the demand for episodes of mental health emmett b....

Journal of Hea!th E ronomics 7 (1988) 369-392. North-Holland

THE DEMAND FOR EPISODES OF MENTAL HEALTH SERVICES*

Emmett B. KEELER, Willard G. MANNING and Kenneth B. WELLS The RAND Corporation, Santa Monica, CA 90406, USA

Received October 1987, final version received March I988

Observational studies of demand for mental health services showed much greater use by those with more generous insurance, but this difference may have been due to adverse selection, rather than in response to price. This paper avoids the adverse selection problem by using data from a randomized trial, the RAND Health Insurance Experiment (HIE). Participating families were randomly assigned to insurance plans that either provided free care or were a mixture of fmt dollar coinsurance and free care after a cap on out-of-pocket sperrding was reached. We estimate the separate effects of coinsurance and the cap on the demand for episodes of outpatient mental health services. We find that outpatient mental health use is more responsive to price than is outpatient medical use, but not as responsive as most observational studies have indicated. Those with no insurance coverage would spend about one-quarter as much on mental health care as they would with free care. Coinsurance reduces the number of episodes of treatment, but has only a small effect on the duration and intensity of use within episodes. Users appear to anticipate exceeding the cap, and spend at more than the free rate after i&y do se.

1. Introduction

Outpatient mental health services are typically not covered as well as medical services [Blostin (1987)]. Employers and unions who provide mental health benefits have found that such services are highly responsive to cost sharing and that extensive coverage may lead to mental health expenditures becoming an unacceptably high proportion of all health expenditures. Many private insurance carriers have reduced coverage, and reductions have been considered for Medicaid and Medicare [Pardes and Pincus (1983)]. On the other hand, the proportion of the population with some coverage is increasing; indeed some mental health coverage is now available to most people.

*This work was financed by a Grant no. 3 ROl MH39571-0 from the National Institute of Mental Health. We are indebted to Paul Widem, project oflicer and Carl Taube of NIMH, for advice and support. This work builds on earlier work on the RAND Health Insurance Experiment done with colleagues Naihua Duan, John Rolph, Daniel Relles, William Rogers and Joseph Newhouse. We benefited from comments by Randy Ellis, Howard Goldman, Deborah Haas-Wilson, Susan Marquis, Thomas McGuire, Barbara Burns, Richard Schemer and two anonymous referees, and by expert statistical advice from Nick Jewell. We also thank Janet Hanley and David Rumpel for help with data processing.

0167-6296/88/$3.50 0 1988, Elsevier Science Publishers B.V. (North-Holland)

370 E.B. Kceier et al,, Demand for episodes of mental health services

If the demand for’ mental health services is more responsive to price than the demand for medical services, then everything equal, the welfare losses due to overuse (moral hazard) provide an economic justification for insuring them less generously than medical services. [Pauly (1968), Baumol and Bradford (1970)]. Data from the HIE show the price elasticity of demand for medical services is only about -0.2. How does the demand for mental health services compare?

Observational studies in the literature have concluded that demand for mental health services is quite responsive to price [Frank and McGuire (1986)]. There was a four to one ratio in mental health spending between the high and low option federal employee plans [Reed (1974), Hustead and Scharfstein (1978)], which differ only slightly in their deductibles and coinsurance rates. McGuire’s (1981) study of patients of office-based psychia- trists showed an elasticity of - 1.0. Ellis (1986) estimated elasticities of around -0.4 for cmndin@ per user as a function of predicted end of year 'r-------o r--

price. Elasticities of spending per user have been reported from two national surveys; Taube, Kessler and Burns (1986) used average out-of-pocket price in NMCUES to derive an elasticity of -0.54. Horgan’s (1986) study of use in NMCES led to an elasticity of -0.44.

The possibility of adverse selection prevents these studies from resolving whether the demand for outpatient mental health services is more responsive to varying insurance coverage than is the demand for medical services. In most studies, the insurance policies of the population studied have been self- selected, making it impossible to discern whether the observed greater use of mental health services is due to the effects of better insurance coverage on the demand for care, or whether people with poorer mental health status or a higher propensity to use mental health services selected better coverage to reduce their expected financial burden.

The RAND Health Insurance Experiment (HIE) was a randomized social experiment of the effect of cost sharing on the demand for health services and on the health status of nonaged individuals. The HIE randomly assigned health insurance coverage to families to avoid the problem of self-selection of insurance coverage that has plagued other studies. In earlier analyses of HIE data, we concluded that demand for ambulatory mental health services was not much more responsive to plans as a whole than demand for ambulatory medical services.1

This result was in sharp contrast to most others in the literature, and Ellis and McGuire (1984) hypothesized that the HIE plans’ cap on out-of-pocket spending (the maximum dollar expenditure, or MDE) might be responsible. They argued that the MDE caused the initial coinsurance rate on HIE plans

‘Spending on the least generous (95 percent coinsurance) plan was about 58 percent the free- plan rate for outpatient medical services and 43 percent the free-plan rate for outpatient mental health services [Wells et al. (1982), Manning et al. (1986)].

E.B. Keeler et al., Demand for episodes of mental health services 371

to be a poor proxy for generosity of plans, and that our results were not inconsistent with the earlier findings of highly responsive demand for mental health services.2

Here we present research on episodes of outpatient mental health treatment undertaken to resolve this issue. We look at decisions within the year to separate the effects of coinsurance from the effects of the upper limit on spending. Our goal is an estimate of the effects of ‘price’ as represented in hypothetical pure coinsurance plans with no upper limits, i.e., plans that give consumers a constant marginal price for care. After presenting the results on demand, we conclude with some discussion of mental health insurance issues.

In a companion paper, we present the theory of how people might respond to prices that change with how much care has been bought, our methods for organizing care into episodes, and our methods for using them to estimate demand [Keeler and Rolph (1988)].3 The material in that paper up to the results in section 4 is a prerequisite for understanding this paper. The focus here is not on methods, but is simply empirical: how elastic is the demand for ambulatory mental health services?

2. Data and methods

Keeler and Rolph (1988) describe the sample, data, variables and methods used in the analysis of episodes of medical services. The data and methods used for episodes of mental health services are similar, and we only note differences.4

Each HIE plan has a coinsurance rate (varying from 0 to 95 percent), an upper limit on out-of-pocket expense (beyond which care is free) called the maximum dollar expenditure (MDE), and a limit of 52 psychotherapy visits per year (additional visits are paid in full by the patient). We group the insurance plans by their initial (first dollar) mental health coinsurance rate. Thus, the 490 people on the plan with 25 percent coverage of medical services and 50 percent coverage of mental and dental services are included with the 383 people on the plans with 50 percent coverage of all services in a 50 percent coverage mental health plan.

