Effect of Patient’s Life Expectancy on the Cost-effectiveness of Treatment for Ocular Hypertension

Abstract

Objectives

To measure the influence of age and/or expected lifespan in determining the cost-effectiveness of treating ocular hypertension to prevent primary open angle glaucoma.

Methods

A Markov model simulated the expected costs and benefits a cohort of people with ocular hypertension would accrue over their lifetime. The outcome of interest was the incremental cost effectiveness ratio. Data was taken from the Ocular Hypertension Treatment Study and public sources. The model was first tested for specific age cohorts to identify the influence of baseline age on the cost effectiveness cost-effectiveness of treatment. We then set each cohort’s life expectancy to determine the influence on cost effectiveness.

Results

At a willingness to pay of greater than $75,000 treatment of people with a ≥ 2% annual risk of developing glaucoma was cost-effective for oeople 45 years of age, with a life expectancy of at least 18 years. However, to be cost-effective a person 55 years old must have a life expectancy of 21 years and someone age 65 must expect to live 23 years.

Conclusions

To meet most commonly accepted standards of cost-effectiveness, a person with ocular hypertension must have a life expectancy of at least 18 years to justify treatment at the ≥ 2% annual risk of glaucoma threshold. At higher levels of risk, a life expectancy of 7–10 years is required.

Introduction

The effects of glaucoma on quality of life, visual function, and heath care costs have been widely documented.^1,2,3 Over 2 million people in the United States have been diagnosed with glaucoma, and it is predicted that over 3 million people in the U.S. will have the disease by 2020.⁴ Fortunately, multiple treatments for glaucoma and its risk factors exist and researchers have conducted cost-effectiveness analyses regarding those treatments. Investigators from the Ocular Hypertension Treatment Study (OHTS) reported that treatment of ocular hypertension was cost-effective when limited to those with a 2% or greater annual risk of glaucoma.⁵ Based upon the prevalence of risk factors in the OHTS, the investigators estimated that this represents nearly 1/3 of those with intraocular pressure (IOP) greater than 24 mm Hg.

The purpose of the original OHTS report on cost-effectiveness of treatment was to examine cost-effectiveness of treatment as a national policy. That is, do the benefits of treatment of ocular hypertension to prevent glaucoma outweigh the costs when treating all people in the U.S. with ocular hypertension, or a substantial subgroup? However, such analysis is limited as it does not consider the impact of individual patient characteristics on the treatment decision. It is probable that some subgroups of patients experience different benefits or costs when receiving treatment. For instance, an 80 year old patient in poor health will have a different perspective on treatment of ocular hypertension compared to a healthy 50 year old because of their differing life expectancy and the consequent risk of development of severe visual impairment. Research that properly implements cost-effectiveness models shows that when authors do account for differences between subgroups, the cost-effectiveness decision may vary substantially between those groups.^6,7

In this paper, we examine how the cost-effectiveness of treatment of ocular hypertension to prevent primary open-angle glaucoma (POAG) varies within subgroups defined by the age of the patient to be treated. We will examine cost-effectiveness in two ways. First, we will look at the cost-effectiveness of treatment of specific subgroups of people who are aged 45, 55, and 65 years at initiation of treatment. Second, we directly examine the influence of mortality on the cost-effectiveness of treatment by modeling specific life expectancy of people within the age cohorts.

Methods

We constructed a Markov decision model to compare the cost and effectiveness of treating ocular hypertension over a person’s remaining years of life. Parameters in the model included estimates of the risk of POAG (with the incidence of POAG defined in the same manner as in OHTS[cite Kass]) among those prescribed pressure lowering medication and those who were not, the probability of progression from early POAG to more severe disease, and estimates of the impact of POAG and blindness on quality of life. We defined the stages of POAG using the modified Hodapp-Anderson-Parish taxonomy employed by Lee et al (cite Lee) (see Figure 1) We considered the cost of medical treatment of ocular hypertension and POAG by stage of disease, and the cost of blindness. Variability in results was evaluated with one-way sensitivity analysis. We examined the influence of life-expectancy on cost-effectiveness by examining three ages at baseline: 45, 55, and 65 years of age.

