# How to estimate the economic cost of a risk factor or disease

We commonly see cost-effectiveness analyses in medical journals or government reports, which provide some sense of how much a new test or procedure might cost, divided by the number of lives saved by the intervention (or some metric related to morbidity or mortality, like “quality-adjusted” years of life saved). But increasing we’re also seeing estimates in the popular press and medical literature of how much a given risk factor—tobacco smoking, junk food, air pollution—or its related diseases—cancer, diabetes, etc—costs a country or state or the world economy in pure dollar terms. What does it mean when we say that “the cost of smoking in California is \$15.8 billion a year” or “the cost of diabetes in theUS is more than \$174 billion a year”? Where do these estimates come from, how are they calculated, and—most importantly of all—should we believe them?

In this blog post, we describe two common (but not exclusive) ways that researchers estimate the cost of a given risk factor like tobacco smoking or air pollution. By understanding the methods behind these approaches, it’s much easier to get a sense of their advantages and drawbacks.

The costs of a risk factor typically consist of three components:

(1)     direct costs,

(2)     indirect costs of lost productivity from related illness, and

(3)     indirect costs of premature deaths caused by related disease

We will discuss two approaches to estimating costs #1 and #2, then revisit cost #3 after a brief discussion.

Option 1: Using a prevalence-based approach to estimating costs #1 and #2

The more complex of the two common procedures is to estimate the economic cost of a risk factor by adding up all illness and deaths that occurred in a given year that resulted from exposure to that risk factor. An attributable fraction (AF) is estimated and applied to the total measure of interest, e.g., the AF for hospitalization expenditures represents the proportion of hospitalization expenditures that are attributable to the risk factor. The AF is therefore multiplied by the total hospitalization expenditures in a community to obtain hospital expenditures attributable to the risk factor.

Direct costs

Multiple types of health care services can be included in the direct cost calculation, such as hospitalizations, ambulatory care, nursing home care, prescription drugs, and home health care.

Many people use derivatives of the following econometric models to estimate direct costs; these consist of multiple equations describing the effect of exposure to a risk factor S (current exposure, former exposure, and never exposed) on the past history of the related diseases D, on self reported poor health status H, on the probability of having health care expenditures X, and on the magnitude of expenditures given that expenditures took place.

Demographic and socioeconomic status Y (age, income, health insurance coverage, etc.) and other relevant risk behaviors R (obesity, seatbelt use, whatever might apply) should be controlled for in the model. The structural forms of these equations are:

(1)     D* = f1 (S, Y, R)

(2)     H* = f2 (S, Y, R,D*|D)

(3)     Prob(X>0) = f3 (S, Y, R, H*|H)

(4)     Log(X|X>0) = f4 (S, Y, R, H*|H)

D is a binary variable that equals one if the respondent reported having one of the diseases related to the risk factor, and zero otherwise. D* is an unobservable variable for the propensity for having a diseases from the risk factor, and is estimated as a probit model. H is self reported health status (e.g., categorized as excellent, good, fair, or poor). H* is an unobservable variable for the propensity of having poor health and is estimated as an ordered probit model. D*|D denotes the expected propensity for having risk-factor-related disease conditional on self reported disease history. Likewise, H*|H denotes the expected propensity for having poor health conditional on self reported health status. Equation 3 is estimated as a probit model. Equation 4 is the logarithm of the magnitude of expenditures for those individuals with expenditures and is estimated using ordinary least squares regression.

The coefficients are estimated from survey data and calculated based on the observed population, then repeated with a fake population of people who are identical in every way except for having no exposure to the risk factor. The difference in X between the two populations, divided by X for the real population, is the AF.

Indirect costs of lost productivity due to illness

Two indicators of morbidity costs are often considered: risk-factor-attributable work loss days and bed disability days. These are determined as the product of the AF and the total number of days lost. The standard epidemiological formula to calculate AFs for work loss days and bed disability days is: AF = [(pn + pc(RRc) + pf(RRf)] – 1 / [(pn + pc(RRc) + pf(RRf)], where pn, pc, and pf denote the percentage of people who have never been exposed, are currently exposed, and were formerly exposed to the risk factor; RRc (RRf) denotes the relative risk of the outcome measure of interest for currently (formerly) exposed people relative to people never exposed to the risk factor.