The sample is the same as in Keeler and Rolph (1988), except that here we

21ndeed, fam’l’e I 1 s on the cost sharing plans that used mental health care in a year had a 65 percent chance of exceeding the MDE (as opposed to a 29-percent chance for families with no use), so use of services when care is free because the MDE has been exceeded could be important [Keeler et al. (1986)].

The theory is needed because the cap on out-of-pocket spending found in HIE plans causes the nominal marginal price to change within the year if the MDE threshold is met. It is difficult to specify ‘price’ in analyzing use from such plans. The theory can also be applied to deductibles and limits on coverage, which are commonly found in insurance for mental health services as further constraints on use [Ellis (1986)].

4The mental health data and methods are fully described in Keeler et al. (1986).

372 E.B. Keeler et al., Demand for episodes of mental health services

exclude babies born or adopted into the study. We include three years of data on all participants where possible, but sample loss over time leads to 16,429 person-years in all.

Our methods for gathering data are aimed at a general population. We use a household sample, and rely on study participants for some information. The sample excludes those with very high income, the military and their dependents, the elderly, those eligible for Medicare because of disability, the homeless and those institutionalized in long-term hospitals and jails. The homeless were excluded because our sample is from dwelling units. The institutionalized were excluded because many have care provided directly. The others were excluded because they have special arrangements for health care financing. However, some of the heaviest users of mental health services, in particular, many of the chronically severely mentally ill are in these excluded groups?

We include sociodemographic variables, measures of mental and physical health, health habits, and other characteristics as explanatory variables. These data were collected prospectively. For details of data collection and other aspects of study design, see Manning et al. (1987).

2.1. Episodes of ambulatory mental health treatment

We have limited our analysis to expenditures for formal mental health services delivered by a mental health specialist (psychiatrist, psychologist, psychiatric social worker, or other mental health provider), or other physician in an ambulatory setting. These expenditures couid be for psychotherapy or evaluation visits, psychological testing, or for psychotropic drugs. They were identified by methods given in Keeler et al. (1986) from claims filed.

Psychiatric inpatient care was excluded. We could not analyze psychiatric inpatient use in detail because there were only 116 psychiatric hospitalizations in the entire study; many of these were for medical treatment of alcohol and other substance abuse. Psychiatric hospitalization rates on the cost- sharing plans were about two-thirds the rate on the free plan, but this difference was not statistically significant. It is plausible that the price responsiveness of psychiatric hospitalizations is no less than of other kinds of hospitalizations, but our sample is too small to tell.

Our definition of mental health services is largely (but not entirely) equivalent tc a focus on care delivered by mental health specialists.6

As explained in Keeler and Rolph (1988), we organize use of services into

50nly 0.2 percent of the sample reached the 52 visit limit each year; a small fraction of the 4.5 percent who used some formal outpatient mental health care [Wells et al. (1982)].

60ver 95 percent 0 [Wells et al. (1982)].

f costs for formal services are attributable to mental health specialists

E.B. Keeler et al., Demand for episodes of mental health sewices 373

episodes to look within the year at spending decisions. Outpatient mental health treatment episodes were formed by collecting visits that were not too far apart and tying psychotropic medication purchases to these visits Feeler et al. (1986)].’ Mental health episodes are generally more regular and easier to identify than medical episodes. Unfortunately, to track changes in marginal price within the year, we must know the MDE remaining and hence must keep track of all medical expenses of all family members. For insurance plans with separate mental health coverage, this task would be much easier than it was on the HIE.

2.2. Modeling annual mental health spending

In previous work [Wells et al. (1982); Manning et al. (198611, we studied average annual mental health spending by plan using an approach common in health economics. We modeled annual spending as the product of the probability of some mental health use and annual spending by user, and estimated how plan affected each of these. A similar approach had also been used to estimate the effects of plan on medical spending [Manning et al. (1987)].

In contrast, the medical episodes analysis looks at decisions to start episodes within the year, using current MDE status and initial coinsurance to measure current price [Keeler and Rolph (1988)]. This approach allows us to separate the effects of coinsurance and deductibles on medical demand. Annual medical spending can be modeled neatly as the product of the number of episodes per year and the cost per episode. Each part can be estimated separately, and cost sharing reduces medicai spending mainly by reducing the number of episodes [Keeler and Rolph (1988)].

We were unable to use the same method to analyze episodes of outpatient mental health treatment for two reasons. First, because some mental health treatment episodes include long scheduled gaps in treatment (monthly visits are not uncommon), the gaps that indicate the start of a new episode must be quite long. We followed the literature in using 56 day or longer gaps as marking a break in treatment [Kessler et al. (1980)]. With this definition, the average number of mental health treatment episodes per year was only I.2 episodes per person with at least one episode. Thus, the demand for number of episodes is essentially for none or one.

Second, annual costs for those with multiple episodes were slightly smaller ($515) than those with single episodes ($610, unadjusted late 70~ dnk@ [Keeler et al. (1986)]. This result is not surprising. Those with multiple

‘Treatment that extends across two accounting years is divided into tuo episodes, because the participant has to start over each year to fulfill the cap on spending. The rate of continuing treatment falls significantly at year end on pay plans for patients who go from temporarily free care to paying again for care [Keeler et al. (1987)].


episodes have stopped treatment for dt least eight weeks, while many of the single episodes last all year long. Still, if those with multiple episodes have lower costs than those with one, it will be misleading to predict the effects of price on numbers and cost per episode separately.

Instead, we focus on when treatment starts, and put the total annual costs into one ‘episode’. We will look at the effect of plan and current MDE status on the decision to start use and on the amount of spending in the rest of the year.

2.3. Survival metho& for analyzing when episodes start

We used survival methods instead of simple analyses of the probability of any use. Survival methods use the additional information on timing of initial treatment within the year. In addition, the time from the first visit to the end of the year is the most important predictor of costs, because of the persistence of treatment.* Hence, survival methods mesh well with analyses of spending over time.

Here we examine the time elapsed from the start of the year until the first use of mental health outpatient treatment. Time to event data are best analyzed using what is variously called survival, hazard, or time to failure methods. They focus on estimating the ‘hazard’ rate, which is the rate at which those who have not yet experienced an event do so. For example, the hazard rate of dying is the death rate of survivors. If the hazard rate varies with price and other characteristics of the population, one can use multiple regression methods to estimate how it varies.

