# A Report on the Actuarial, Marketing, and Legal Analyses of the CLASS Program. VII. Benefit Payments

Benefit payments are calculated by multiplying the number of beneficiaries times the average number of days in an episode of care times the daily benefit amount. Benefit payments are split into years by the use of continuance tables. This allows for the proper indexation of benefits and the discounting for present values. These calculations are done separately for those in a nursing home and those in home care. For those in a nursing home an episode of care is referred to as the length of stay and the beginning of the episode is marked by the admission into a nursing home. Key to the calculation of beneficiaries is the concept of an incidence rate, which is the number of persons with a new episode of care during the year divided by the number exposed to such an incident in the middle of the year. This is as opposed to a prevalence rate, which is the number of beneficiaries at any point in time divided by the total number of participants at that time.

The number of new beneficiaries each year is calculated as the number of policyholders not already in claim status times the incidence rate of new episodes of care. The incidence rate is adjusted for the effects ofantiselection and selection. Thus, the general equation for the number of new beneficiaries each year is:

NHA = (P – NHC) * IR * ASF * SF

Where:

NHA = the number of admissions to a nursing home each year

NHC = the number of beneficiaries already in a nursing home, i.e., in claim status

P = the number of policyholders in force

IR = the incidence rate

ASF = the antiselectionfactor

SF = the selection factor

The term (P - NHC) is referred to as the exposure to admission. The number of beneficiaries in claim status in home care is not subtracted from the number of policies to determine the exposure to admission because those in home care could transfer into a nursing home, just as those not yet in claim status could be admitted directly to a nursing home.

A similar equation is used to calculate the number of new beneficiaries that start an episode of care at home or in the community.

HCE = (P – HCC) * IR * ASF * SF

Where:

HCE = the number of episodes of care that start in home care each year

HCC = the number of beneficiaries already in home care, i.e., already in claim status

The ARC Model keeps track of new claims by age, sex, year of claim, issue year, and subsidy status. The dimensions of age, sex, and year of claim are necessary for projection purposes, because the continuation in claim depends on age, sex, and duration in claim. The dimension of issue year is kept track of for purposes of calculating premiums. Each year of issue must be charged a premium that will support that cohort from issue until the end of life. Therefore, the experience of each cohort of new policy issues is kept track of separately, and each is charged a unique premium. The dimension of subsidy status is kept track of separately because those with subsidized premiums (i.e., those whose income is below the poverty line) pay only \$5 per month, while everyone else must pay for themselves plus subsidize the premiums for those with low income.

Therefore, in the ARC Model, the variables for new beneficiaries would look like this:

NHA(age, sex, claim year, issue year, subsidy status) and

HCE(age, sex, claim year, issue year, subsidy status)

The incidence rates vary by age, sex, and the number of activities of daily living (ADLs) needed to qualify for benefits, which is either 2+ or 3+ ADLs. There are six ADLs listed in the law: eating, toileting, transferring, bathing, dressing, and continence. Participants may also qualify for benefits based on cognitive impairment. Although this is taken into account in the model’s incidence rates, the rates of cognitive impairment do not vary with the level of ADLs needed to trigger benefit payments.

Total benefit payments for each new episode of care (i.e., for each new claim) is determined by disaggregating the average length of episode into up to 25 calendar years. The disaggregation is done by using a continuance table, which gives the fraction of total days that occur above selected durations in each episode of care. For example, for a new episode of home care that starts at age 65, the average length of care for a female with 2+ ADL is 1,328 days. The continuance table for an episode of care that starts at age 65 shows that .886 of the days of care are above the 6th month, .691 are above the 18th month, .535 are above the 30th month, etc. Thus, the number of days of care in the first several calendar years from incidence would be determined as follows:

D(0) = ALOE * (1 - CT(6)) = 1328 * (1 - .886) = 1328 * .114 = 151.4

D(1) = ALOE * (CT(6) – CT(18)) = 1328 * (.886 - .691) = 1328 * .195 = 259.0

D(2) = ALOE * (CT(18) – CT(24)) = 1328 * (.691 - .535) = 1328 * .156 = 207.2

Where,

D(0) = the average number of days of benefit payments in the calendar year of incidence (assuming that new claims occur on average at the midpoint of the year)

D(1) = the average number of days of benefit payments in the calendar year after incidence

D(2) = the average number of days of benefit payments in the second calendar year after incidence

ALOE = average length of episode

CF(n) = the value from the continuance table at duration n months

It can be seen that eventually the value in the continuance table will reach zero, and that the summation of all fractions applied to the ALOE will equal 1.0, so that all days in the ALOE will be allocated to a calendar year. The user may also specify a deductible period and / or a lifetime maximum. In such cases, the continuance table also determines whether the day of frailty is a day in benefit status.

An input is provided in the “Assumptions” tab of the input workbook that allows the user to manually adjust the average length of stay. This factor, referred to as the “Average Length of Stay Modifier,” allows the user to scale the average length of stay up or down to simulate longer or shorter long-term care stays. When the user modifies the average length of stay the Model adjusts the continuance table to match the new length of stay by adjusting the probabilities of termination between thresholds in the table. Specifically, this adjustment is performed by first transforming the continuance probabilities into termination rates by dividing the probabilities at each threshold by the probability at the prior threshold and subtracting from 1. After the termination rates are obtained between each threshold, they are multiplied by factor to get adjusted termination rates. The factor that produces the assumed average length of stay is found and used to adjust the termination rates. The continuance table is then reconstructed using these modified termination rates.

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