Figure 1.

Diagram of the Markov model used to evaluate the effect of life expectancy on the cost-effectiveness of ocular hypertension treatment to prevent glaucoma. POAG indicates primary open-angle glaucoma.

This paper expands on our previous work by measuring the minimum number of years a member of an age-cohort needs to live in order for a particular treatment to be cost-effective.⁵ In our previous report, we assumed members of each age-cohort were exposed to age-specific death rates. This provides the average risk of mortality for a particular age-cohort and consequently the results from the model measure average cost-effectiveness for that group. However, those who have life-threatening chronic or acute illnesses have a life-expectancy that is less than the average, and therefore are exposed to less risk of progression, and accumulate less vision related costs. The overall cost-effectiveness estimate for the cohort would not be generalizable to people in this group. In other words, it may not be cost-effective to treat a person who has fewer than 10 years of life left, but it may be cost-effective to treat a person with a life-expectancy of more than 15 years.

We use a Markov model to describe the progression of a chronic disease process through a series of mathematical relationships.⁸ For instance, we begin with three hypothetical cohorts that represent each starting age. During the first year, a certain percentage of a cohort will progress to first stage glaucoma or die of other causes. During the next year (in this context each year is a “Markov cycle”) a certain percentage of the cohort die, a certain percentage of those with ocular hypertension progress to the first stage of glaucoma (joining those who progressed there during the first year), and a certain percentage of those who progressed to the first stage of glaucoma during the first year progress to the second stage of glaucoma. Estimation of the model continues in an iterative manner until the entire cohort has died of other causes (see Figure 2 for a graphic description of the model used in this report). The parameters in our model are described in Table 1 and were described in detail in our previous report, as well as the accompanying Technical Appendix (see https://vrcc.wustl.edu).

Figure 2.

Cost-effectiveness threshold for treatment by age and willingness-to-pay (WTP) threshold. POAG indicates primary open-angle glaucoma; QALY, quality-adjusted life year.

Table 1.

Staging Model for Primary Open-angle Glaucoma Used in Model^a

Stage	MD Score	Probability Plot, Pattern Deviation	Decibels Plot (Stages 2–4) or CPSD/PSD (Stage 1)	Decibels Plot (Stage 2–4) or Hemifield Test (Stage 1)
1, Early glaucoma	−0.01 to −6.00 (P<.05)	>3 Contiguous points <5% and >1 point <1%	CPSD/PSD significant at P<.05	Glaucoma hemifield test results outside normal limits
2, Moderate glaucoma	−6.01 to −12.00	19–36 Points <5% and 12–18 points <1%	>1 Point within central 5° with sensitivity <15 dB and 0 points within central 5° with sensitivity <0 dB	1 or 2 points with sensitivity <15 dB within 5° of fixation (only 1 in hemifield)
3, Advanced glaucoma	−12.01 to −20.00	37–55 Points <5% and 19–36 points <1%	Only 1 point within central 5° with sensitivity <0 dB	≥1 Point with sensitivity <15 dB within 5° of fixation in both hemifields
4, Severe glaucoma	≤−20.01	56–74 Points <5% and 37–74 points <1%	2–4 Points within central 5° with sensitivity <0 dB	2 Points with sensitivity <15 dB within 5° of fixation in both hemifields
5, End-stage glaucoma or blindness	No static threshold for perimetry in worse eye	Static threshold perimetry not possible owing to central scotoma in worse eye, or worse-eye visual acuity of ≤20/200 due to glaucoma; better eye may fall into any of the above stages

Abbreviations: CPSD, corrected pattern standard deviation; MD, mean deviation; PSD, pattern standard deviation.

^aFor each stage, the eye must have the given MD score and its accompanying probability plot or decibels plot (stages 2–4) or CPSD/PSD (stage 1) or decibels plot (stages 2–4) or hemifield test (stage 1).