Survival methods are necessary when, as here, most observations are ‘censored’. That is, the period of observation (in our case, the year) ends before most people have an event (have started any mental health treatment). Because there is information on whether people do or do not get treatment, such observations can not be thrown out, even though we know only that they had not been treated by the end of the year. Survival methods use the censored observations appropriately, in effect including the experience of the censored observations in estimating the hazard up to the point of censoring, but not beyond. (See the appendix for further details.)9

2.4. A model of within-year price effects

We use the methods presented in section 4 of Keeler and Rolph (1988) to analyze spending decisions within the year. These methods are designed both

*For example, a Markov analysis showed that 79 percent of those spending in one month would also be spending in the next [Keeler et al. (1987)].

gFor a thorough exposition of these methods, see Kalbfleisch and Prentice (1980), or Cox and Oakes ( 1984).


to address the econor.3 issue that individuals may anticipate different marginal prices, and the statistical issue of endogenous prices that are related to spending propensities.

Because menta! health episodes are typically large, a small limit on out-of- pocket spending (MDE) may not deter spending as much as a large one. Just as with hospital care, if the planned treatment costs more than the MDE remaining, the total price of the episode is fixed, and the cost of the last bit of care is zero. Because our statistical methods require that we split all MDE and coinsurance situations into a few types, we could not discriminate precisely how different amounts of MDE remaining affected use. We simply used the same categorization that we used for hospital (medical) care, splitting all situations with MDE remaining into either $400 or more MDE remaining at the start of an episode (called the big MDE period), and between 0 and $400 MDE remaining (called the small MDE period).

To examine ‘pure’ price effects (i.e., the effects of constant marginal price from hypothetical coinsurance plans without upper limits on out-of-pocket spending), we assume that people who have no limit on out-of-pocket spending would behave like those with more than $400 of MDE remaining. This assumption is supported by two empirical facts. First, people in the experiment did not seem to look beyond their current episode in making decisions. There was little anticipation even for small amounts of MDE remaining in outpatient medical episodes. Second, mental health expenditures alone were rarely enough to exceed the MDE when there was more than $400 leftJo

Health care services in the HIE showed surges at the beginning of the experiment in care on the free plan for the most deferrable types of treatment-dental and well care. However, rates of spending after the MDE was exceeded did not exceed free plan rates (after adjustment for sickliness) even for dental and well care. Instead of initial surges in mental health services, use of services on both the free and pay plans increased steadily throughout the first year, perhaps because people came to appreciate their possibilities [Keeler et al. (1986)J Still, it is possible that intermittent users of mental health services on the pay plans may have learned to schedule treatment for ‘sale’ periods when some other large medical expenditure by their family makes such treatment temporarily free, We will check 3 they did take advantage of sale periods (when the MDE has been exceeded) by spending at a higher rate than people do on the free plan.

In sum, we check the rate of starting mental health treatment, under the

toOnly 8 of 10’7 cases starting mental health treatments in that situation exceeded the MDE on the basis of the mental health spending alone. If only a small amount of MDE remains, the situation is different - for example, 86 of 116 individuals starting mental health treatment with some of their individual deductible unmet exceeded their $150 limit just with their mental health spending [Keeler et al. ( 1986)].


cost-sharing plans, in each of the inree economic periods in each accounting year: the period when the MDE remaining is large, the period when it is less than $400, and the free period after the MDE is exceeded.

Just as in Keeler and Rolph (1988), we have computed the effects of a pseudo-MDE for the free plan to test our methods. We observe what happens when families approach and exceed their pseudo-MDE. Since care was in fact always free for them, any response to this hypothetical MDE indicates a problem in the assumptions underlying our methods.

2.5. Untangling sickness and price effects

For health insurance plans with MDEs, prices are lower on the average for those who tend to have more episodes. This problem is more serious for the analysis of medical spending than for mental health spending, which is a small fraction of total spending. Still, to the extent that use of mental health care is correlated with use of medical services, groups defined by more or less previous spending in a year will differ in their non-price-related tendencies to use mental health services. For mental health spending, some of these differences are captured in our analysis by covariates such as age, mental health status at enrollment, and prior use of services. Still, our statistical methods must also allow for unmeasured differences between those who do or do not exceed the MDE or the results will be biased.

The model of within-year price effects presented in Keeler and Rolph (1988) addresses these problems. We separate price effects from sickliness effects by assuming that unobservable individual propensities to spend are constant over the year, and we compare behavior before and after the MDE is exceeded with behavior on the free plan (where presumably there are no within-year price effects). The only difference in statistical methods from the medical model is that the negative binomial regression for the number of medical episodes is replaced by a Weibull regression of the hazard of starting outpatient mental health treatment.l*

At each site regression models were used to compute the hazard of starting mental health treatment for each person, based on personal factors but not plans. The hazard was adjusted to the rate that would have occurred if the individual were on the free plan (by changing the plan dummies to free in the prediction step). The hazards and times that each individual is in each MDE remaining period are summed over family members. The gamma distribution of unmeasured family propensities is estimated using free plan experience. Finally the hazard ratios for the different coinsurance periods are estimated using maximum likelihood [Keeler et al. (1986)].

l1 For a proof that the identical maximum likelihood formulae binomial and hazard models, see Appendix F of Keeler et al. (1986).

work for both negative


Table 1 Hazard ratios relative to free plan.

MDE remaining

Plan

Individual deductible 95 SO 25

Total cost sharing Freeb

Over !§400 - (big) -

O<X<$400 0.74 (small) $10)

None 1.08 (0.24)

0.24 0.37 0.79 0.42 0.95 (0.05) (0.07) (0.14) (0*04) (0.12)

0.46 1.16 0.61 0.73 1.06 (0.16) (0.31) (0.26) (0.08) (0.16)

1.54 0.84 0.76 1.10 1.07 (0.34) (0.34) (0.37) (0.15) (0.23)

“Standard errors in parentheses as given by the Maximum Likelihood program. bPeriods for pseudo-MDE described in text. Free for the whole year = 1.00.

3.1. Estimated rates for starting

Table 1 shows the estimated

treatment episodes

hazard ratios in each period relative to the overall free plan. A hazard ratio of 0.24 means (since the hazard is small) that those on the 95 percent plan initiate mental treatment at a rate that is 24 percent as large as the rate they would have exhibited on the free plan. The ratios for over $400 MDE remaining (Big MDE period) decline sharply with increasing coinsurance. The $150 Individual Deductible plan starts in the small MDE period with hazard ratios similar to other pay plans with a little MDE remaining.

3. Results

The amount of MDE remaining has a strong influence on spending. The small MDE remaining period ratios are usually greater than the big MDE remaining period ratios and the no MDE remaining ratios are greater still. Because most families do not exceed their MDE in any one year, there is more experience in the big MDE period than in the other two periods on all but the Individual Deductible plan. Thus, the standard errors for the later periods’ estimates are larger, and the estimates are less stable. The overall pay plan estimates are 0.73 in the small MDE remaining period and 1.10 once the MDE is exceeded. These combined estimates are significantly different from each other (p cO.OS), but the estimated differences among the individual pkzs are not.

