COST-BENEFIT ANALYSIS OF FLUORIDATION IN HOUSTON, TEXAS

88 Journal of Public Health Dentistry

COST-BENEFIT ANALYSIS OF FLUORIDATION IN HOUSTON, TEXAS

William Nelson, PhD, and J. Michael Swint, PhD’

Recently there has been considerable interest in applying cost-benefit analysis (CBA) to the delivery of dental s e r v i c e ~ P ~ ~ ~ ~ J ~ Davies’ has summarized several studies which show that a lifetime’s exposure to fluoridation may reduce DMF teeth by 30-80 percent and def teeth by 17-78 percent, depending on the place and child’s age. However, in view of the public resistance to fluoridation, an analysis of the financial benefits may prove a convincing selling point for worthwhile programs. Several such analyses have been at- tempted. Typically such studies have measured the benefits of fluoridation by either (1) using indices of dental health (e.g., DMFT and deft) to determine the reduction in the need for dental services‘ or (2) directly measuring the reduction in dental services attributable to fluoridation.7J0 These benefits are then priced and compared with the costs of fluoridation. Unfortunately, none of the analyses which could be found in the dental literature have given adequate consideration to the time valuation of the benefits and costs and thus have improperly determined their value-that is, the costs and benefits of a fluoridation program will occur in different magnitudes over varying time periods. For example, it is generally accepted that a fluoridation program will prevent more carious lesions in the tenth year than the first. As will be seen, both costs and benefits are worth less if they occur in the future. And if, as suggested Boggs4 and by Grainger,12 the cost- benefit technic is to be useful in public health dentistry, it is particularly important that the early applications use it in a technically sound manner lest other users be led astray.

In this paper an attempt will be made to show how time may be explicitly brought into the analysis. Also, unlike most fluoridation studies, in which analyses have been performed retrospectively on fluoridated cities, a prospective cost-benefit analysis (CBA) of an unfluoridated city, Houston, Texas will be performed. Naturally, a prospective study is more useful for public policy purposes as it informs decision-makers of the proposed project’s effectiveness before their decision has been made-that is, to predict the impact of fluoridation on an unfluoridated city. Doherty and Powellg statistically estimated the relation between age and dental costs and the cost differential attributable to fluoridation in New Britain, Connecticut (again, they too neglect the time valuation of the costs and benefits). Perhaps this approach can be refined to predict the benefits of fluoridation without expensive clinical trials by isolating the relevant and easily attainable variables (e.g., sex, age, and income). Upton and Sil~erman’~ have estimated the effects of fluoridation on the demand for various dental services for 15 midwestern towns. Still it is not clear how these results may be applied to other cities. Thus the results of past studies on the effects of fluoridation were applied to Houston.

The Need for Cost-Benefit Analysis (CBA) Whereas this article is not the place to discuss the role of government in the market-

place, it is useful to ponder why fluoridation most likely will not be provided by the private sector. Perhaps it is because fluoridation has the characteristics of what econo- mists call “a public good.” A public good possesses two characteristics. First, if the good is produced there is usually no additional cost in allowing additional individuals to consume it. Second, it would be difficult to exclude additional consumers. In the instance

ODepartment of Finance, The Cleveland State University, Cleveland, Ohio 44118, and Department of Economics and Business, Western Washington State College, Bellingham, Washington 9822.5, respectively. The authors gratefully acknowledge the University of Texas Health Science Center at Houston, School of Public Health, for support of earlier research.

Vol. 36, No. %Spring Issue, 1976 89

of a water fluoridation system, because it would be in each individual’s self-interest to avoid paying while accepting the benefits, there would be no way of preventing a given consumer from accepting the benefits if he did not want to pay. Thus, a private firm would find it difficult to ascertain consumer preferences that would normally be mani- fested in the market and probably would be unwilling to provide the service. If the service is to be provided, the government will probably have to do it.

