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ESTIMATING the COST of PREVENTIVE SERVICES
in Mental Health and Substance Abuse Under Managed Care

Technical Appendix

This Technical Appendix supplements the manuscript by the same title. It contains detailed statistical information on the results of a simulation of costs for the following six preventive interventions:

1. Prenatal and Infancy Home Visits for High-Risk Mothers
2. Targeted Cessation Education/Counseling for Smokers
3. Targeted Short-Term Mental Health Therapy
4. Health Promotion Through Self-Care Education
5. Presurgical Educational Intervention With Adults
6. Brief Counseling/Advice to Reduce Alcohol Use

The rationale for the selection of these six interventions and a complete description of each intervention, its intended target audience, and its impact on health outcomes and costs appear in Dorfman (2000) and are summarized in the main text of this report, "Estimating the Cost of Preventive Services in Mental Health and Substance Abuse Under Managed Care."

A cost model of each of these preventive interventions was designed and then simulated under four different scenarios. At one extreme was the Least Expensive Scenario, defined as the scenario that assumed the least expensive values from among a reasonable range of values for each cost driver (e.g., prevalence, intensity of the intervention units/time period, staff salaries). At the other extreme was the Most Expensive Scenario, which assumed the most expensive values from among the same range of reasonable values.

Table A.1 summarizes the relative values of the various cost drivers in each model.

The critical dependent variable for each model was the PMPM cost, which is the total cost divided by the total annual membership months (average membership per month over the year, multiplied by 12) of the managed care organization (MCO) that was assumed to sponsor the intervention.

Each model was simulated over 1,000 iterations using Monte Carlo simulation (Winston, 1966), resulting in a distribution of 1,000 possible PMPM cost values for each intervention.

This Technical Appendix presents the details of the four PMPM cost distributions for each intervention and the details of the assumed values of the cost drivers used as inputs to each model.

Monte Carlo Simulation and the "Flaw of Averages"

Each cost model must take into account the fact that the "average" value that is entered for any of the multiple variables represents nothing more than one of many possible values. In fact, the average value may not even be the most likely value to occur in the real world if the distribution of all possible values is highly skewed, positively or negatively.

Whenever most people are told of an average value (e.g., average number of outpatient visits per closed outpatient episode), they generally do not consider the impact of variation around that average value. If they do consider possible variation, they generally assume a symmetrical distribution of variation around the average value. This type of distribution is called a "normal" distribution, and it is the distribution that most people implicitly assume in their heads when they think about risky variation.

The problem with that kind of thinking, however, is that most distributions of health care services and costs are not normally distributed. Rather, because there are a small number of very high values that "drag up" the average, they are "skewed" distributions, wherein the average value is greater than the "modal" (i.e., most likely) value. In other words, there are small probabilities of very large values and very large probabilities of moderate or small values.

The page limitations do not allow a full exposition of the various types of theoretical statistical distributions that may best describe such variables as Users/1,000, Units/User, Cost/Episode, and Cost/User/Year. Some of these distributions can be extremely skewed (e.g., Pareto distributions) and others less skewed or nearly normal (e.g., Poisson distributions). Furthermore, the reliability of the average that can be expected is a function of the total number of entities or events being considered. With very large populations and very large numbers of episodes and service units, some skewed distributions will begin to approach "normality" in their shape.

Because variation is not likely to be symmetrical, one should not look only at average values for such variables. Understanding and measuring the possible variation above or below the average that can occur in both cost and utilization variables is critical to estimating the possible range of costs.

Controllable and Uncontrollable Sources of Variation

Not only does one need to measure the variation, one needs to understand the underlying factors that are driving the variation. Many sources of variation may be managed or controlled in order to reduce the upside variation. For example, formal algorithms for triage-to-service programs and formalized treatment protocols can reduce variation that arises from the day-to-day decisions made by clinicians. Some of the factors that affect variation cannot be easily managed and changed in the short run. For example, factors related to characteristics associated with a particular population of eligible members (e.g., poverty, underlying prevalence of disease, culturally learned values about treatment use) may not easily be changed.

Closely related to the distinction between controllable and uncontrollable variables is the distinction between variation that is uncontrollable because of randomness and variation that is controllable but represents uncertainty due to the ignorance of the model builder.

Variation Due to Chance (or "Probabilistic Variability") The first type, called "stochastic" or "probabilistic" variability, is the effect of chance and uncontrollable variation. Generally, such variation cannot be directly controlled by management decisions. (Note: such variation can sometimes be "influenced" in the long run through policy-related decisions and actions.) Examples of this type of variable are the percentage of mothers in the plan who will deliver a low-birth-weight baby or the percentage of teenagers in the plan who will become pregnant. These are examples of members with a certain type of condition or set of risk factors for which a preventive intervention is intended. MCOs are used to dealing with such variability using historical data that can provide a distribution of previous values from which they can derive a reliable "average" estimate of future demands of use.

For variables known to have systemic variability, the models used stochastic (probability) distributions from which the computer software could sample values from within a defined distribution of all possible values. This functionality in the spreadsheet was possible with an "add-in" type of software that supports Monte Carlo simulation. This "add-in" software, called "@Risk," allows any specific single value of a variable in the model (e.g., the percentage of teenage members who would become pregnant) to be replaced by a distribution of all possible values, a method known as Monte Carlo simulation (Winston, 1996).

For example, the variable "percentage of eligible members who will become teenage mothers" is represented in the model by a triangular distribution with three parameters:

1. The "minimum possible" value
2. The "most likely" value
3. The "maximum possible" value

During the simulation of the spreadsheet, with each "iteration" of the model, a different value would be "sampled" from among all possible values within the range of minimum and maximum values. For example, after thousands of iterations ran, an estimate of the "average percentage of member lives that will be teenage mothers" would be based on the average of these thousands of values sampled during the simulation. The initial values used to establish the parameters of the distributions were based on the best available data for each variable. For example, U.S. Census Bureau data listing the percentage of women ages 14 to 19 who had a live birth in the most recent year for which data were available (Bureau of the Census, 1998) were used to estimate the number of eligible members who would become teenage mothers.