The estimated standard errors of the big MDE period hazard ratios range from 0.05 on the 95 percent plan to 0.14 on the 25 percent plan (table l).‘* Although these estimates are substantial, they underestimate the true error, because they are conditional on certain parameters that are assumed known, but in fact were estimated. In Keeler et al. (1986), we determined that the

‘*Estimates are computed by maximum likelihood theory using a RAND version of B. Hall’s MAXLIK program.


true error is less than twice the error given in table 1. Thus, it is no accident that the ratios for the coinsurance plans line up, and that the Individual Deductible plan has ratios similar to the other small MDE pay plans.

As a test of the method of estimating ratios, we estimated price effects on the pseudo-pay free plan, where the effects of a counterfactual MDE can be computed, but there are no real price effects. As can be seen, the hazard ratios on the free plan are not far from one and are never significantly different from one. The big MDE period estimate is slightly less than one, and the later period estimates are slightly greater than one. This may be due to the correlation of mental and medical spending. Our methods take other mental health spending in the family into account but assume that people in different MDE remaining situations are otherwise similar in their unmeasured characteristics. Because mental and medical spending are correlated, those over the MDE are more likely (for non-price reasons) to spend on mental health. In the later simulations of pure price effects, the estimated hazard ratios on the pay plans will be divided by the corresponding free estimates for that period to correct for the correlation.

If people were economically myopic; i.e. if they did not plan ahead but did know their current insurance status, we might expect the over MDE hazard on the pay plans to be one, showing a hazard of starting mental health treatment that was the same as the free-plan hazard. It is close to one, but there are other possible explanations besides myopia. There may be some delay before people realize that their care is now free. Even if they do realize their care is free, initial low use could affect use after the MDE is exceeded in two compensating ways. The initial low use might result in unmet needs on the pay plans for the care of accumulated untreated sickness. However, low or non-users might also form the habit of not seeking help from mental health specialists for psychiatric illness.

3.2. Cost of outpatient treatment episodes

The cost of an episode (defined here as all spending within an accounting year) depends on the intensity of treatment as well as when treatment starts. Outpatient mental health episode costs roughly follow a lognormal distribution, except for the lower tail .I3 The CO:G of episodes were similar on free and cost-sharing plans, the 329 cost-sharing episodes had mean costs of $463 and a mean of log costs of 5.39, whereas the 226 episodes on the free plan had corresponding means of $447 and 5.44.

The amount spent depends on when in the year spending starts. Fig. 1

13Small values heavily influence the mean log, but they have little effect on total spending. We tried various lower bounds on episode costs to reduce the influence of these small values. After some investigation, we set the log costs to be the log of the maximum of $20, and costs. (The resulting distribution had skewness = - 0.1.)

E.B. Keeler et al., Demand for episodes of mental health services

600 I

.

Log = 6.21

Log - 5.62 N-107

Log - 5.45 N =59

Log - 5.33 N-47 Log -5.14

151-200 201-250 251-300 301-350

Daysleft

Fig. 1. Average spending in the year by days left after start of episode.

gives the mean spending as a function of how many days are left in the year.14 The relation is striking. The figure suggests that once people get into treatment, they spend about $50 a month for the rest of the year, with those who start in the first few weeks spending a little more.

The cost of the episode depends on factors at the start of the treatment, such as the time remaining (days from the first visit until the end of the year) and the MDE remaining. We specify log (costs) as a linear function of the log of the hazard index (the linear combination of independent variables that best predicts the hazard of starting treatment), other personal characteristics, plan and MDE period, site, year, and time remaining?

Table 2 shows the results of estimation with a large number of plan dummies (first column) and with the final specification used.

The hazard index and ‘logtime’, a function of the number of days to the

14The big surge in episodes early in the year reflects treatment continuing from one accounting year to the next. After that surge, rates ~1’ initiation are approximately constant through the year [Keeler et al. (1986)].

t5 We fit the time remaining in days, t, in a peculiar way to facilitate modeling. We find K such that log(K-t) had coefftcient 1 in a regression of log costs. In our final specification, K is 517.87 days. This specification makes it easy to find the total cost on various pure price plans [Keeler et al. (1986)]. Results from fitting log (costs) as a cubic in t are also given there.


Tacrle 2

Regression of log(cost) on MDE period and insurance plan.

Variable

Column ( 1)

Coeff. t

Column (2)

Coeff. t

Intercept Year 1 Year 3 Log (Hazard Index) Small MDE ID Planb Over MDE ID Plan Small MDE Pay Planb Over MDE Pay Plan Big MDE 25 Coins. Big MDE 50 Coins. Big MDE 95 Coins. Dayton South Carolina Massachusetts Log (Time’)

4.74 10.80 - 0.27 -2.19 - 0.08 - 0.67

0.27 5.07 0.15 0.66

-0.15 -0.60 -0.12 - 0.56

0.32 1.70 - 0.03 -0.17 -0.71 -3.17

0.06 0.29 > - 0.62 - 3.69 -0.04 - 0.26 - 0.55 -4.21

0.99 9.44

4.8 10.96 - 0.27 - 2.22 -0.09 -0.79

0.29 5.38

-0.01 -0.06 0.26 1.70

-0.2 - 1.45

-0.57 - 3.42 - 0.07 -0.44 -0.52 - 3.98

1 9.48

R-squared =0.261 = 0.248

“Based on the 555 person-years with outpatient mental health spending.

bIncludes all cost-sharing plans; so relative to free the cost of an episode on the ID plan after the MDE is exceeded is ( -0.15 + 0.32) = 17 percent larger.

‘Log (Time) = log (5 17.87 - t); see text.

end of the year, are the most important factors in explaining costs per episode. Once the hazard index is included, the other personal characteristics add little. This implies that researchers with partial data (i.e., lacking data on either costs per user, or on who uses) can get a rough idea of the relation between personal characteristics and total spending by studying just the part they have. For example, with just claims data from users of mental health services, one could study what determines the magnitude of episode costs to get ideas about who might be expected to use treatment.

Year and site also have strong effects on costs per episode. The omitted site and year was Seattle year 2, so the regression coefficients in the table can be interpreted as percentage differences from that site year. Expenses per episode went up strongly from year 1 to year 2 (the combined effect of inflation and increased intensity), but declined in the third year. Dayton and Massachusetts have lower costs, conditional on starting time.

We obtain our estimates of the effects of being in each coinsurance status period on costs per episode from the contrast of that period with the entire free plan experience. There are large differences between the three periods for the pay plans. Episodes that started when a large MDE remained are 18


Table 3 Expected probability and costs of mental health episodes if insurance plan

has no MDE.