CBA is an analytical tool designed to help government decision-makers decide whether the service is indeed worth providing. In the private sector a service will be provided if its revenues exceed its costs, i.e., it is profitable. In the public sector, CBA argues that an analogous criterion should be used. CBA attempts to compare all the costs and benefits of providing a service. If the benefits exceed the costs, the CBA criteria suggest it should be provided.

However, the benefits and costs are considered more broadly than in the private sector. In the private sector the only benefits or costs considered are those accruing to the firm, whereas in the public sector any benefit or cost is considered no matter to whom it accrues. Hence, CBA is often referred to as “social profitability analysis.”

Background Until 1970 the majority of Houston’s water supply was derived from wells with vary-

ing fluoride concentrations. However, problems with falling water tables have caused increasing dependence on surface water from Lake Houston, a source with virtually no fluoride. Thus this analysis of the impact of fluoridating Houston’s water supplies will be restricted to that portion of the city served by Lake Houston (this area includes ap- proximately 40 percent of the city’s children). The technic used here could in principle also be used to perform a CBA on fluoridating each individual well; however, this approach would add many repetitious calculations and many of the data would be difficult to derive.

Program Costs

The cost data shown in Table 1 are derived from a preliminary study” by Williams of the costs of fluoridation for Houston. The study assumed that all wells and surface waters would be fluoridated. With the Williams’ assistance the report was adjusted to reflect only the costs of fluoridating the surface water and brought the cost figures in line with 1975 prices. It was assumed that an additional plant would be built in five years (the earliest possible date) causing labor and maintenance costs to double, but not to change for the rest of the project’s life. While it is not known with certainty how long the equipment would last, 20 years is thought to be a reasonable estimate. Chemical costs are expected to rise with increasing water consumption and thus are adjusted every five years.

In an effort to simplify the calculations, both benefits and costs are assumed to accrue at the end of the year (this assumption will cause little loss in accuracy). For example, capital costs will accrue at the beginning of the year as they must be met on the first day of the year. Thus, in Table 1 the capital costs are shown in year 0 and year 4 (not years 1 and 5) .

Program Benefits The calculation of the benefits was hampered by the lack of solid epidemiologic

data for Houston. Ideally one wants to know the dental needs of Houston children in the unfluoridated portion of town (e.g., the number of one-surface amalgams, two-or- more-surface amalgams, and extractions). Then the savings in dental services attributable to fluoridation in the Denby-Hollis: Ast et. a1.,3 or other studies, could be applied to


find dental services saved. This reduction would then be multiplied by the relevant prices of the dental services to find the value of the benefits. This information apparently does not exist for Houston. Thus perforce DMF rates found by Friedman” for a sample of 1011 Catholic parochial students in the age group 6-13 were used. The water supply of the sample population has fluoride in varying amounts; however, the manner in which the benefits of fluoridation are calculated will intentionally bias the estimate of the benefits downward in an effort not to “ovcrsell” the case for fluoridation.

TABLE 1 Costs of Fluoridation

Personnel/ Chemical Total Year Capital Maintenance costs cost

0 $100,000 $100,000 1 $115,000 $34,000 149,000 2 115,000 34,000 149,000 3 115,000 34,000 149,000

5 230,000 47,600 276,000 6 2330,000 47,600 276,000 7 230,000 47,600 276,000 8 230,000 47,600 276,000 9 230,000 47,600 276,000

10 230,000 47,600 276,000 11 230,000 61,300 291,300 12 230,000 61,300 291,300 13 230,000 61,300 291,300 14 230,000 61,300 291,300 15 230,000 61,300 291,300 16 230,000 75,000 305,000 17 230,000 75,000 305,000 18 230,000 75,000 305,000 19 230,000 75,000 305,000 20 230,000 75,000 305,000