Variation Due to "Unknowns"

The second type of variability is due to the uncertain knowledge of the modeler. Such uncertainty represents the model builder's lack of knowledge about the actual value of some variables. Although the model builder may lack knowledge about the proper values to give to these types of variables, their values are readily known or controlled by the system operators. For example, the salary level and fringe-benefit costs of various staff working within different managed care plans are "unknown" variables in the model, not because these values randomly fluctuate within any given MCO but because the model builder is not certain what values would fairly represent the universe of all MCOs.

For variables whose values were uncertain due to lack of knowledge about the specific operating costs (e.g., salary level of nurses) of a particular managed care plan that may wish to implement an intervention, four alternative fixed values were used to reflect a reasonable range. A different one of the four values would be used during each scenario simulation, consisting of 1,000 iterations per simulation. A social worker's salary, for instance, could be set at $30,000 for one 1,000-iteration simulation, $35,000 for another simulation, and $40,000 and $45,000 for the two remaining 1,000-iteration simulations. For example, during each of the four 1,000-iteration simulations of the Prenatal and Infancy Home Visits for High-Risk Mothers model, cost factors that could vary by chance within any given year for any particular managed care plan (e.g., rate of low-birth-weight births per 100 births) were simulated using stochastic distributions. Because there would be more than one uncertain variable in each model (e.g., salary level, average staff productivity level, percent of total expenses due to general and administrative [G&A] expenses), the four values were always ordered from least to most expensive.

Therefore, the first of the four simulations represents the combination of circumstances when all the least expensive values are assumed for each of the uncertain variables (the Least Expensive Scenario), while the fourth simulation represents the circumstances when all the most expensive values are assumed for each of the uncertain variables (the Most Expensive Scenario). The other two scenarios assumed values for uncertain variables that were intermediate between the least costly values and the most costly values. This pattern of assumed values was illustrated in Table A.1.

The simulation of each of the model's four scenarios produces four distributions of possible values of the output variable PMPM cost. Therefore, the result of the cost simulation of each intervention can be expressed as a distribution of possible PMPM costs, for each of the four scenarios. While the single PMPM cost reported in the parent publication represents the midpoint value between the median cost of the Least Expensive Scenario and the median cost of the Most Expensive Scenario, this Technical Appendix presents greater details on the cost distributions for all four scenarios.

Thus, by using the Monte Carlo simulation, a continuum of probabilities can be generated, reflecting a continuum of possible PMPM costs based on the potential variabilities of the cost drivers entered into a model, outlined in Table A.1. Such cost drivers include the types of enrollees (public or private), prevalence of conditions, participation rate in the intervention, time, intensity, and staffing pattern to deliver the intervention, salaries of staff, fixed and variable expenses, and administrative overhead. Any managed care plan considering implementing an intervention can assume that its likely PMPM cost is somewhere between the Least Expensive Scenario and the Most Expensive Scenario.

Assessing the Cost for a Specific Managed Care Organization

Which of the four cost scenarios is most applicable to any specific MCO would depend on a number of factors, such as the demographics of its membership and the prevalence of the conditions targeted by each preventive intervention. For example, with reference to the Prenatal and Infancy Home Visits intervention, if the MCO has a predominantly Medicaid-eligible population of members, with a high prevalence of teenage mothers and higher risk pregnancies, it should consider the higher end scenarios that assume a higher prevalence. If its membership is predominantly a commercial population of employed and well-educated members with a lower-than-average birth rate and incidence of high-risk pregnancies, the MCO should choose the Least Expensive Scenario.

Another consideration should affect the choice of scenario. Each preventive intervention model was designed on the basis of a number of different published studies specific to that type of intervention; each study was not a strict replication of the other. In most cases, there were variations in the specifics of each intervention. For example, among the various studies on Health Promotion Through Self-Care Education, the research teams used a variety of specific components. One study might have used the following components:

1. Group-based health education classes
2. Self-care guidelines and booklets
3. Videotapes
4. Access to a self-care hotline where questions would be answered by a trained nurse or health counselor
5. Individualized letters from a primary care physician recommending certain health-related behavior changes

Another study of self-care might have used different components:

1. An individualized health risk appraisal assessment
2. Personalized reports on recommended health-related behaviors based on the risk appraisal
3. Individual sessions with a nurse or health counselor
4. Access to a health drop-in center

A particular MCO may wish to use only some of the components of both studies. Therefore, the Self-Care model incorporates all nine components and estimates the PMPM cost for each component as well as the total PMPM costs for all nine combined. For such circumstances, tables in this appendix provide the Least Expensive and Most Expensive PMPM cost for each separate component.

It is highly recommended that any MCO considering the implementation of any of these six preventive interventions read the original research studies to assess the applicability of the specific components used by the researchers.

Other General Assumptions

In addition to the general assumption that such interventions would be offered on an ongoing basis, assumptions of costs were generally fiscally conservative or toward the "high side." For example, some interventions required a receptionist to hand out an assessment form to patients arriving in the waiting room. The time and labor costs for this task were estimated and added to the total cost estimates. In most circumstances, however, such effort, time, and costs would not actually be incremental because they could readily be incorporated into the receptionist's regular patient-related duties.

In addition, each intervention's cost assumptions included the cost of training staff to carry out the intervention. To that extent, the costs are based on the first-year startup costs. The effective PMPM costs would likely go down in subsequent years if the staff did not have to be retrained each year.

The following information is provided for each of the six recommended interventions.