Mental health episodes

Pure coinsurance plans

Free (0) 25 50 95

Annual probability Cost per episode

Total costs Plan relatives

0.039 1 0.0336 0.0181 0.0124 $659 $540 $536 $534

$25.78 $18.16 $9.68 $6.62 100 70 38 26

aAdjusted to rates and costs in second-year Seattle (1977). The total costs and annual probability are derived first and the cost per episode obtained by division of costs by probability.

percent less expensive than the average free plan episode [exp( - 0.2) in second column =0.82], so the arc elasticity per user is -0.10.16 Episodes that started with a small MDE remaining cost the same as free. The costs per episode starting after the MDE is exceeded are 30 percent higher. None of these differences is statistically significant (p > O.l), but they are all plausible.17

3.3. Estimates of overall pure price effects

We now can put together the estimates of effects on the rate of starting episodes and on cost per episode to compute the overall effect of ‘pure’ coinsurance plans without limits on out-of-pocket spending. We call this the pure effect of price on mental health spending and assume it is approximated by the behavior of people in the big MDE period. In table 3, we show the expected number of episodes and total costs of these episodes for four hypothetical plans with constant coinsurance rates.18 Coinsurance leads to a decline in the probability of episodes and smaller episodes when they occur. The rates decline sharply with coinsurance, with the 95 percent coinsurance

16The estimated 18 percent reduction in cost per episode is based on pooled data from the 25, 50 and 95 percent plans. The arc elasticity starting from 0 = dq/dp - (0+ p)/2/(q,, + 4)/2 = - 18/91 i2= -0.10.

“Because there are so few cases in some periods and plans, it is not feasible to estimate the full 15 different plan-period effects. The major issue for estimating the effects of insurance on cost per episode is whether to use the three separate plan estimates from the big MDE period, or to pool them into one estimate, as in column 2. (Unfortunately, the massive 50 percent coinsurance big period decrease is based on only 29 observations.) We decided to use the pooled estimates, because the data were scarce, and we could see no particular reason for the U-shaped response. The site differences noted in Wells et al. (1982) are explicitly controlled for here.

18Probability of use and total costs are predicted for each person on the free plan in the second year of the study. (The free plan had lower refusal rates and fewer dropouts than the other plans, so this should be quite representative of the sites.) The occurrence rates and costs are adjusted to Seattle year 2 by changing dummies in the prediction step.


Table 4

Sensitivity of predicted mental health spending to assumptions.

Plan

Assumptions

Assumption Base case

Cost/episode changes: No difference in cost/episode Plan specific cost/episode

Hazard ratio changes: All pre-MDE experience

Both changes: Base+ 1 combined std. dev. Base- 1 combined std. dev.

95 50 25

0.26 0.38 0.70

0.31 0.46 0.87 0.33 0.23 0.84

0.28 0.47 0.66

0.32 0.46 0.86 0.20 0.31 0.58

Free (0)

1.00

having only 32 percent of the episodes that would be started each year with full coverage (0.0124/0.0391=32 percent).19 The difierences in cost per episode are mainly determined by the estimated factor by which pay plan episodes are smaller. The product of these two effects leads to a strong decrease in costs as coinsurance increases. The pure 95 percent coinsurance plan is estimated to spend at 26 percent of the free-plan rate, and spending on the pure 50 percent coinsurance plan is not much larger, at 38 percent of the free-plan rate .20 The spending with a pure 25 percent coinsurance plan is estimated to be 70 percent of the free-plan rate.

In table 4, we show the results of varying some of the parameters that go into the final mode1.21 The top row gives our best-guess estimates of the ratio of total costs of outpatient mental health services for each coinsurance rate to such costs on the free plan. The next two rows show the result of varying assumptions on cost per episode. Because even the pooled 18 percent decrease in cost per case with cost sharing used in the estimates was not a significant decrease, we might assume that coinsurance has no effect on cost per episode. This is shown in row 2. Next, we show the effect of using the plan-specific cost per episode reductions estimated from the data rather than the pooled plan estimates. As shown in row 3, the 50 percent coinsurance

t9This is bigger than the estimated 0.24 hazard ratio, because of selection within the year. Later in the year, there are more people on the 95 percent coinsurance plan with poor mental health who are not yet under treatment than there are on the free plan.

20The actuarially fair premiums for these plans can be computed from (l-coinsurance) *(Total costs). These are $25.78, $13.62, $4.84, and $0.33 for the free, 25, 50 and 95 plans respectively.

21 Because the model is made up of several distinct pieces, we cannot easily compute an overall standard error of the estimates. This is the cost of using a more complicated model that tries to fit behavior more closely.


Table 5 Comparison of price effects for outpatient mental health and medical spending.

Plan

Free (0) 25 50 95

Arc-elasticity

O-95 25-95

Pure coinsurance Mental health Medical”

HIE plans Mental healthb Medicaid

100 70 38 26 0.59 0.79 100 71 58 49 0.34 0.31

100 67 76,33” 43 0.40 0.37 100 78,74= 63 58 0.27 0.23

aSource: Keeler and Rolph (1988). bSource: Manning et al. (1986). ‘First element in pair is the 25/50 plan; second is the SO/SO plan. dSource: Manning et al. (1987). ‘First element in pair is the 25/25 plan; second is the 25/50 plan.

plan has much smaller costs than the 95 percent plan, reflecting the raw experience in the study.

The last three rows reflect changes in the hazard ratio parameters. First, if people are myopic and look only at immediate costs in deciding whether to start treatment, there would be no difference between use in the big and small MDE period. The effects of this assumption is shown in the next row, where only the 50 percent rate changes much. Finally, if the errors in estimates of price on episode st ~-d~~ -n+am r)*a ;nA~nmdent nf thncp nf pf&ctq al rllig la&b3 ocbw rrkir~k_i~~-+~~~, GL WplIu-_, -0 L--,,‘_’ - on cost per episode, we can combine them by adding the variance of the errors (because both estimates are on the log scale). If the other parameters in the model are accurate, then we think there is a 68 percent chance that the true cost ratios lie between the values in the last two rows. Any positive correlation between the errors in the hazard and cost equations would increase these bounds. There is obviously a lot of uncertainty in the estimates.

3.4. Comparing medical and mental health care demand

We can now address the question that motivated the study. Is outpatient mental health care more responsive to price than outpatient medical care? Table 5 gives cost ratios and arc elasticities for both ambulatory mental health and medical spending by plan and by pure coinsurance.

Although there is little difference between the outpatient mental and medical response to 25 percent coinsurance, larger amounts of coinsurance with no MDE have a larger effect on the use of mental health services. The estimated mental health spending with a pure 95 percent coinsurance plan is


about 55 percent of what it would be if the price response was the same for outpatient medical spending as a whole.

