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MEDICAID EXPANSION ENROLLMENT AND COST PROJECTIONS Wyoming Department of Health December 15, 2018

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Page 1: MEDICAID EXPANSION...MEDICAID EXPANSION ENROLLMENT AND COST PROJECTIONS Wyoming Department of Health December 15, 2018

MEDICAID EXPANSION ENROLLMENT AND COST PROJECTIONS

Wyoming Department of Health

December 15, 2018

Page 2: MEDICAID EXPANSION...MEDICAID EXPANSION ENROLLMENT AND COST PROJECTIONS Wyoming Department of Health December 15, 2018

Wyoming Department of Health | Director’s Unit for Policy, Research, and Evaluation | Page 1

TABLE OF CONTENTS

Enrollment and Cost Summary ............................................................................................ 2

Motivation ............................................................................................................................... 5

Methodology ........................................................................................................................... 6

Technical details .................................................................................................................... 13

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ENROLLMENT AND COST SUMMARY Executive summary If Wyoming were to expand Medicaid to non-disabled childless adults under 138% of the Federal Poverty Level per the Patient Protection and Affordable Care Act (the “ACA”), the Department of Health would recommend an initial biennial appropriation of $33 million in State General Funds and $246 million in Federal Funds to cover associated costs. This assumes a start date of January 2020. While there is significant uncertainty in our projection, we are confident that enrollment growth will be slow enough for the Department to be able to adjust its estimates after the first year of expansion without exceeding this initial biennial figure (and, if necessary, submit a supplemental request). Enrollment After four years, we expect monthly Medicaid expansion enrollment to plateau at approximately 27,000 people. The 89% credible interval around this figure is between 10,000 and 42,000 enrolled individuals — these are our “low” and “high” estimates, respectively. This projection is visualized in Figure 1, below. The graph on the left shows the expected growth over time (blue line), as well as an 89% uncertainty interval around that growth (shaded area). Our “high” and “low” estimates are represented by the dashed blue lines. The graph to the right of the trend shows a “slice” of the last month (month 48) in the projection, showing the probability density within the 89% interval, e.g., what enrollment values are most likely within this “high” to “low” range.

Figure 1: Projected Medicaid expansion enrollment

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Costs We project Medicaid medical costs for this population will plateau at approximately $17 million per month (89% credible interval between $9 million and $25 million), after an initial ramp period. Figure 2, below, shows the projection for cost. As with Figure 1, the dashed lines represent the 89% credible interval “high” and “low” estimates, and the solid line represents the expected costs.

Figure 2: Projected monthly Medicaid medical expenditures (total)

In order to translate these monthly medical costs into a potential appropriation, we make some adjustments:

Per the ACA, the Federal government will pay 90% of these medical costs after CY 2020.

With a “vanilla” expansion (e.g., no waivers or other administrative overhead), we estimate administrative costs at 5% of total medical costs. In any other scenarios, administrative costs would certainly increase. The Federal government will pay 50% of administrative expenditures.

With these adjustments, Table 1 shows the expected costs for each year. This is the basis of our appropriation recommendation. Note that, because figures are shown to the hundreds of thousands, rounding means that totals may not add up exactly in the table.

Table 1: Costs – Expected (mean) scenario by calendar year, in millions

Cost category 2020 2021 2022 2023

Medical costs $94.8 $170.6 $190.5 $198.0

Medical (FF) $85.3 $153.6 $171.4 $178.2

Medical (SGF) $9.5 $17.1 $19.0 $19.8

Administrative costs $4.7 $8.5 $9.5 $9.9

Admin (FF) $2.4 $4.3 $4.8 $5.0

Admin (SGF) $2.4 $4.3 $4.8 $5.0

Total Federal Funds $87.6 $157.8 $176.2 $183.2

Total State General Funds $11.8 $21.3 $23.8 $24.8

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Table 2, below, shows the “high” (e.g., at 42K enrollment) estimate. Note that the recommended biennial appropriation ($33 million SGF and $246 million FF) can cover the first year of costs in this scenario, allowing the Department to submit a supplemental request if actual enrollment and costs end up closer to this scenario.

Table 2: Annual costs – “high” scenario (89% probability that costs will be below this value)

Cost category 2020 2021 2022 2023

Medical costs $144.16 $243.20 $268.40 $292.34

Medical (FF) $129.75 $218.88 $241.56 $263.11

Medical (SGF) $14.42 $24.32 $26.84 $29.23

Administrative costs $7.21 $12.16 $13.42 $14.62

Admin (FF) $3.60 $6.08 $6.71 $7.31

Admin (SGF) $3.60 $6.08 $6.71 $7.31

Total Federal Funds $133.35 $224.96 $248.27 $270.42

Total State General Funds $18.02 $30.40 $33.55 $36.54

Because the model incorporates adverse selection (e.g., the first people to sign up will be the least healthy), the costs on a per-member per-month basis are expected to gradually decrease. Adverse selection also means that, in the model, enrollment has an inverse relationship with per-member per month costs. In other words, if take-up is low, we anticipate the covered population to be sicker (and therefore more costly) than if take-up rate is high.