Results

For each intervention, the model assumed an MCO membership of 100,000. The PMPM cost of each scenario within each intervention is calculated as its total aggregate cost divided by 100,000, divided by 12. This publication reports a single PMPM cost, calculated as the midpoint between the median cost of the Least Expensive Scenario and the median cost of the Most Expensive Scenario. This appendix provides statistical details (minimums, maximums, means, medians, and 5th and 95th percentile values) of the cost distributions of all scenarios for each intervention.

It is important to note that the PMPM cost of each intervention is calculated on the entire membership of 100,000, not just the subset of members that corresponds to the target group for the intervention. For example, if an intervention costing a total of $520,000 is targeted toward children, who represent 26,000 of the 100,000 members, the PMPM would be calculated as ($520,000/100,000/12 = $0.43), not ($520,000/26,000/12 = $1.66). In other words, the preventive intervention costs are calculated at a rate representing the amount that an MCO would have to add to every member's premium.

Design and Input Values Used in the Model

"Design" means identifying the set of variables used as inputs for calculating the cost drivers and how these inputs were organized and used in calculations. "Values" are the figures assigned to the input variables used during each simulation. For example, when social worker's salary was an input variable, the model used four values for the salary, ranging from a low value to high value (e.g., $30,000, $35,000, $40,000, and $45,000). In most cases, the values assigned to an input variable were actually a distribution of values. For example, a value of 15 minutes for a staff activity may represent a normal distribution with a mean of 15 minutes and a standard deviation of 5 minutes.

In general, when there was no relevant benchmark information available in the published research or other sources, "best guesses" were the basis of reasonable values. When using best guesses, the model always used a value that was biased in the direction that would drive costs up. Therefore, the models are producing a conservative result-that is, cost estimates that are probably on the high side.

Discussion

A brief discussion of any issues specific to that model that could affect its implementation in an MCO follows the presentation of cost results.

Results

Model 1: Prenatal and Infancy Home Visits for High-Risk Mothers

This cost model was designed based on an amalgamation of two publications-Olds, Henderson, Phelps, Kitzman, and Hanks (1993) and Ramey and Ramey (1992)-and reviewed by Dorfman (2000) in references respectively numbered 2 and 5. A third study, reviewed by Dorfman and that supported the final recommendations, was not included in this cost model. It used an additional classroom-based intervention and thus would have required a separate cost model (Field, T., Widmayer, S., Greenberg, R., & Stoller, S., 1982).

PMPM Cost

Table A.2 summarizes the statistical parameters of the distribution of PMPM values for each scenario. The Least Expensive Scenario has a mean PMPM cost of $0.58 and the Most Expensive Scenario has a mean PMPM value of $1.49. The median PMPM cost in all scenarios is lower than the mean cost because the mean value in all four scenarios was being "dragged up" by a few high-cost outlier values.

To further assist with the interpretation of the results, upper and lower limits were established, respectively, at the 95th percentile of the Most Expensive Scenario ($1.47) and at the 5th percentile of the Least Expensive Scenario ($0.30). Across all four scenarios, the lower limit is $0.51 and the upper limit is $1.68, with 90 percent of the estimated 4,000 PMPM values across the four scenarios falling within this range of $1.17. In other words, it can be said with 90 percent certainty that the actual PMPM costs for this type of intervention will be between $0.30 and $1.47. While that range of $1.17 may seem relatively large, it is more likely that the range will be much smaller depending on which of the four scenarios is representative of the cost structure (e.g., salaries, overhead) of a particular MCO. For example, as shown in Table A.2, the range in the average PMPM cost of Scenario 1 is from a minimum of $0.46 to a maximum of $0.73 (i.e., a range of $0.27). Scenario 4 has the greatest range ($0.72) between the minimum and maximum PMPM (i.e., $1.17 minimum to $1.89 maximum).

Figure A.1 illustrates the distributions of simulated values for each of the four scenarios.

As can be seen in Figure A.1, as the mean PMPM cost gets higher, so does the variability around the mean. These mean PMPM values are the average of the 1,000 iterations within each scenario, and the values used for uncertain variables got progressively higher with each scenario. These results reveal the amplification effects of variability coupled with uncertainty.

Design and Input Values Used in the Model

Number of Lives Covered by the Managed Care Plan
This model, as well as all other models, assumed there are 100,000 enrolled lives (members) in the MCO.

Number of Intervention Cohorts Served Within a 12-Month Operational Cycle
Because many of the preventive interventions required less than a full year, the model used 26 weeks (i.e., half a year) as the number of weeks required to start and complete a preventive intervention for a single cohort of participants. The model also assumed that the program would run throughout the year, so the total number of participants could be doubled if the intervention was offered twice in one year.

Size of the Cohort That Participates in Each Intervention Cycle
Based on the enrolled members, the first crucial calculation must estimate the average number of persons who will participate in the intervention. Most often the published research specifies some number of participants but does not provide enough information to allow a calculation of the participation rate from among all the persons who had access to the intervention or were "approached" and invited to participate.

In determining what values to use to populate these variables, U.S. Census Bureau data for 1998 for the percentages of the general population represented by females of each age group (teens = ages 14 to 19, adults = ages 20 to 44) who were potentially able to bear children were reviewed as well as separate tables on the birth rates of these age groups. The rate of low-birth-weight babies was estimated from the managed care plan "HEDIS Report Card" developed from 1995 to 1996 for the National Council on Quality Assurance (NCQA). (This measure is no longer monitored by NCQA's HEDIS Reports.) Conservatively large percentages for initial rates of participation ("Starters") and for rates of completion ("Completers") were used. The model assumed that adult women would have a higher rate of starting and completing the program than teens.