The MDE mutes the impact of coinsurance on spending (last two rows of table 5). This is true for both mental health and medical spending, but especially true for mental health spending. Both medical and mental health rates of having episodes increased after the MDE was exceeded, which makes the plan effect a mixture of coinsurance and free price effects. Although the mental health spending itself did not usually cause a family to exceed the MDE, about two-thirds of thoose families with mental health spending exceeded the MDE, as compared to only 30 percent of families with no mental health spending. This explains why there is a bigger difference between mental health spending with pure coinsurance and spending observed on the HIE (rows 1 and 3) than there is for medical spending generally (rows 2 and 4). The 52 visit limit on outpatient psychotherapy had little apparent effect as only 0.2 percent of the population reached this limit. Except for some additional use of very intensive therapies under free care, we would expect little difference with more generous limits.22

The main reason for the difference in price effects between mental and medical is the effect of the MDE on cost per episode. Mental health episodes that started in the big MDE period were less costly than free episodes, and episodes starting after the MDE was exceeded were more costly than free. By contrast, there was no difference between the costs of medical episodes that started in the big, small or no MDE remaining periods.

Second, the rates of starting for mental health came all the way up to the free-plan rate in the period after the MDE was exceeded. For outpatient medical care, only well care episodes did so. This suggests that people use more discretion in timing their mental health care, like their well care, than they do in timing their acute and chronic outpatient medical care.

4. Conclusions

The economic analysis of episodes was designed to take a closer look at behavior that could not be studied in our earlier aggregated annual analysis of outpatient mental health spending by plan. The episodes approach yielded some new insights into decisions to spend on mental health treatment. We found, just as with medical care, that cost sharing mainly affects the rate of

22Because the HIE plans did not vary the 52 visit limit, any estimates of the effects of lower limits from this data are indirect. Limits on coverage lead to transitions from low out-of-pocket cost to higher cost care. Such transitions occurred only at the end of the year in the HIE, when participants who are over the MDE revert from a situation where care is free to one where they have to pay. Use drops significantly, but there were not enough occurrences for a precise estimate [Keeler et al. (1987)J Thus, the HIE does not give much information on the effects of low limits on coverage, which are common in mental health care insurance.


starting episodes of outpatient mental health treatment. (In our analysis, such episodes are equivalent to years of any use.) Cost sharing reduces costs per episode only slightly even when the family is well below the MDE?

We found both anticipation and sales effects of the MDE on the use of mental health services. Spending in the period when the MDE remaining was small was considerably more than when the MDE remaining was big (an anticipation effect), but less than when the MDE was exceeded. Once the MDE was exceeded, episodes were initiated at the same rate as on free-plan and they were somewhat more expensive than similar episodes on the free plan would be (a sales effect).

There are five major findings on the demand for mental health care in the HIE, combining results reported here and earlier [Wells et al. (1982), Manning et al. (1986)].

(1) The use of outpatient mental health care is responsive to the price paid out-of-pocket by the patient. In the absence of insurance, spending is one fourth that of free care. Spending with a 50 percent coinsurance rate is about two-fifths that of free care, and with a 25 percent rate is about 70 percent that of free care.

(2) Outpatient mental health use was much more responsive to price than outpatient medical use at the higher coinsurance rates, but not in the free to 25 percent range. Outpatient medical spending with a pure 25 percent plan was also about 70 percent of that with free, but with no insurance only drops to one half of that with free care.

(3) Mental health use was less responsive in the experiment than in most observational studies. Earlier studies showed elasticities on total use of - 1.0 and even more (for federal employees), and elasticities per user of -0.4 to -0.54. By contrast, our work shows an elasticity of total use of only -0.59 and an elasticity per user of -0.10.24 Although there are uncertainties in all estimates and differences in the populations studied, we believe the main explanation for the discrepancies is an upward bias in the earlier estimates resulting from adverse selection effects. Other studies have relied on nonexperimental data, where sicker individuals might have selected better coverage (to lower their out-of-pocket costs). Such selection is not inefficient, but it leads to an overestimate of the

23 Because mental health episodes are so rare (555 in our sample, as opposed to over 50,000 other medical episodes), our estimates of the effects of plan on cost per episode are quite imprecise. Also, if those getting treatment on cost sharing plans are sicker than those getting treatment on free plans in unmeasured ways, our cost per episode estimates underestimate the effect of cost sharing on treatment.

24McGuire notes that episodes that cross over years will be counted as two smaller episodes in our annual analysis. In an analysis of probability of use and amount of use over a long period, we would expect to see slightly less effects on number of users, and larger effects on use per person.

386

(4)

(5)

E.B. Keeler et al., Demand for episodes of mental health services

price response because some of the difference resulting from sickliness would be attributed to price. Given the ease with which federal employees can switch among plans with varying mental health coverages, this may explain why Reed’s (1974) results for federal employees showed so much response.

If this explanation for the difference between our results and others is true, then employers and insurance companies should be careful about increasing their benefits much beyond the prevailing level. They could observe a substantially larger response to decreases in coinsurance than we observed. However, if everyone’s coverage changed (e.g., by mandated coverage), then an individual firm would be less at risk for adverse selection, and our results should apply. Even with free care, few people use outpatient mental health care, so relatively little is spent on outpatient mental health care. We found that only 4.5 percent used any care in a year, and only 14 percent had any use in five years on the HIE free plan. Those who did use such care commonly used it over a period of several years. With free care, average annual expenditures per enrollee are about $32 (1984 dollars), which for the nonaged is 9 percent of outpatient medical care and 4 percent ci al! medical care. Modest deductibles have little or no effect on the use of outpatient mental health care. People on the $150 Individual Deductible plan (approximately $300 in late 1980s dollars) had overall spending similar to the free plan. People on that plan had low MDE, but almost all mental health users deductible.

use before exceeding the exceeded the individual

4.1. Should mental health coverage be less generous than medicalP

Mental health coverage is often separated from other medical coverage. The administrative costs involved in checking that mental health use is not being disguised as medical are manageable because almost all costs are

a--,,,L, attributable to a distinct set of providers. Thus it is feasible to have sCpdIUG

cost-sharing and restrictions on mental health coverage, but are additional restrictions desirable? Insurance design involves trading off the welfare costs of moral hazard against the benefits of risk reduction [Arrow (1971), Zeckhauser (1970)]. We discuss these in turn?

25 We only consider outpatient coverage. The issues in psychiatric hospitalization are different; expenses are much higher, and the patients may be less able to make appropriate decisions about care.

26We will not discuss other possible social goals of insurance such as improved access, gr income transfers to the sick poor.