4 $100,000 115,000 34,000 249,000

As the full effects of fluoridation do not apply immediately, it is necessary to estimate the time pattern of the benefits. It is assumed that after 10 years most of the impact of fluoridation will be felt. To do so the reduction in the increment in DMF and hence the average increase in carious permanent teeth attributable to fluoridation in the Grand Rapids studyZ will be calculated. The method used to calculate the incremental DMF was described by D a ~ i e s : ~

. . . taking the mean number of DMF teeth for children aged 7 years in say, 1946, and aged 6 in 1946. The result is the expected average increase in carious permanent teeth in children aged 6 in 1946. In Table 2 the incremental DMF rate for the base year and the tenth year of the

Grand Rapids study for ages 6-13 are shown in columns 1 and 2, respectively. Column 3 shows the percent reduction in DMFT attributable to fluoride for the last 10 years of the program. It is this percentage, not the absolute amount, which is applied to the Houston data. Column 4 shows the incremental DMF rates for Houston as calculated from the Friedman” study. Column 5 shows the expected reduction in carious teeth in

Vol. 36, No. 2-Spring Issue, 1976 91

Houston; this is found by multiplying the baseline data column 4 by the percent in column 3.' Tables 3 and 4 give the same information for the first nine years of fluoridation and are calculated in a manner similar to the calculations for Table 2.

Four population forecasts for the years 1-4, 5-9, 10-14, and 15-20 of the program for each age group were prepared permitting estimation of the total caries reduced by fluoridation in each year (as shown in Table 5 ) . These benefits were valued at $12 per restoration, the price paid by welfare under Title XIX.

There are several sources of downward bias in the estimate of the benefits. First, since the baseline data include some members of the population ingesting fluoride in varying amounts, the baseline estimate of the expected increase in carious teeth was biased downward. Since the benefits attributed to fluoridation were a percentage of this estimate, it too is biased downward. Second, no credit was given to fluoridation for re- ducing extractions and multisurf ace amalgams-both of which are more expensive than single amalgams. Third, the intangible (or unmeasurable) benefits have been intentionally omitted. For example, by preventing the need for dental services, considerable pain, travel, and waiting time are avoided. Further, an undamaged tooth is presumably more desirable than a filled tooth. The most serious downward bias arises because it was not possible to calculate the saving for primary teeth. While def data are available (and the effect of fluoridation on def rates is known) annual increments cannot be calculated because of, as Davies7 notes: ". . . the unknown number of deciduous teeth which are exfoliated each year and because the status of exfoliated teeth is unknown.': A final source of bias is that limitations of data only allowed consideration of children age 6-13, whereas children as old as 16 will benefit, and adults too may benefit.

There are three sources of upward bias in these estimates. They are not, however, likely to outweigh the aforementioned downward biases. Because all cavities are not filled, it seems that consumers value the services at less than the market price but not necessarily a zero price. There is likely a price greater than zero but less than the market price at which a consumer will choose to have the cavity filled. It is this price, rather than the market price, that represents the true value of the filling to society. But this discussion assumes that consumers know the benefits from filling a cavity and consciously neglect to have it filled. However, the dental market is characterized by imperfect consumer information. It is not clear whether the appropriate price would rise or fall if consumers had perfect knowledge. Second, it is assumed that all children are con- tinuous residents and would either be permanently exposed to or denied fluoridation. To the extent some children migrate in from fluoridated communities, estimates are

'A referee suggested that it is improper to apply the percentage reduction found in Grand Rapids to the expected reduction for Houston. Table 2 shows that the prefluorida- tion increment in Houston is much less than in Grand Rapids and that where lower absolute increments are found, lower percentage reductions are found with fluoridation. In the absence of fluoridation increments comparable to Houston's that an additional 50 percent reduction in the expected decrease in caries (Table 2, column 5) would be appropriate. Although this suggestion has merit, we did not follow it. As we argue, the baseline data include people ingesting fluoride in varying amounts averaging about 0.5 ppm. Thus, the Houston's prefluoride increment is biased downwards. Thus, some of the force of this criticism is attenuated. However, the effects of fluoridation upon the current residents of the city are probably low; fluoridated well water has been declining since 1970 (when the sample was taken). Lenke et al.I3 found for Antigo, Wisconsin that four years after fluoridation stopped, DMF rates were again comparable to those of nonfluoridated areas in Wisconsin. If, nevertheless, the reader feels a 50 percent reduction is warranted, then this would simply reduce the number of cavities prevented by fluoridation and hence, present value of the benefits by 50 percent and reduce the benefit-cost ratio to 0.75. Still, this need not mean the project is not cost-effective because there are other factors to be discussed shortly that seriously bias our results downward.