To establish the average number of participants, a series of assumptions and calculations was required. Starting with the number of enrolled lives (100,000), the following variables were calculated:

1. Percentage of members having the attribute for which the intervention is intended
2. "Starters": the percentage of the above number who agree to start participation
3. "Completers": the percentage of the Starters who complete the program
4. Average number of participants, as estimated by this formula: [STARTERS + COMPLETERS] / 2

Attrition

The above calculation assumes that the rate of attrition throughout the time period of the intervention is uniform. Therefore, the average number of participants is the number active at the midpoint between the start and the end of the program. This "Average Participants" value is used for further calculations of costs. For example, Average Participants is used to calculate the number of classrooms needed if each class were to last X hours and meet Y days a week for Z consecutive weeks and have a limit of no more than N (number of) participants meeting in each classroom.

Time and Services

For each setting, the model assumed that all participants would undergo an initial private, one-on-one assessment and orientation visit with a social worker, lasting an average of 1 hour (standard deviation [SD] = 15 minutes).

The next set of critical calculations was to determine the average time each participant would spend in the program, which is used for subsequent calculations of the units of service that each participant would receive. For example, if the average participant spends 24 weeks in a 26-week program and receives 1 visit per week of participation but has a 5 percent no-show rate, the model can calculate that this participant will receive 23 visits. The following factors were used in making these calculations:

1. Frequency of scheduled visits per week: The model assumed a value of 0.5 or 1 visit every other week.
2. Percentage of scheduled visits that were not completed (e.g., mother is not home when the staff arrive): The model assumed 10 percent were not completed.
3. Average round-trip driving time per visit: The model assumed 20 minutes per round trip.
4. Average visit time in the home: The model assumed 2 hours based on the literature.

Using these estimates, the model can calculate the staff hours spent in driving and the staff hours spent in providing the intervention services within the home.

The model requires the variable costs of scheduled but incomplete visits because of the cost incurred (e.g., variable expenses, gas, staff time) by driving out to a home as well as completed visits because of their costs (e.g., supplies, gas, staff time).

The model also asks for salary levels, fringe-benefit rates, staff productivity, supervisory staff, and G&A expenses plus profit margin. The same values were used for these as were used in the classroom version.

Because there is inherent variability in the "average weeks per participant" across all participants, the model asks for four parameters that will establish a "beta-subjective" stochastic distribution for the average number of weeks, from which it will sample possible values during a simulation:

1. The minimum number of weeks
2. The maximum number of weeks (which cannot exceed the number of weeks the program is operational)
3. The modal number of weeks (i.e., the number of weeks characteristic of most participants)
4. The average number of weeks (the number of weeks for each participant added together and divided by the number of participants)

The average weeks per participant, along with other estimates such as the maximum size of a group using a classroom, is later used for further "downstream" calculations, such as the average participants active per week, the number of classrooms needed to support this number of participants, and the fixed costs of each classroom.

Once the number of required classrooms was calculated, it was necessary to have estimates of the number of staff present for each group meeting being held in each classroom. The total necessary staff hours, based on the number of classroom meetings per week and the number of weeks the program is operational, allows for the calculation of the number of full-time equivalent (FTE) staff that would have to be employed. The model also calls for the types of staff to be hired so average salaries can be entered. Because Total Staff Hours Required assumes these hours are "productive" time, the number of FTE staff needing to be hired must be adjusted upward by a factor representing the percentage of time that the average FTE staff is not productive (e.g., because of sick leave, vacation, or internal meetings). Again, a very optimistic range for estimating the rate of productivity was used (from a high of 90 percent for the Least Expensive Scenario to a low of 60 percent for the Most Expensive Scenario).

The model also asks for entries of the one-time startup costs and annual fixed, as well as variable, expenses.

Fixed expenses would be such items as rent, furniture, computer equipment and software, and any other supplies that would be required (e.g., sensory stimulation toys for the mothers to use with the children). Direct expenses are entered on a "per classroom" basis, with any equipment that is "shared" being proportionately assigned to each classroom. Again, relatively generous amounts were entered for such items.

The model also asked for the variable expenses on a "per class meeting" basis or a "per home visit" basis. Examples of variable cost per class meeting would be any certain supplies or other items that are consumed at each meeting (e.g., snacks for mother and child, transportation vouchers). A "per home visit" cost would be transportation to the participant's home.

Once it has the number and type of staff needed to meet the demand for each intervention within each modality, the model asks for the percentage of each employee's time devoted to this program. The model assumed 100 percent for each direct service staff member; 50 percent for a manager, but at a higher salary; and 25 percent for FTE support staff for clerical duties (e.g., sending out invitations to participate, recording attendance, ordering necessary supplies). The model also required their average salary and the percentage of salary spent on fringe benefits.

The final variable that had to be valued is the percentage of total expenses required to cover G&A expenses plus any profit margin. A fairly generous amount of 10 percent, increasing by 1 percent for each of the four scenarios from Least Expensive to Most Expensive, was entered.

Model 2: Smoking Cessation Targeted at Pregnant Women

This cost model was designed on the basis of an amalgamation of three publications-Marks, Koplan, Hogue, and Dalmat, 1990; Windsor, Lowe, Perkins, Smith-Yoder, Artz, Crawford, Amburgy, and Boyd, 1993; and Cummings, Rubin, and Oster, 1989-and reviewed by Dorfman (2000) in references respectively numbered 1, 3, and 26.

The intervention that was most extensive (Windsor et al., 1993), targeted toward pregnant women receiving prenatal care in a public health clinic, consisted of the following components:

• A brief (15-minute) counseling session, supplemented by the use of written materials
• Medical chart reminders during prenatal visits
• Followup phone calls and letters
• A "buddy contact"
• A 2-minute no-smoking reminder embedded within a 20-minute prenatal education class

The second publication (Marks et al., 1990) reported using only a single 15-minute counseling session, simple instructional materials, and two followup phone calls. The third publication (Cummings et al., 1989) reported on the cost-effectiveness of a 4-minute counseling session by a physician, a 1-year followup, and a self-help booklet administered to a "hypothetical" group of adult male and female patients.