E.B. Keeler et al., Demand for episodes of mental health sewices 387

4.2. Welfare losses due to higher use with insurancez’

Because small deductibles have little deterrent effect on mental health use, there is little reason to have them. They impose some cost on the patients, with little gain in reduced overuse.

The substantial response to coinsurance implies that there are welfare losses from higher use associated with insuring mental health care.28 However, because current coverage is less generous than that of medical care, the welfare loss from overuse due to the current insurance of outpatient mental health care is relatively less. If the average current policy has a 50 percent coinsurance rate, then ignoring deductibles and upper limits, the welfare loss from outpatient mental health insurance is roughly $360 million per year. However, to go from a 50 percent coinsurance rate for mental health services to 25 percent coinsurance would generate additional welfare losses of $1.45 billion per year.

The Ramsey pricing criterion for minimizing the welfare losses from taxes or subsidies on several goods is to set taxes so that the proportional deviation from the equilibrium quantities with no taxes is the same for each good [Baumol and Bradford (1970)]. This criterion is only a partial guide for health insurance since it ignores any benefits of risk reduction? The common policy with 25 percent coinsurance for outpatient medical and 50 percent coinsurance for mental health satisfies the Ramsey pricing criterion, since coinsurance causes about a 50 percent increase over the uninsured demand for each service.

4.3. Financial risks of mental health spending

To reduce financial risks, insurance must cover services that are truly

27The standard welfare economic theory, assumptions, and calculations underlying these conclusions are presented in Appendix E of Keeler et al. (1986). In these calculations we do not include the value of risk reduction, and possible externalities from treating patients with mental problems, including altruistic concern. National estimates are based on 1984 dollars and totals.

281s it reasonable to use decisions of people with mental problems to buy or fail to buy mental health services in valuing these services? The economic theory says that services that are bought with 25 percent coinsurance, but not with 50 percent coinsurance, are worth between 25 and 50 percent of their cost of provision to the recipient, and the rest is waste. Computing the waste from overuse of outpatient mental health services, based on observed demand of troubled people, makes us uneasy but we do so for two reasons. First, most people with psychiatric disorders in a general population are not psychotic [Myers et al. (1984), Bumam et al. (1987)]. Second, we found that anxiety and depression were the major determinants of L* in our general population [Keeler et al. (1986)]. We think it would be paternalistic and unhelpful to say that persons with mental disorders, especially those who are not psychotic, can not judge what is best for them.

2gMere is a (not very plausible) scenario where it applies. Suppose a company or government chooses to subsidize health care spending (or, equivalently, to reduce the financial burden of the sickly) by paying the premiums, separately, for medical and outpatient mental health care spending. Ignoring other benefits of coverage, it wants to allocate a fixed total subsidy with minimal welfare loss from overuse.

388 E.B. Keeler et al., Demand-for episodes qf mental health services

risky. If there is asymmetric information and policyholders know whether or not they will use coverage, then insurance simply transfers money from non- users to users. (Non-users must buy group or mandatory insurance, even though they know they won’t benefit.) There is a gain to society only if users are considered to be a particularly worthy group. By contrast if the outcome were truly risky, insurance reduces the risk to everyone.

In any given year, spending on mental health care, like care for many chronic diseases, is mainly foreseen. From a longer term view, it is risky who will become mentally ill (or who will have mentally ill children) and suffer the financial burden of continuing care.

Risk aversion is generally much greater for potential large losses than for small. Outpatient mental health spending is medium sized - about $1000 per year (in 1987 dollars) on average for those with use. This is large compared to outpatient medical spending, but small compared to the costs of hospitalization. Depending on their income and attitudes, people might think insuring against the financial risks of such losses was reasonable. The rareness of mental health episodes means that the premiums for coverage can be small.

Appendix: Survival methods

The distribution of time to events can be described by three related functions. The first is the survival function F(t), which represents the proportion of people who have not yet started treatment by time t; our estimate of the probability p(t) of any use by time t is then just 1 -F(t). The second is the probability distribution function (pdf) of time to events f(t) = -dF(t)/dt, which is the instantaneous rate of events (incidence of first treatment) at time t for all people. Finally, the hazard function h(t) = f(t)/F(t) is the rate of events for those who have survived (had no treatment) up to time t.

If the hazard rate varies with different characteristics of the population (e.g., if young educated women or those with poor mental health are more likely to get treatment and get it sooner), one can use multiple regression methods to estimate how it varies. Here, we rely on a Weibull regression, a relatively easy to use method (now available in the SAS statistical package) based on assumptions that appear to fit our data well.

If the hazard is constant over time, h(t) = h, then we can integrate

h=f(t)/F(t)= -d log (F(t))/&

to obtain

F(t) = exp ( - ht) and f(t) = h exp ( - ht).


If people have covariates X, then we can fit h as some function of a weighted sum of X, h=g(bx). Because h must be greater than zero, we normally fit h =exy (5x).

If the hazard rate changes over time, we can model it as h(t) = P. This corresponds to the simple survival function F(t) = exp [ -(ht)p]. The hazard is constant if (p - 1) = 0, increasing if (p - 1) is positive, and decreasing if (p- 1) is negative. In a Weibull regression, we simultaneously fit the hazard rate h =exp (bx), and the time transform p.30

Equivalently, a Weibull regression model assumes that the time t to first visit follows a model:31

ln(t)=xfl+s,

where PO= - b,a - 0 In 0, is the intercept, fli (i = 1,. . . , k) = - bia are the slopes, and E is an unobserved log Weibull error term with scale parameter o= l/p. The error E is independent of X. The likelihood Li for the ith individual is

Li = exP MlOg (t) - xis)/~~ - exp ((log (0 - Xis)lo)]

if uncensored, and

if censored at time t. The uncensored expression is the pdf $ for the Weibull, and the censored expression is the survival function F(t). The model is estimated by maximum likelihood, correcting for sample loss (e.g., censoring on the right)?

30For further discussion see Kalbfleisch and Prentice (1980, p. 24). If we make the time transform T= tp, expanding the early part of the year? then the declining (since pc 1) hazard in real time t becomes a constant hazard in transformed time r Because the subsequent maximum likelihood models used to compute price effects assume a constant hazard, we always transform time. The likelihood for constant hazard time to events is a special case of the likelihood for Poisson distribution of number of events (and the likelihood function of the Pareto resulting from mixing over a gamma distribution of unmeasured characteristics is a special case of the negative binomial model from mixing Poisson arrivals over a gamma). For this reason, the same estimation methods and software used in analyses of medical spending can be used here. [Keeler et al. (198Q.3

31A more general model is the Cox proportional hazards model, which does not assume any particular parametric form for the change in hazard over time. In our case, the Weibull regression parameters are very similar to those given by the Cox model. We have used Weibull regression rather than the more general Cox proportional hazard models for three reasons. First, we have software that allows us to correct for correlations across observations for the Weibull, but not for the Cox models. Second, the Weibull assumption appears to fit our data well. Finally, we are interested in time per se. For example, we are interested in the likelihood that an individual will have any use by the end of the first year.