In our previous report⁵, we examined four possible treatment thresholds: Treat no one until there is evidence of glaucoma-related nerve damage (Treat No One); Treat those with a ≥ 5% (Treat 5%) or a ≥ 2% (Treat 2%) annual risk of developing glaucoma; and Treat everyone with ocular hypertension (Treat all). We previously found the “Treat all” strategy was both more expensive and less effective than other treatment strategies (i.e., “dominated” in the language of ecoomics), we did not consider it for this report. However, we did consider two additional treatment thresholds: Treat those with a ≥ 4% (Treat 4%) or a ≥ (Treat 3%) annual risk of annual risk of developing glaucoma. Instead of calculating the incremental cost-effectiveness ratio (ICER) comparing each treatment option to the next least expensive one¹⁷, we constructed our ICER by comparing each treatment option to the “Treat no one” threshold. We did this because when incorporating life span into the decision to treat someone with ocular hypertension, the most logical alternative would be to “not treat”. To determine the number of years someone must live before treatment would be considered cost-effective, we eliminated annual mortality from the model, and sequentially tested different lifespans ranging from 1 to 54 additional years of life past their baseline age. This was done for each age cohort, with all other age-specific variables remaining unaffected. We report the minimum number of additional years of life past an individual’s baseline age that is needed to produce an ICER less than a standard willingness to pay (WTP).

An intervention is considered “cost-effective” if the value society places on a quality adjust life year (QALY) is greater than the resources required to “purchase” the QALY. This is based upon the “willingness to pay” (WTP) threshold, or the social value of the QALY. While some health economists argue the threshold should exceed $200,000¹⁸, most health economists recognize $100,000/QALY as the upper limit¹⁹. In this analysis we tested three WTP thresholds: $50,000, $75,000, and $100,000. In sensitivity analyses we only examine the standard of $75,000/QALY.

We conducted this evaluation according to the guidelines described by the Panel on Cost-Effectiveness in Health and Medicine.¹ We took a societal perspective by considering all relevant costs and benefits associated with the intervention whether they were borne by the person or society. All costs and benefits in the model were discounted at a 3% annual rate.¹ Statistical analyses were performed with SAS software (version 9.1; SAS® Institute INC, Cary, North Carolina, USA). Decision analyses were performed with TreeAge Pro 2007 software (Suite version release 1.1; TreeAge Software Inc, Williamsport, Massachusetts, USA).

Results

The minimum annual risk of POAG at which it is cost effective to treat ocular hypertension for each age-cohort is presented in Figure 2. This graph shows that in general, younger people are more likely to benefit from a more aggressive treatment strategy than are older people. For example, using a WTP of $50,000 it is cost effective to treat those with a 2% or greater annual risk of developing glaucoma for those age 45. However, using that same WTP, it is only cost effective to treat those over the age of 65 with a 4% or greater annual risk of developing glaucoma.

The minimum number of years needed to live in order for an intervention to be cost effective for each age-cohort is reported in Table 2 (While we present here the results of modeling for three ages---45, 55, and 65---it should be noted that examining other ages, particularly those older than 65 did not appreciably change the cost-effectiveness decision). The table shows that within a particular age-cohort, as the intervention becomes more restrictive and treats fewer people (i.e. only those with a higher annual risk of developing glaucoma), the minimum years of life needed for that intervention to be cost-effective decreases. That is, for those age 45 with 2% or higher annual risk of developing glaucoma, the individual must live for 18 years (at a WTP of $75,000) compared to only 7 years if the individual had a 5% or higher annual risk. Note also that there is considerable difference between age cohorts in the life expectancy that the person must have in order to justify treatment. For example, someone age 65 with a 2% annual risk of glaucoma must have a life expectancy of 21 to 26 years (depending on the WTP threshold chosen) for treatment to be cost-effective, while the someone age 45 must have a life expectancy of 17–21 years. For those with a 5% annual risk of developing glaucoma, the difference is even more extreme. These differences are driven by the increased proportion of people in the age cohort who fall under the treatment threshold as the age cohort becomes older.