biased upwards. Lastly, account has not been taken of the costs a fluoridation program inflicts upon those who believe fluoridation is harmful. Even if this belief is mistaken, an intangible social cost is incurred and should be taken into account.

TABLE 2 Derivation of the Reduction in Cavities in Permanent Teeth

After 10 Years of Fluoridation

(1)" (2) (3) =

Annual Increment Annual DMFT Increment Percent Reduction in

in Grand Rapids in Grand Rapids in Grand Rapids

DMFT

Before Fluoridation After 10 Years Fluroidation DMFT Due to Fluoridation

Age 6 .78 .19 7 1.11 .50 8 1.06 .58 9 1.05 .70

10 1.02 .37 11 1.49 .64 12 1.66 .89 13 1.66 1.18

(4Id ( 5 ) DMFT

76 55 45 33 64 57 46 29

Annual Increment Before Fluoridation in Houston

Expected Reduction in Cavities in Permanent Teeth Attributed to Fluoridation in Houston

Age 6 .46 7 .26 8 .61 9 .39

10 .25 11 .22 12 .80

.35

.14

.27 a - Derived from Davies7

.13

.16

.13

.37

b - Derived from Arnold, et aL2 c - (3) = (1) - (-2) / (1) d - Derived from Friedmang e - (4) x (3)

Time Valuation of Costs and Benefits With the monetary value of benefits and costs arrayed for each year, it is necessary

to convert them by a common denominator adjustment for comparison. To see this point, simply consider whether one would prefer one dollar now or 10 years from now. Obviously one prefers the dollar now as one could invest it for 10 years and have more than the dollar. As such, benefits and costs accruing in different periods must be adjusted by some procedure for a common denominator comparison. Neglecting this procedure in the case of a fluoridation program leads to an overstatement of the benefits. To avoid this error, it is necessary to compare them at one given time period. The


present time period is chosen for obvious convenience and future costs and benefits are discounted to their present value by use of the social discount rate.'

Decision There are two decision rules that will be applied-the net present value rule

(NPV) and the benefit-cost ratio. In the present case (though not in all situations) the rules yield the same results."

TABLE 3 Percent Reduction in DMF Teeth in First Nine Years

of Fluoridation in Grand Rapids

Years of Fluoridation

1 2 3 4 5 6 7 8 9

Age 5-6 6-7 7-8 8-9 9-10

10-11 11-12 12-13 26

71 21

58 29 64

22

-

-

53 67 35 30

52 65 57 18 49" 46

13 99

- -

- -

51 66

70

2A

34

-

-

-

67 - 31 48 30 38 42 56 23 13 20 50

93 57 - -

- - 43 - 50 60 32 43 48 52 07 01 50 78

aDavies7 second method used to avoid result of 100 'No observations

TABLE 4 Expected Reduction in DMF Teeth in Houston

for the First Nine Years

Years of Fluoridation

1 2 3 4 5 6 7 8 9

Age 6 7 8 9

10 11 12 13 -

.13 .33 .05 0

0 - a .23

.07

.14

.17 .16

0

0

(I -

.24

.09

.20

.14

.ll

.09

-

-

.31

.08

.29

.05

.lo

.72

-

-

.23

.17 -

.27

,563

2.5

-

-

.31

.08

.18

.16

.06

.04

.68 -

No observations Derived from Table 1, Table 3, and Arnold, et a1.2

- - .12 - 2.3 .26 .22 .20 .03 .08 .ll .ll - .06 .42 .37

- .23 .ll .11 .01 .57

*The present value of the benefits (costs) is what an investor would pay now to receive (avoid) the benefits (costs) as they are scheduled to accrue.