Once again, in order to make the cost model as generic as possible, it was designed to include all the various types of component interventions across all three studies.

PMPM Cost

Table A.3 summarizes the statistical parameters of the PMPM costs for the most expensive smoking cessation intervention (Windsor et al., 1993) of the three publications reviewed by Dorfman (2000). The Least Expensive Scenario estimates an average PMPM of $0.02, with the Most Expensive Scenario totaling not much more ($0.06). Again, as in the Prenatal and Infancy Home Visits model, variability increases as the average cost increases. Across all four scenarios, 90 percent of the estimated PMPM values are within the range of $0.02 to $0.06.

Figure A.2 graphically portrays the range of costs and the variability around the mean PMPM costs of each scenario. Again, as with the first model, as the assumed costs of the unknown variables increases, the variability increases as well.

Design and Input Values Used in the Model

Number of Lives Covered by the Managed Care Plan
This model, as well as all other models, assumed there are 100,000 enrolled lives (members) in the MCO.

Number of Intervention Cohorts Served Within a 12-Month Operational Cycle
This intervention was assumed to be one that could be offered on an ongoing basis to patients as they came in for their routine medical visits (i.e., prenatal visits, in the case of pregnant women).

Number of Likely Participants Completing the Intervention
The same information that was used for the first model was used to populate this model, namely, estimates of the number of members who would be women in their childbearing years. In determining what values to use to populate these variables, U.S. Census Bureau data for 1998 were reviewed for the percentages of the general population represented by females of each age group that were potentially able to bear children (teens = ages 14 to 19, adults = ages 20 to 44), and separate tables on the birth rates of these age groups.

Once the number of likely pregnant patients in a year was estimated, an average of 21 percent of them could be estimated to be smokers, as reported by Marks et al. (1990) based on a "1985-1986 Behavioral Risk Factor Surveillance System . . . of American women from 25 states and the District of Columbia" (Dorfman, 2000, p. 31). In the actual calculations, the model used a triangular distribution (minimum, most likely, maximum) of values around this estimate of 21 percent for each of the four scenarios:

In other words, in Scenario 1 the model assumed a minimum prevalence of smoking among pregnant women at 18 percent, a maximum of 22 percent, with a most likely value of 20 percent. Each successive scenario assumed higher values for each of these three parameters, increasing by 1 percent.

Having established the percentage of members having the attributes of pregnancy and smoking, the model estimated the number of such members who would be willing to participate. Based on a figure of 93.7 percent reported by Windsor et al. (1993), the model used a range of estimates of the percentage of "Starters": the percentage of the pregnant smokers that agree to start participation:

Next, the model had to estimate the "Completers": the percentage of pregnant smokers that would complete the program:

These values were selected based on attrition rates reported by Windsor et al. (1993). Women left Windsor's planned intervention for such reasons as losing benefit eligibility, having abortions, or having miscarriages.

As in Model 1, the Average Number of Participants was estimated by this formula: [STARTERS + COMPLETERS] / 2.

Materials, Staff Time, and Related Services

The model assumed each patient received in person two pamphlets and a "smoking cessation guidebook" or "self-help book." Items were assumed to cost $4. Cummings et al. (1989) reported an estimate of $2 for a self-help booklet, and Windsor et al. (1993) estimated $6 per patient for the cost of materials, reproduction, and labor.

The value of nurses' time was the same as that used in the first model, based on a salary of $50,000 incrementing in each scenario by $1,000, an average productivity of 70 percent of payroll hours, and a 29 percent fringe-benefit rate.

In the second component, Windsor et al. (1993) reported that each patient received patient reinforcements through a "medical letter" emphasizing the importance of smoking cessation and had a reminder placed in his or her medical chart so the doctor could ask questions at subsequent prenatal visits. The clerical time required for these activities was estimated at a mean of 10 minutes (SD = 3 minutes). Clerical salaries were estimated to start at $20,000 (with $1,000 increments for each successive scenario) with a productivity rate of 80 percent and a fringe-benefit rate of 29 percent. The letter and postage costs were estimated at $0.41 per patient.

The third component reported by Windsor et al. (1993) also reported on "social supports," which consisted of the following activities:

• Sending a "buddy letter" with a contract and tipsheet to each patient
• Sending a quarterly newsletter to each patient
• Giving two pamphlets to each patient

These five mailings were assumed to require an average of 10 minutes of clerical time (SD = 3 minutes) and $0.45 for reproduction and postage per patient.

The model also builds in the cost for the 2-minute reminder delivered by a nurse as part of a 20-minute prenatal class.

The model assumed there were no other variable or one-time startup costs beyond the smoking cessation guides/self-help booklets and pamphlets.

The final variable that had to be valued is the percentage of total expenses required to cover G&A plus any profit margin. Each of the four scenarios used 10, 11, 12, and 13 percent, respectively.

Model 3: Targeted Short-Term Mental Health Therapy

This cost model was designed on the basis of interventions described in research by Finney, Riley, and Cataldo (1991) and Goldberg, Allen, Kessler, Carey, Locke, and Cook (1981) and reviewed by Dorfman (2000) in references respectively numbered 15 and 41. As with all the other models, this model was designed to estimate PMPM costs for a managed care plan with 100,000 members that implements a brief psychotherapy (6 to 16 visits) benefit for its members age 0 to 17 and for its adult members (ages 18 to 65).

Finney et al. (1991) focused on children ages 1 to 15 treated with brief therapy within a pediatric clinic of a staff-based health maintenance organization (HMO). Goldberg et al. (1981) did their research based on the claims paid for psychotherapy provided to adult members (ages 18 to 65) of the Federal Employees Health Benefit Plan. The cost model was designed to accommodate both child and adult age categories, and the cost results of each subgroup were combined, assuming an MCO would use this intervention with either group. Both age categories had a similar cost design but different input assumptions (i.e., values assigned to various stochastic distributions).