Table 2.

Ranges of life-expectancy needed for intervention to be cost-effective conditional on age when starting treatment, percentage treated, and willingness to pay

	Willingness to pay
	$50,000	$75,000	$100,000
Age 45 - Treat 2%	21	18	17
Age 45 - Treat 3%	15	14	13
Age 45 - Treat 4%	11	9	8
Age 45 - Treat 5%	9	7	7
Age 55 - Treat 2%	24	21	20
Age 55 - Treat 3%	19	17	16
Age 55 - Treat 4%	18	16	15
Age 55 - Treat 5%	10	8	8
Age 65 - Treat 2%	26	23	21
Age 65 - Treat 3%	25	22	21
Age 65 - Treat 4%	23	21	19
Age 65 - Treat 5%	21	19	17

We performed multiple one-way sensitivity analyses to test the robustness of certain parameters in our model. Results are shown in Table 4. The range of utility values tested behaved as expected with the assumption of the least utility loss (0.0125) from POAG resulting in a need to live between 2 to 5 years more than those with the highest utility (0.05) to achieve cost-effectiveness. Those with the lowest rate of progression from stage 1 POAG to stage 2 POAG (0.01 per year) needed to live between 1 to 6 years longer than those with the highest rate of progression (0.1 per year). Those with the highest annual medicine costs ($1,000) needed to live anywhere from 6 to 16 years longer than those with the lowest annual medicine costs ($150). For certain combinations of risk and age, facing the highest annual increase in incidence rates (2.7%) did not change a person’s needed life expectancy to reach cost effectiveness when compared with the lowest annual increase in incidence rates (0.9%). However, using higher baseline ages or more restrictive treatment regimes required a person to live up to 20 years longer in order to reach cost effectiveness if they faced the highest annual increase in incidence rates compared to the lowest. However, with the exception of the utility and cost of medication results, the extremes tested here have little impact on the model.

Table 4.

Sensitivity analyses for ranges of life-expectancy needed for intervention to be cost-effective conditional on age when starting treatment and percentage treated. (Willingness to pay = $75,000)

	Base Case	Low Utility (0.0125)	High Utility (0.05)	Low POAG Progression Rate (0.01/year)	High POAG Progression Rate (0.1/year)	Low Annual Medicine Cost ($150)	High Annual Medicine Cost ($1,000)	Low Annual increase in Incidence (0.9%)	High Annual increase in Incidence (2.7%)
Age 45 - Treat 2%	18	20	16	22	17	14	26	18	18
Age 45 - Treat 3%	14	15	12	15	13	10	20	14	14
Age 45 - Treat 4%	9	10	8	10	9	7	14	9	9
Age 45 - Treat 5%	7	8	6	8	7	5	11	7	7
Age 55 - Treat 2%	21	23	19	25	19	16	31	21	23
Age 55 - Treat 3%	17	18	15	19	16	13	24	14	19
Age 55 - Treat 4%	16	17	14	18	15	13	22	12	22
Age 55 - Treat 5%	8	9	7	9	8	6	12	6	11
Age 65 - Treat 2%	23	25	20	27	21	18	34	21	25
Age 65 - Treat 3%	22	24	20	26	20	17	32	17	26
Age 65 - Treat 4%	21	22	19	23	19	17	29	16	36
Age 65 - Treat 5%	19	20	17	20	17	15	25	8	26

Discussion

In our previous report, we found that treatment of people with ocular hypertension (i.e., IOP ≥ 24 mm Hg in at least one eye) met accepted standards of cost-effectiveness when applied as a standard management strategy on a population basis. However, in our previous report we did not discuss the impact the patient’s non-vision related prognosis might have in recommending treatment to specific patients. In this report we have addressed that issue.