"'The rules are discussed thoroughly in Weston and Brigham.lB


TABLE 5 Expected No. of Permanent Cavities and Their Value Saved by Fluoridation for

Each Year of the Program

Year 1 2 3 4 5 6 Cavities 4,297 14,279 12,771 22,459 21,230 30,682 Dollars $51,573.00 171,348.00 153,257.28 269,509.00 254,769.00 368,194.00

Year 7 8 9 10 11-15 16-20 Cavities 31,033 32,952 46,954 43,956 51,136 64,140 Dollars $372,404.00 395,424.00 563,448.84 527,476.00 613,632.00 769,880.00

The NPV rule entailed finding the difference between the present value of the benefits and costs. Mechanically this is done by multiplying the benefits (costs) in each

where i is the social rate of discount, assumed to be 10 percent here, and Year by n is the year. This is then summed for all years, yielding the present value of the benefits (costs). The present value of the costs is then subtracted from the benefits. If this difference is positive, one may, roughly speaking, say the investment is socially profitable and the project is acceptable by the cost-benefit criterion; whereas, if it is negative, the project is unacceptable by the cost-benefit criterion.’

Unfortunately, precise empirical determination of the social rate of discount is not possible; i.e., while the topic has been an object of many sophisticated theoretical analyses,I4 the practical determination of this rate(s) appears to be unresolvable. Thus we are forced to choose a rate(s) somewhat arbitrarily, but not without some justifiable basis. In Prest and Turvey14 (p. 699-700) there is a discussion of the practical basis for choosing four percent (the cost of government borrowing) or 10 percent (the approximate, before tax, observed yield on corporate stocks); however, practically speaking, choosing between these is somewhat analogous to “trying to unscramble an omelette, and no one has yet invented a uniquely superior way of doing this.”’4

In this study a 10 percent discount rate is used because if fluoridation meets the criterion even at this high rate, a fortiori it also will at four percent. As such, using a 10 percent discount rate, calculations revealed that the present value of the benefits of fluoridating a segment of Houston’s water supply is equal to $3,267,164 and the present value of the costs is $2,164,1!34-yielding a “social profit” of $1,102,970. The benefit- cost ratio is simply the ratio of the present value of the benefits ($3,261,164) to the present value of the costs ($2,164,194). In this analysis it is 1.51. This ratio means for every $1.00 spent today there are benefits worth $1.51 today. If this ratio exceeds one, the project is acceptable on the cost-benefit criterion.

To underscore the impact of discounting, one should examine how the analysis would have been conducted without it. Typically a calculation is made for the ratio of the benefits in a year when all the benefits of fluoridation accrue to the “annual” costs (the capital costs are annualized and added to the operating costs). Thus in the Houston example, the ratio of the benefits in year 10, $527,476 to the costs, $zsS,OOO ($276,000 and $10,000), results in a ratio of 2.15, which is considerably higher than the benefit-cost ratio found with discounting. To be sure, Davies’ and otherse often consider more than one year, but nevertheless fail to incorporate the benefits of a lifetime’s exposure to fluoride for each year. Clearly, the failure to discount causes the analyst to give too much

I

‘By itself, either finding of course does not mean the project should or should not be undertaken as noneconomic factors must be considered as well. CBA provides economic information that must be combined with distributional, sociopolitical, humanitarian and other information by the decision- maker. In other words, CBA is only one input in the decision-making process.


weight to future periods. Since benefits rise more rapidly than costs, the effect is to over- state the benefit-cost ratio and the net present value. The higher the discount rate utilized, the larger this bias will be.