PMPM Cost

Table A.4 summarizes the primary statistics generated for PMPM costs for each scenario. The average PMPM cost for the Least Expensive Scenario was $1. The average PMPM cost for the Most Expensive Scenario was $1.96. Across all four scenarios, the lower limit (5th percentile) is $0.17 and the upper limit (95th percentile) is $3.60, with 90 percent of the estimated 4,000 PMPM values across the four scenarios falling within this range of $3.43.

This statistical pattern of costs is unusual compared to all the previous models. The distribution of potential costs is well illustrated in Figure A.3.

The distributions of estimated PMPM costs for all four scenarios are considerably more uniform in shape, with more variability. The variability of each scenario's distribution of PMPM costs is quite large, ranging from $0.29 to $1.12. The average range (maximum PMPM cost minus minimum PMPM cost) across all four scenarios is almost $2. Ninety percent of the estimated 4,000 values are between $0.17 and $3.60, a range of $3.43.

The relatively "uniform" shape of each distribution implies that a wide range of PMPM values have about equal likelihood of occurring. Clearly, the Most Expensive Scenario is also the one with the greatest variability.

The uniform shape of these distributions is due to the distributions and values the model assumed in its design, based on the data reported in the literature. According to Goldberg et al. (1981), the proportion of persons receiving 1 to 5 visits, 6 to 15 visits, and more than 15 visits was about the same. As the primary driver of total costs, this uniform distribution of visits per participant accounts for the uniformity of the final PMPM distributions.

Design and Input Values Used in the Model
Membership and Treated Prevalence

The model assumed any MCO would use "medical necessity" criteria when evaluating the need for brief psychotherapy, as was used in the study by Goldberg et al. (1981). Therefore, the model assumed that indicators of treated prevalence would best estimate the number of persons who would receive brief therapy.

For the child subgroup, the model assumed a prevalence rate of 9 to 12 percent (in 1 percent increments in each scenario) based on median estimates from a meta-analysis of the epidemiological research reported by Friedman, Katz-Leavy, Manderscheid, and Sondheimer (1996). A study on treated prevalence of mental health problems among children and adolescents indicated that 23 percent of privately insured children with any mental health disorder (serious emotional disturbance [SED] or non-SED) received some outpatient therapy (Burns, 1991).

For the adult subgroup, the model assumed an outpatient treated prevalence rate of 14 to 15 percent (in 0.5 percent increments) based on an average treated prevalence rate for adults based on epidemiological research reported by Bourdon, Rae, Narrow, Manderscheid, and Regier (1994). That rate of treated prevalence is further reduced by 44 percent, a rate reported by Goldberg et al. (1981), of index patients with psychiatric diagnoses who received zero visits.

Volume of Service, Type of Provider, and Copayments

The child subgroup assumed a "triangular" distribution with an average of 2.75 visits per child (minimum = 1, most likely = 1.25, maximum = 6) to describe the frequency of therapy visits. Finney et al. (1991) reported a range of 1 to 6 visits and an average of 2.4 visits, but no measure of variability around this mean.

The model assumed each therapy session per child participant lasted 60 minutes, which includes the 50-minute sessions reported by Finney et al. (1991) and Goldberg et al. (1981) and 10 minutes for clinical record keeping. Based on the data reported by Goldberg et al. (1981), the model assumed a uniform distribution of eight visits per adult participant, each one requiring 50 minutes of therapist time and 10 minutes for record keeping.

The model assumed that the therapy was provided by a licensed mental health professional (psychologist or psychiatric social worker) with an annual salary of $50,000, a fringe-benefit cost of 29 percent, and a productivity rate of 70 percent, yielding an "effective cost per hour" of $44.30.

Because most insurance plans, including HMOs and behavioral health care "carve outs," have a mental health copayment requirement, the model assumed a copayment of $20, $15, $10, and $5, respectively, for the four scenarios from Least Expensive to Most Expensive. In other words, the copayment effectively reduces the "effective cost per hour" by $20 to $24.30 for the Least Expensive Scenario and by $5 to $39.30 for the Most Expensive Scenario. The model assumed 100 percent of all copayments were collected.

Other Expenses

Finney et al. (1991) reported that "behavioral treatment guidelines" (e.g., how to respond to bed wetting, the use of "timeouts") were given to the parents of the children in treatment. The model assumed a cost of $2 to $5 in $1 increments for the cost of reproduction and distribution of these guidelines.

Finney et al. (1991) also reported that "most families also received a number of planned telephone contacts after therapy was begun to ensure adequate implementation of recommended therapeutic techniques and to troubleshoot problems" (p. 452). Therefore, the model assumed 100 percent of the families would each receive two phone calls (i.e., using a triangular distribution with a minimum = 1, most likely = 2, and maximum = 3). The model assumed the phone calls took 5 minutes (SD = 2 minutes) and were made by the therapist.

The model assumed no supplies or phone call expenses for the adults.

The model also increased the total cost by applying a G&A overhead plus profit rate of 10, 11, 12, and 13 percent to the direct services cost in each of the four scenarios.

Model 4: Self-Care Health Education for Adults and Older Adults

This cost model was designed on the basis of an amalgamation of six publications-Kemper (1982); Vickery, Kalmer, Lowry, Constantine, Wright, and Loren (1983); Fries, Fries, Parcell, and Harrington (1992); Kemper, Lorig, and Mettler (1993); Leigh, Richardson, Beck, Kerr, Harrington, Parcell, and Fries (1992); and Vickery, Golaszewski, Wright, and Kalmer (1988)-and reviewed by Dorfman (2000) in references respectively numbered 29, 32, 40, 43, 51, and 52. Each study described a variety of interventions provided to adults or older adults. Five of the six studies were conducted within a managed care setting and one within the worksite.