In general, we have found that regardless of the patient’s age or other risk factors for glaucoma, they must have a life expectancy of at least nine years (see Table 3) to meet the most stringent standards of cost-effectiveness (a willingness to pay of $50,000/QALY). Implementation of the ≥ 2% threshold as a standard of treatment as found in our earlier work² requires that the person have a life expectancy of 21 years if they are 45, or 24 years if they are 55, both of which are well within the life expectancy of the average person of that age.²¹. However, for someone over the age of 65, even those at the highest risk (i.e., 5% or greater) and using the most liberal standard of cost-effectiveness, there is not an age at which treatment of men of average health would be considered to be cost-effective (as their life expectancy would be less than 17 years). Treatment of women of average health would be cost-effective up to age 70, but again this would only be for those at the highest risk of disease and if the more liberal standard of cost-effectiveness is employed.

Table 3.

United States Life Table (2003)

Age	Average Years of Life Expectancy
	Males	Females
45–46	32.8	36.9
46–47	31.9	36.0
47–48	31.0	35.1
48–49	30.2	34.1
49–50	29.3	33.2
50–51	28.5	32.3
51–52	27.6	31.4
52–53	26.8	30.6
53–54	26.0	29.7
54–55	25.1	28.8
55–56	24.3	27.9
56–57	23.5	27.0
57–58	22.7	26.2
58–59	21.9	25.3
59–60	21.2	24.5
60–61	20.4	23.7
61–62	19.6	22.8
62–63	18.9	22.0
63–64	18.2	21.2
64–65	17.5	20.4
65–66	16.8	19.7
66–67	16.1	18.9
67–68	15.4	18.1
68–69	14.7	17.4
69–70	14.1	16.7
70–71	13.4	15.9
71–72	12.8	15.2
72–73	12.2	14.5
73–74	11.6	13.8
74–75	11.0	13.2
75–76	10.5	12.5
76–77	9.9	11.9
77–78	9.4	11.3
78–79	8.9	10.7
79–80	8.4	10.1

Information from the Center for Disease Control (CDC) National Vital Statistics Reports (Volume 54), Number 14.²¹

We previously reported that based upon the findings of the Baltimore Eye Study over 50% of all people with intraocular pressure over 24 mm Hg are over the age of 65.² There was a similar findings in the Beaver Dam Study (among a largely white population).³ Given that we based our previous model upon the distribution found in the Baltimore study, it might seem counterintuitive that we have found here that treatment would not be cost-effective among the older group. However, Figure 2 provides some direction concerning the resolution of this apparent contradiction. Note that for people age 45, it is cost-effective to treat people with a ≥ 2% risk of glaucoma, even at the most stringent WTP ($50,000/QALY). For people 55, it is cost-effective to treat people with a ≥ 2% risk, but only at higher levels of WTP (i.e., > $75,000), but for people who are 65 or older, the cost-effective threshold for treatment is a risk of ≥ 4% at a WTP of $50,000, and 3% at the higher levels of WTP.

Thus, the findings reported in Figure 2 confirm our previous report, but seem to be in conflict with our findings reported in Table 2. In the cohort modeled in Figure 2, participants left the cohort as they died each year. So, as the cohort aged the number of people treated and the total cost of treatment declined. There was less benefit required from treatment of the remaining cohort members in order to offset the cost of treatment. In contrast, in modeling to create Table 2, all cohort members lived their full lifespan (including all those being treated for ocular hypertension), thus more benefit was required per cohort member in order to offset the cost of treatment. This is the consequence of evaluating the cost-effectiveness of a population based guideline versus that for the treatment of an individual patient.

Many undoubtedly find it unethical to argue that it is not “cost-effective” to treat older people with ocular hypertension to prevent glaucoma. It is important to remember that weighing costs and benefits are but one component of a health care decision and the process of economic evaluation is radically neutral concerning other factors such as equity in distribution of health care resources or social and ethical values.⁴ Therefore, if a societal decision maker, including physicians and patients, feel that treatment of a person over the age of 65 is justified, they might choose to disregard the recommendations presented here and accept treatment based upon non-economic factors.