To calculate RR, first work loss days or bed disability days are estimated as a function of risk factor status, controlling for geographic region, demographic and socioeconomic variables and other risk modifiers using a Tobit model. Then the relative risk for currently (or formerly) exposed people is calculated as the ratio of predicted days for currently (formerly) exposed to predicted days for a hypothetical group of currently (formerly) exposed people with all the same characteristics except for not having any history of exposure to the given risk factor.

Option 2: Using an incidence-based approach

The morbidity costs of a disease or condition can also be estimated using an incidence-based cost of illness approach. This approach is generally considered to yield a conservative estimate of the true cost of disease.

The Healthcare Cost and Utilization Project has data from which we can derive average length-of-stay and medical costs for hospitalizations from different conditions. The Medical Expenditure Panel Survey provides the average cost per emergency department visit, annual out-of-pocket expenses for hospitalized patients, and outpatient expenses by diagnostic condition category. We can use these two data sources to calculate the direct medical costs associated with disease incidence attributed to a given risk factor of interest. This is easiest to do when there is a discrete risk factor from which incidence can be easily assessed, such as in natural disasters. Then we can add in lost work productivity estimated from hospital stays based on the usual median weekly earnings of full-time employees as reported by the Bureau of Labor Statistics.

Of note, we have to convert reported hospital charges to actual hospital costs, since hospitals tend to bill much more than the actual cost of providing healthcare (a fact worth extensive commentary on its own). The Healthcare Cost and Utilization Project has a web tool that allows researchers to do the conversion easily. The tool uses cost-to-charge ratios based on national and state hospital accounting reports (the cost-to-charge ratio is usually around 0.65).

Adding in indirect costs of lost productivity due to premature death: cost #3

Approaches to estimating the “cost” of premature death are heavily debated. The “value of a statistical life” approach assumes a particular value for a persons’ life (e.g., a typical American’s life, based on court litigation rewards and numerous other indexes, was valued at \$7.9 million in 2008 dollars according to the FDA), which is of course an inherently ethically confusing and scientifically debatable concept. Regardless, the use of this number is standard in insurance and related markets. Simply multiply the portion of life lost by this number to estimate the quantified “cost” of years lost per this index of society’s valuation of life. Some people also use a “willingness to pay” approach, in which people are asked through surveys how much they are willing to pay to avoid the costs of pain and suffering associated with illnesses; this of course also comes with many caveats.

The related human capital approach to measure the value of lost productivity accounts for value lost due to risk-factor-attributable diseases. The cost to society of attributable premature death is calculated as the product of attributable deaths and the present value of lifetime earnings (PVLE) for each person. The number of attributable deaths is estimated by multiplying the AFs by total deaths for each underlying cause of death reported as being causally linked to the risk factor. The AF is determined for each age group and sex according to the epidemiological formula above. The relative risk of death from each associated disease is taken from real-world data. Risk factor exposure rates are also estimated from epidemiological survey data. Total deaths for each risk-factor-related diagnosis by sex and age can be obtained from government death registries.

The number of years lost from risk-factor-caused death is estimated by sex and age group as the product of the number of attributable deaths and the average number of years of life expectancy remaining at the age of death. PVLE per person is estimated by age group and sex by estimating the life expectancy for different sex and age groups, varying rates of labor force participation, and changing pattern of earnings at successive ages. This assumes that people will be working and productive during their lifetimes in accordance with the current pattern of earnings and work experience for their sex and age groups.

Important caveats

In studies that use any of these approaches, there are multiple data sources and assumptions being combined into one estimate, as with any mathematical model or economics assessment. Variability is introduced with each illnesses considered, with each direct costs included or excluded, and with numerous inferences about those costs. Where the data presents a range of options, it’s important to conduct a sensitivity analyses to determine how differences in inputs to the estimate can result in different estimates of ultimate cost.

Regardless, in looking at these two methods, it’s clear that a lot of assumptions and loose estimates are needed to arrive at any sense of the economic impact of a risk factor or disease. Nevertheless, these approaches may help us to gain some quantitative sense of a risk’s impact—let alone alert the public to a major public health issue that might otherwise seem diffuse and difficult to understand the importance of.