Across the six studies, there was a wide range of activities that were provided to participants in order to promote positive health behaviors and self-care:

1. Workshops to train nurses to provide psychoeducational support to patients, including written materials, pamphlets, and booklets
2. Self-care guidelines, newsletters, books, and booklets for participants
3. Videotapes covering self-care
4. Access to telephone information service staffed by a nurse
5. Individualized health conferences with a nurse
6. Computer-based, serial, personalized health risk reports
7. Individualized recommendation letters and reports
8. One-on-one educational sessions with a physician
9. Access to a "self-care drop-in center" (Dorfman, 2000, p. 21)

The model was designed to incorporate all nine activities and estimate the PMPM costs of all nine combined. Therefore, the PMPM costs are overstated for any MCO that may wish to use only a subset of all activities.

PMPM Cost

Table A.5 summarizes the PMPM cost parameters that were generated in a simulation of Model 4. The average PMPM cost for the Least Expensive Scenario was $1.06. The average PMPM cost for the Most Expensive Scenario was $2.02. Across all four scenarios, the lower limit (5th percentile) was $0.99 and the upper limit (95th percentile) was $2.14, with 90 percent of the estimated 4,000 PMPM values across the four scenarios falling within this range of $1.15.

The results are presented graphically in Figure A.4. The distributions of PMPM values for each of the four scenarios of this model are clearly more separated than any of the other models. This large degree of separation is due to the wide range of assumed values for the input values of each scenario.

Design and Input Values Used in the Model

The model begins with an estimation of the number of adults and older adults who are members of an MCO with 100,000 members. Based on 1990 U.S. Census Bureau figures, these percentages were valued at 59 percent for adults and 11 percent for older adults. It then calls for an estimation of the percentage of each age group that is likely to agree to participate in a "Health Promotion Campaign" (i.e., a series of health promotion and self-care activities throughout the year). These estimates for adults ranged from 45 to 90 percent in increments of 15 percent for each scenario (Least Expensive to Most Expensive). For older adults the percentage started at 60 percent (Least Expensive Scenario) and went as high as 90 percent (Most Expensive Scenario) in increments of 10 percent.

Because some activities are costed out by household (e.g., a videotape mailed to a home), it is necessary to estimate the number of covered members per household for adults and older adult members. Based on data reported by Vickery et al. (1983), the ratio of older adult participants to households was set from 1.26 (Least Expensive) to 1.20 (Most Expensive) in increments of 0.02. For adults, this ratio ranged from 3 (Least Expensive) to 2.4 (Most Expensive) in increments of 0.20.

The rest of the model consisted of ten separate modules reflecting the various types of specific intervention activities that were described in the various studies reviewed by Dorfman (2000). Each module allowed for the cost estimation of written material as well as clerical and professional labor spent in conducting one-on-one activities or group activities. In each module, the model used a separate estimate for the level of participation by adults or older adults. For example, although 9,000 adults may agree to participate in the series of activities, only 25 percent may actually show up to participate in a particular activity, such as educational workshops.

Staffing and Materials

Slightly different staff salaries, fringe-benefit rates (29 percent), and rates of productivity were assumed in Model 4 than were assumed in Models 1 through 3:

• Clerical at $20,000 in $500 increments and 80 percent productivity
• Nurses at $50,000 in $1,000 increments at 70 percent productivity
• Psychologists at $50,000 in $1,000 increments at 70 percent productivity
• Physicians at $100,000 in $2,000 increments and 70 percent productivity

Table A.6 summarizes the values assumed for each module in the model. The first column is a summary description of the activity. The second column is the percentage of total participants assumed to participate in each activity. The next four columns are the four values assumed for each successive scenario for the cost of purchasing or reproducing whatever supplies, booklets, or written material is required of each activity. The seventh column notes the type of professional staff member who carries out the activity. Columns 8 and 9 are the assumed mean and standard deviations of the assumed time required for each activity. The third-to-last and second-to-last columns reflect the total aggregate costs for adults and older adults, and the last column shows the PMPM costs for both age groups combined.

Model 5: Presurgical Educational Intervention With Adults

This cost model was designed on the basis of three research publications-Devine and Cook (1983); Devine, O'Connor, Cook, Wenk, and Curtin (1988); and Egbert, Battit, Welch, and Bartlett (1964)-and reviewed by Dorfman (2000) in references respectively numbered 35, 36, and 38. One publication (Devine and Cook, 1983) was a meta-analysis of 49 other studies. This meta-analysis and the remaining two studies described a variety of component interventions provided to adults undergoing a wide range of inpatient surgical procedures:

• Nurse-conducted group workshops, which focus on the benefits of psychoeducational supports, including written materials and videos
• Presurgical and postsurgical visits by an anesthetist
• Skills or exercises training to promote postsurgical recovery
• Psychosocial support by a health care provider

PMPM Cost

Table A.7 summarizes the PMPM cost parameters that were generated in a simulation of Model 5. The average PMPM cost for the Least Expensive Scenario was $0.22. The average PMPM cost for the Most Expensive Scenario was $0.31. Across all four scenarios, the lower limit (5th percentile) was $0.16 and the upper limit (95th percentile) was $0.40, with 90 percent of the estimated 4,000 PMPM values across the four scenarios falling within this range of $0.24. Figure A.5 presents the results graphically.

Design and Input Values Used in the Model
Membership and Participation

The level of agreement to participate for the Least Expensive Scenario was set at 50 percent, increasing in 5 percent increments up to 65 percent for the Most Expensive Scenario.

Staffing and Materials

While the original research reports that an anesthetist made bedside visits to patients the night before the surgery, the model assumed that a nurse with specialty training in anesthesiology could carry out this task.

