms. The price of a QALY was derived from an age-specific VSL estimate given in the literature, with life expectancies being different for those with and without dementia. We took a conservative approach whereby the QALYs generated by HAs only came from increasing utilities and not extending the lifespans of wearers. The direct and indirect effects of HAs on utility were estimated from a fixed effects regression on a large panel data set provided by NACC where we used a negative proxy for the QoL. We also used a fixed effects regression for the estimate of the indirect benefits involving HAs reducing dementia symptoms.

Our results confirm the findings in the literature that HAs reduce the symptoms of dementia. As expected, reducing the symptoms of dementia increases a client’s quality of life, as does hearing normally due to wearing a HA. We found that the total benefits, mainly coming from the direct benefits, were around a quarter of a million dollars and very large relative to the costs, with a benefit-cost ratio of around 30. However, the indirect benefits were sizeable in that, even if they were the only category of benefits, they alone would be sufficient to cover the HAs costs. The capacity for HAs to reduce the symptoms of dementia needs to be acknowledged and added to the list of interventions helping to mitigate the spread of this increasingly prevalent disease.

At this time, Medicare does not cover the costs of HAs.¹⁵ Given our CBA results, this needs to be changed, as investing in HAs is something very socially worthwhile and current private market utilization levels do not reflect their advantages. Although Medicare has been shown to reduce the symptoms of dementia, and pass a CBA test as a beneficial intervention in its own right, it turns out, as shown in the appendix, that the lack of coverage of HAs by Medicare means that Medicare eligibility does not help to raise HA utilization even by those experiencing HL. Medicare could therefore have even more beneficial effects if HAs are included as a standard part of the health insurance package provided to older adults.

Appendix: Determinants of Hearing Aid Use

The main body of this article focused on HL with and without a HA. In this appendix we complete the hearing picture by turning the attention to some possible reasons why someone with HL would or would not wear a HA. In the NACC data set, clients were not asked questions about their HA preferences and perceptions as was carried out in the nationally representative survey of HA acquisition out carried by Fischer et al. (2011). Therefore, we will just use the controls that we have in our data set to see how much of an explanation they can provide of HA non-use behavior. Clients with HL may not usually wear a HA either because they do not own a HA, or own one, but choose not to wear it regularly.

Table A1 shows the two-way contingency table related to the absolute frequencies for visits by clients with and without normal hearing (H0=1 and H0=0) and those who do and do not usually wear a HA (AID=1 and AID=0). As we can see, of the 107,692 visits where hearing was assessed, for 26,540 (24.64%) of the visits clients did not have normal hearing (had a HL with H0=0); and of these visits, 10,707 (40.34%) took place with clients without using HAs (with AID=0) even though they were needed.

Table A1:

Contingency Table

	AID
H0	AID = 0	AID = 1	Total
H0 = 0	10,702	15,838	26,540
H0 = 1	79,972	1,180	81,152
	90,674	17,018	107,692

Our analysis will focus on the 26,540 client visits with HL who decide whether to usually wear a HA, or not. The dependent variable is a dummy variable AID = 1 when the client with HL usually wears a HA, and is AID = 0 otherwise. This is a binary outcome, which makes Probit a suitable estimator. As a fixed effects Probit model provides inconsistent estimates when applied to panel data due to the “incidental parameters problem” (Wooldridge, 2002), we will carry out estimation using a random effects Probit model.

We continue to treat age as a key potential determining influence in the context of hearing. Our analysis focuses on the extent to which HA use depends on a client’s independent living status L, where L1 is independent living (without a caregiver), L2 is living with some assistance, L3 is living with a lot of assistance, and L4 is living completely dependent (see Tables 2 and 3). We will focus on the two polar cases, one where the client lives independently L1 and the other where the client lives completely dependently L4, and contrast this with the two intermediate cases L2 and L3 (the reference cases). Our main hypothesis is that L1 would have a positive effect on HA use, and L4 would have negative effect, if HA use is a client’s choice and this is what was preferred with independent living. Alternatively, the signs for L1 and L4 would be reversed if HA use is a caregiver’s choice or its use is required by the caregiver to facilitate better communication with the client.