32 We used software developed for SAS by Rogers and Hanley (1982).


Table A.1

Actual vs. predicted probabilities of any use (in percentages).

Bias

Time period Residual Standard

(years) Actual Predicted mean error

oso.2 1.57 1.49 + 0.08 0.09 050.4 2.12 2.17 - 0.05 0.10 050.6 2.62 2.70 - 0.08 0.11 050.8 3.10 3.15 - 0.05 0.12 05 1.0 3.54 3.55 -0.01 0.13

“Model includes plan dummy variables rather than price variables Feeler et al. (1986)]. Standard error of other mean bias assumes parameter estimates are constants.

The Weibull model seems to fit the annual pattern any use of mental health care. Table A.1 presents the probabilities of any use based on Table 6.2 in Keeler et al. ( 1986) for of 0.2 years.

for the likelihood of actual and predicted

the specification of the model given in periods of 0.2 to 1.0 years in increments

Elasticities of survival and expected cost

We can interpret the regression coefficients of the hazard function in terms of effects on the probability of an event in a year and in terms of total costs. For simplicity, we computed all our formulas assuming time transformed so that the hazard rate is constant.

Let

G(x) = prob (treatment) = 1 - F(T) = 1 - exp ( - T exp (bx)).

Then the elasticity of the probability of treatment with respect to xi

m bixi( 1 - h T/2) for hT small.

We can compute hT F/( 1 -F) at the mean, and use it to multiply bixi for each i.

It may be more interesting to consider the effect of changes in a variable x (e.g., price) on total outpatient spending on mental health care. To do so, we expressed costs per episode as a function of transformed time remaining and hazard h, Because no independent variables other than price, year, and site


have significant effects on costs per event once we control for h, only those personal characteristics that increase the chance of initiating outpatient treatment also increase the intensity of that treatment.

We used a simple specification of the hazard and cost per episode estimates to permit us to calculate price effects in closed form. We fit costs as a multiplicative function of plan, MDE status, hazard, site, year, and times of start. That is, the log cost per episode for each individual is estimated by

logcost=log(K-t)+axlOg(h)+bx(X)+cx(site-year),

where

t is transformed time of the start of episode, h is the index of demographic variables predicting the hazard of starting an

episode, X is an indicator of price and MDE status at start of episode, K is chosen so the coel’kient of log (K - t) is 1.0.

Exponentiating, we obtain

cost=(K-t)xh”xPxC, (A-1)

where P=exp (bx), and C is the site-year adjustment. In other words, the cost conditional on starting an episode at transformed time t for a person with hazard h is CP(K-t)h”, where C depends on plan, site, and year. We can write the expected costs, M, as the sum of the probability of starting times through the year multiplied by costs conditional on starting times.

M={hexp(-ht)h”(K--t)dt

=CPh”[(K--l/h)(l-exp(-hT))+Texp(-hT)].

For hT small, exp ( - hT) N 1 - hT + h2T2/2. Using this approximation and dropping terms in h2 the expected costs

M ill Ch”hT( K - T/2).

Then the derivative d (log M)/dh =(a + 1)/h, so the elasticity with respect to xi, is (a + I)&+ since h =exp(bx). In these data, a is estimated to be 0.29.

References

Arrow, Kenneth J., 1971, Essays in the theory of risk-bearing (Markham Publishing, Chicago, IL).

Baumol, William J. and D.F. Bradford, 1970, Optimal departures from marginal cost pricing, American Economic Review 60,265-283.


Blostin, Allan I?, 1987, Mental health benefits financed by employers, Monthly Labor Review 110,23-27.

Brook, Robert H., John E. Ware, Jr., William H. Rogers et al., 1984, The effect of coinsurance on the health of adults: Results from the RAND Health Insurance Experiment, R-3055HHS (The RAND Corporation, Santa Monica, CA).

Burnam, M. Audrey, Richard L. Hough, Javier I. Escobar et al., 1987, Six-month prevalence of specific psychiatric disorders among Mexican Americans and non-hispanic Whites in Los Angeles, Archives of General Psychiatry 44,687-694.

COX, DR. and David D. Oakes, 1984, Analysis of survival data (Chapman and Hail, New York). Ellis, Randall P., 1986, Rational behavior in the presence of coverage ceiling and deductibles,

RAND Journal of Economics, Summer, 158-175. Ellis, Randall P. and Thomas G. M&tire, 1984, Cost sharing and the demand for ambulatory

health care services, American Psychologist 39, 1195-l 199. Frank, Richard G. and Thomas G. McGuire, 1986, A review of studies of the impact of

insurance on the demand and utilization of specialty mental health services, Health Services Research, part II, 21,241-266.

Horgan, Constance M., 1986, The demand for ambulatory mental health services from specialty providers, Health Services Research, part II, 21,291-3 19.

Hustead, Edwin C. and Steven S. Sharfstein, 1978, Utilization and cost of mental illness coverage in the Federal Employees Health Benefits Program, 1973, American Joumal of Psychiatry 135,315319.

Kalbfleisch, John D. and Ross L. Prentice, 1980, The statistical analysis of failure time data (Wiley, New York).

Keeler, Emmett B. and John E. Rolph, 1988, The demand for episodes of treatment in the Health Insurance Experiment, Journal of Health Economics, this issue, 337-367.

Keeler, Emmett, B., Kenneth B. Wells and Willard G. Manning, 1987, Markov and other models of episodes of mental health treatment, in: Thomas G. McGuire and Richard M. Schemer, eds., Advances in health economics (JAI Press, Greenwich, CT).

Keeler, Emmett B., Kenneth B. Wells, Willard G. Manning et al., 1986, The demand for episodes of mental health services, R-3432-NIMH (The RAND Corporation, Santa Monica, CA).

Kessler, Larry G., Donald M. Steinwachs and Janet R. Hankin, 1980, Episodes of psychiatric utilization, Medical Care 8, 1219-1227.

McGuire, Thomas G., 1981, Financing psychotherapy; costs, effects, and public policy (Ballinger, Cambridge, MA).

Manning, Willard G., Joseph P. Newhouse, Naihua Duan et al., 1987, Health insurance and the demand for medical care: Evidence from a randomized experiment, American Economic Review 77, no. 3, June, 251-277.

Manning, Willard G., Kenneth B. Wells, Naihua Duan et al., 1986, How cost sharing affects the use of ambulatory mental health services, Journal of the American Medical Association 256, no. 14, 1930-1939.

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