Table A.8 summarizes the assumed levels of participation for each component activity, the costs for the materials and supplies for each scenario, and the assumed time and effective cost per hour for the nurses, psychologists, nurse anesthesiologist, and health counselor.

As expected, the most expensive component would be the time spent pre- and postsurgery. The postsurgical component cost more than the presurgical component because it was assumed that most patients would receive two postsurgical visits before their discharge.

Model 6: Brief Counseling to Reduce Alcohol Use

This model was designed on the basis of four research publications-Bien, Miller, and Tonigan (1993); Fleming, Barry, Manwell, Johnson, and London (1997); World Health Organization (1996); and Fleming, Barry, Manwell, Adams, and Stauffacher (1999)-and reviewed by Dorfman (2000) in references respectively numbered 33, 39, 50, and 53. As with all the other models, this model was designed to estimate PMPM costs for a managed care plan with 100,000 members that implements a screening and brief intervention to reduce excessive alcohol use by its adult members (ages 18 to 65) as well as its older members (age 66 and older), male and female.

PMPM Cost

Table A.9 summarizes the primary statistics generated for PMPM costs for each scenario. The average PMPM cost for the Least Expensive Scenario was only $0.36. The average PMPM cost for the Most Expensive Scenario was $0.85. Across all four scenarios, the lower limit (5th percentile) is $0.31 and the upper limit (95th percentile) is $0.93, with 90 percent of the estimated 4,000 PMPM values across the four scenarios falling within this range of $0.62.

If all the input variables were at their maximum possible values, there is a 90 percent probability that the PMPM cost would be $0.93, although it would probably be less.

Figure A.6 is a graphic representation of the distribution of average PMPM costs for each scenario. As with Model 1, as the average PMPM cost increases, so does the variability surrounding the average.

Design and Input Values Used in the Model
Screening for Alcohol Use

The model assumed 68 to 71 percent (in increments of 1 percent for each scenario) of those screening positive would agree to go through the initial 30-minute interview with a nurse to further screen participants and collect baseline behavior on health-related behaviors (e.g., smoking, exercise).

Based on data reported by Fleming et al. (1997), the model assumed 42 to 45 percent (in increments of 1 percent for each scenario) of those completing this interview would go on to start participation in the intervention. The model assumed 95 to 98 percent (in increments of 1 percent for each scenario) of the "Starters" would be "Completers."

Service Interventions

As described by Fleming et al. (1997), the model assumed participants would receive two brief counseling sessions with their primary care physician, each lasting 15 minutes (SD = 3 minutes). This time includes the few minutes required for the physician to enter brief documentation in the medical record.

Each participant was given a "workbook." The workbook used by the participant and the physician "contained feedback regarding current health behaviors, a review of the prevalence of problem drinking, a list of the adverse effects of alcohol, a worksheet on drinking cues, a drinking agreement in the form of a prescription, and drinking diary cards" (Dorfman, 2000, p. 61). The model assumed this workbook was provided to 100 percent of the participants. The model assumed the cost per workbook for each of the four scenarios was $5, $6, $7, and $8, respectively, from least to most.

The model assumed that 100 percent of participants received a followup phone call by a nurse following each of the two sessions with the physician (mean = 5 minutes, SD = 2 minutes).

The cost of these interventions by clerical staff, nurses, and physicians was determined by multiplying the cost of a productive staff hour (based on salary, fringe benefits, and nonproductive time) against hours spent to train, including travel time. The annual salaries of each category of staff were assumed as follows: clerical, $20,000 with $500 increments for each scenario and 80 percent productivity; nurses, $50,000 with $1,000 increments and 70 percent productivity; physicians, $100,000 with $2,000 increments and a 70 percent rate of productivity.

Fringe-benefit costs were assumed at 29 percent for all personnel. The model assumed there were no expenses associated with the need for additional supervisory or management staff because such an intervention could blend into the ongoing clinical operations of each physician's office.

Physician Recruitment and Staff Training

Based on ratios of participants to physicians reported by Fleming et al. (1997), the number of physicians that would have to be invited to participate was estimated. Assuming a rate of agreement to participate at 80 to 95 percent in 5 percent increments for each scenario, the number of physicians to invite and the number needed to participate in order to handle the number of expected participants could be calculated. Invitation costs were estimated at $35 to $50 in $5 increments. For each scenario, from Most Expensive to Least Expensive, the model assumed there would be 4, 3, 2, or 1 doctor per office site. That way, the number of office sites where personnel and physicians would need to be trained could be calculated.

The model assumed that all involved office personnel would require some training on the use of the protocol. For each office site, the model assumed a 20-minute (SD = 5 minutes) training for clerical personnel who distributed and scored the health screening instrument and a 60-minute (SD = 5 minutes) training session for the nurses who would administer the interview and make the followup phone calls. The model assumed an initial training session of 60 minutes (SD = 10 minutes) for all agreeing physicians working in a single site. The model assumed two "booster" training sessions of 15 minutes each (SD = 10 minutes) for physicians.

The training costs were determined by multiplying the average salary and fringe-benefit costs of a "trainer" (salary, i.e., $40,000 in $1,000 increments for each scenario, with 70 percent productivity and 29 percent fringe-benefit costs) against time spent to train, including travel time. The model assumed there were no expenses associated with the need for additional supervisory or management staff because such an intervention could blend into ongoing office operations.

Because the original research by Fleming et al. (1997) reported a $300 payment to the physicians, the model assumed payments to each participating physician of $300, $500, $700, and $900 for each scenario. This payment would be made to compensate the physician for "lost patient revenue" related to the need for staff and physician to participate in the training.

As in Model 1, this model assumed some percentage should be added for G&A plus profit. A fairly generous amount of 10 percent increasing by 1 percent for each of the four scenarios from Least Expensive to Most Expensive was entered.

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