Summary and Conclusions

Most previous cost-benefit analyses of fluoridation programs have been retrospective in approach and have biased their results in favor of fluoridation. This study performed a prospective cost-benefit analysis of fluoridating a segment of the water supply for Houston, Texas, and explicitly introduced and evaluated the time pattern of the costs and benefits. It was shown that neglect of the time structure of the costs and benefits would significantly bias the results.

A benefit-cost ratio of 1.51 and a net present value (or “social profit”) of $1,102,970 were found. The results are biased downwards and should be considered a lower bound. Thus the results indicate an investment in a fluoridation program by Houston would be a socially profitable one.

References

1. Arnold, F.A. Grand Rapids fluoridation study-results pertaining to the eleventh year of fluoridation. Am. J. Pub. Health, 47:539-45, May 1957.

2. Arnold, F.A., et al. Effect of fluoridated public water supplies on dental caries prevalence: tenth year of the Grand Rapids-Muskegon study. Pub. Health Rep., 71652-8, July 1956.

3. Ast, D.B., et al. Time and cost factors to provide regular, periodic dental care for children in fluoridated and nonfluoridated areas: final report. Am. Dent. A. J., 80:770-6, Apr. 1970.

4. Boggs, D.C. Applying the techniques of cost effectiveness to the delivery of dental service. J. Pub. Health Dent., 33222-37, Fall 1973.

5. Brown, H.K., and Poplove, Myron. Bratford-Sarnia-Stratford fluoridation caries study: final study, 1963. Canad. Dent. A. J., 31505-11, Aug. 1965.

6. Cuzacq, Genevieve, and Glass, R.L. The projected financial savings in dental restorative treat- ment: the result of consuming fluoridated water. J. Pub. Health Dent., 32:52-7, Winter 1972.

7. Davies, G.N. Cost and benefit of fluoride in the prevention of dental caries. ISBN 92 4

8. Denby, G.C., and Hollis, M.J. The effect of fluoridation on dental public health programs. N.Z.

9. Doherty, Neville, and Powell, Elbert. Effects of age and years exposure on the economic bene-

10. Douglas, B.L., et al. Impact of water fluoridation on dental practice and dental manpower. Am.

11. Friedman, L.A., et al. Dental survey of Houston Catholic parochial school children. Tex. Dent.

12. Grainger, R.M. Cost-benefit analysis: application to dental services. Canad. Dent. A. J., 39:693-9,

13. Lemke, C.W., et al. Controlled fluoridation: the dental effects of discontinuation in Antigo,

14. Prest, A.R., and Turvey, R. Cost-benefit analysis: a survey. Econ. J., 75:683-735, Dec. 1965. 15. Upton, C., and Silverman, R.‘The demand for dental services. J. Hum. Resources, 7:250-61,

16. Weston, F., and Brigham, E. Managerial finance. New York, Holt, Rinehart, and Winston, 1972. 17. Williams, W. Preliminary report: Cost of fluoridation of the public water supply, city of Hous-

170009 2, Geneva, World Health Organization, c1974. 91 p.

Dent. J., 62:32-6, Jan. 1966.

fits of fluoridation. J. Dent. Res., 53:912-4, Aug. 1974.

Dent. A. J., 84355-67, Feb. 1972.

J., 89:16-21, Nov. 1971.

Oct. 1973.

Wisconsin. Am. Dent. A. J., 80:782-6, Apr. 1970.

Spring 1972.

ton, Texas. July 1972.

Did You Note That . . .?

Jay Friedman says, “ ... our interest . . . is not to spend less on dental care, but to ensure that the money spent is spread as far as possible for everyone . . . That is the true meaning of PSROs in dentistry, to assure the quality of care for the entire population.”

-American Journal of Public Health for December, 1975. (KAE)

COST-BENEFIT ANALYSIS OF FLUORIDATION IN HOUSTON, TEXAS

Documents

Transcript of COST-BENEFIT ANALYSIS OF FLUORIDATION IN HOUSTON, TEXAS