Recent reports have shown that in clinical practice that over-treatment of the elderly based upon non-clinical factors may not be the case. Boland et al recently reported the results of a survey of 58 glaucoma specialists asked to make treatment recommendations based on scenarios of patients with ocular hypertension. On average, before presentation of a risk estimate, the average threshold for treatment was 4.6%/year. After presentation of a risk estimate, the average threshold was 3.4% per year. Both of these thresholds are well above the 2% threshold previously recommended. Another finding was that the increased risk associated with age was not a significant predictor of physician treatment recommendations in the absence of the risk calculator. This is despite the fact that increased age results in an increased risk of developing glaucoma. On the other hand, this finding is consistent with the scenario in which clinicians recognize that older patients have less lifetime risk of significant vision loss and therefore do not recommend treatment at the same risk level they might use with younger patients. When the risk calculator was used, increasing age was predictive of a recommendation to treat although its role was still not as significant as suggested by the OHTS results. (CITE Gordon et al. Arch. Ophthalmol. 2002 120(6):714–20) The same glaucoma specialists were also asked how many patients with ocular hypertension they would treat to prevent one of them from developing glaucoma. This self-reported number needed to treat was significantly higher when the question specified patients from 40–50 years old versus when it specified patients 70–80 years old, again indicating that clinicians probably already recognize the paradoxical role of age in ocular hypertension.

Risk calculators do not consider patients attitudes towards disease when creating a treatment recommendation. However, note that in the results of our sensitivity analysis we found that utility loss associated with progression to the first stage of POAG was an important factor for determining cost-effectiveness. Utility is representative of the person’s attitude towards disease and its consequences, and therefore, may provide direction in recommending treatment of people for whom treatment might have marginal cost-effectiveness. For instance, if treatment of an older person with moderate risk of progression to POAG was being considered, our sensitivity analysis indicate that it is important for the clinician to understand the patient’s attitudes and knowledge of the risks and consequences of her/his disease. If the clinician learns that the patient’s view of his/her prognosis is unrealistically severe, careful education concerning the risks associated with ocular hypertension might be a more effective approach than medication. On the other hand, if the patient has a realistic understanding of the risks and consequences of the disease, but has a highly risk adverse attitude towards visual impairment, they might benefit from treatment (due to larger than average utility loss) in spite of a lifespan that is less than that which would indicate cost-effectiveness.

Limitations

Results in the model may be biased to the extent that we have incomplete knowledge of the parameters or distributions used to calibrate the model. However, this should not be a large concern since the results of the model were robust to a large range of parameters as tested through sensitivity analysis. An additional problem is our results represent the cost-effectiveness related to treatment for particular age subgroups. Since we have found differences in the cost-effectiveness based on a person’s age, it is possible that differences in cost-effectiveness will exist for other sub-groups such as gender or race. It is unclear how those characteristics may influence the progression of disease or other factors influencing cost-effectiveness and our results still represent the cost-effectiveness of a person with the average characteristics (i.e. race or gender distributions or distributions of other characteristics) of each age sub-group.

Conclusion

Previous work from the OHTS showed that on average, treatment of people with ocular hypertension and a ≥ 2% risk of progression to glaucoma met commonly accepted standards of cost-effectiveness. Here we have found that where the person’s life expectancy was taken into consideration, the ≥ 2% threshold was cost-effective only where the person has a life expectancy of over 20 years for the most stringent standard of cost-effectiveness and for people age 40–49. Treatment of those who are in their 50s requires a life expectancy of 24 years, or acceptance of a more liberal standard of cost-effectiveness. Treatment of people who are over the age of 65 could not be justified on economic grounds for men, and only for women at the greatest risk of progression to glaucoma. However, the patient’s attitude towards treatment and disease progression remains an important factor in determining cost-effectiveness of treatment, independent of life expectancy.