In the latent variable interpretation of a binary choice model, where AID is assumed unobservable and represented by AID*, the regression equation in a random effects context is:

$$AID{*}_{\text{iv}}={\pi }_0+{\pi }_{1}L{1}_{\text{iv}}+{\pi }_{2}L{4}_{\text{iv}}+{\pi }_3{A}_{\text{iv}}+{\pi }_Z{Z}_{\text{iv}}+{\text{λ}}_{\text{i}v}+{\text{ψ}}_{\text{iv}}$$ (A1)

where L1 and L4 are entered separately with age A; the controls Z are demographic and socio-economic determinants of HA use that were used previously in the estimations and are present in our data set; the π coefficients are the regression coefficients to be estimated; the random effects λ_iv are assumed to be uncorrelated with the independent variables; and ψ_iv is the random error term. We observe AID_iv = 1 when AID_iv* ≥ 0, and AID_iv = 0 when AID_iv* < 0. Using equation (A1), this implies:

$$\text{Pr}\left({\text{AID}}_{\text{iv}}=1|L,Z\right)=\text{Pr}\left({\text{ψ}}_{\text{iv}}\le {\pi }_0+{\pi }_{1}L{1}_{\text{iv}}+{\pi }_{2}L{4}_{\text{iv}}+{\pi }_3{A}_{\text{iv}}+{\pi }_Z{Z}_{\text{iv}}+{\text{λ}}_{\text{iv}}\right)$$ (A2)

The right-hand side of equation (A2) defines a cumulative distribution function, and when this is assumed to be normally distributed, the Probit model can be used for estimation of the π regression coefficients.

The Probit random effects marginal probabilities are shown in Table A2. In this table we present the results focusing on independent living with and without the other controls, but all of the controls in this table are now of separate interest.

Table A2:

Probit Random Effects Estimates (Average Marginal Effects) of Living Independently on Hearing Aid Use (p-values in parentheses)^†

Variable	Without Controls	With Controls
Independent Level L1: π1	0.0662*** (0.000)	0.0575*** (0.000)
Independent Level L4: π2	−0.3022*** (0.000)	−0.2477*** (0.000)
Age A: π3	0.0305*** (0.000)	0.0261*** (0.000)
Medicare		0.0610*** (0.000)
Ln Education		0.2490*** (0.000)
White		0.4059*** (0.000)
Married		0.0521*** (0.003)
Female		−0.1472*** (0.000)
Number of Obs.	26,481	26,184
Pseudo R2	0.0333	0.0516

^†Significance levels on coefficients:

^*10%;

^**5%;

^***1%.

All variables are significant at least the 1% level, except for the Medicare eligibility variable that was not significant even at the 5% level. As one would expect, age always has a positive effect on HA use (π₃ > 0). With and without controls, L1 has a positive effect on HA use (π₁ > 0) and L4 has a negative impact (π₂ < 0) as hypothesized. This confirms the likelihood that client choice, in the context of the extent of independent living, seems to strongly influence the decision whether to wear a HA as in our main hypothesis.¹⁶

The insignificance of the Medicare eligibility variable is noteworthy in the context of the fact that Medicare does not cover HAs. Given that the age variable related to all age groups had a significant positive effect, one would have expected that the over-65 population subset, being more elderly, would be more in need of HAs. Thus, one would have expected that Medicare eligibility would have had a large positive impact. Having a financial incentive to not have a HA, when a HA is something that we found to be highly beneficial, is something that needs to be remedied. With HA usage being so low, it is important that any unnecessary barriers be removed.

Of the four controls other than Medicare, three of them (race, education, and being married) had a positive impact on HA use and being female had a negative effect. An explanation for this negative female sign can perhaps be found in the Fischer et al. study of HA acquisition. They found that, even though all those covered in the survey were told that they had a demonstrated HL, women were more likely than males to say that: (a) they did not need a HA (60% for women; 50% for men) and that (b) cost was a main factor in them not acquiring a HA (70% for women; 55.2% for men).