Figure 3: Projected per-member per-month costs

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MOTIVATION Why revise Wyoming’s projections for Medicaid expansion? The simple answer is that recent experience from expansion states has shown that actual enrollment has often exceeded original projections. This gap — between original projections1 and actual enrollment2 — is shown in Figure 4, below.

Figure 4: Gap between projected and actual enrollment, by state. Dark blue bars show actual enrollment, and light blue bars show original projections.

Figure 4 clearly demonstrates the need to thoroughly revise Wyoming’s estimates of enrollment and costs. We do so using two important principals:

Projections should either be based on (a) empirical data or (b) fully-explained assumptions grounded in health economic theory.

Modeling and quantifying uncertainty is just as important as a making point estimates. We want to know not just the estimate, but the uncertainty around that estimate. Accordingly, the uncertainty inherent in all models should be propagated (to the extent possible), into the final estimates and fully communicated.

1 Projections collected by the AP, available here: https://www.washingtontimes.com/news/2015/jul/19/projected-

actual-enrollment-for-medicaid-expansion/ 2 https://www.kff.org/health-reform/state-indicator/medicaid-expansion-enrollment

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METHODOLOGY These estimates come from a simulation-based approach that combines the most recent and detailed Census data available for Wyoming with four different models to project (a) which members will enroll in Medicaid and (b) how much those members will incur in health care costs to the Medicaid program. Figure 5, below, shows how the models interact with the core Census data (black) in the simulation.

Figure 5: Medicaid expansion model framework

Generally speaking, the simulation follows a series of steps for each iteration:

(1) The simulation starts by narrowing the universe of potentially eligible members from all Wyoming residents to civilian, non-institutionalized adults between the ages of 19 and 64 who are under 175% of the Federal Poverty Level.3 We also exclude individuals who already have Medicare or Medicaid as their primary insurance.

3 The actual income eligibility criteria for Medicaid expansion is 138% of FPL, but the simulation allows for the

potential of individuals close to the eligibility criteria to intentionally reduce their income in order to qualify for

health care coverage.

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Using the person-level and replicate weights included in the microdata, we estimate an expected total (this happens to be 59,653 in the 2016 5-year ACS data) and standard deviation (1,466) for this subset of people. We then draw a value from this (assumed normal) distribution to use as the eligible population count for each iteration. This allows us to propagate some of the error in the Census microdata into the results.

We use the replicate weight variable with the total number of people closest to this draw as the base weight for each iteration, and use that weight to expand the Census microdata into a simulated group of people. In this case, there are 2,642 observations in the survey data that are repeatedly expanded into between 56K and 63K “people”.

(2) At this point, we need some mechanism to sort the simulated group of people by their propensity to enroll in Medicaid. We make the assumption that those individuals with higher personal health care costs are more likely to enroll. This is due to adverse selection, but also to the fact that eligibility in Medicaid can be ‘retroactive,’ which allows for many of the sickest members to automatically be enrolled post hoc if the hospital they end up in finds they are uninsured.

This is where the Medical Expenditure Panel Survey (MEPS) data and take-up assumptions come into play. While this is a national dataset (not Wyoming-specific), it covers a large universe of individuals (e.g., including the uninsured), and contains a lot of demographic information that might help model annual health care costs.

The MEPS model (described in later pages) allows us to predict health care utilization based on demographic factors (e.g., age, sex, education level, insurance coverage). We use this model to estimate average health care utilization for every member of the simulated population in each iteration.

After each member is assigned an average total cost, we use the following take-up assumptions to modify that total cost into an estimated personal cost (e.g., out-of-pocket costs to the individual). These simplifying assumptions include:

o Insured individuals, whether with employer-sponsored insurance (ESI) or directly-purchased insurance, will only personally face 20% of their costs, with a maximum out-of-pocket of $5,000.4

o Uninsured individuals (including those with only VA/TRICARE or IHS) will only have a willingness-to-pay that is ~20% - 35% of their total costs.5 Health care economists generally believe this to be the effect of EMTALA and uncompensated/ charity care.

o Individuals with ESI will face an approximate “hassle cost” of $500 in order to switch from their employer plan to Medicaid.

4 This is based on the 20% coinsurance and approximate MOOP in the State Employees Group Insurance plan. 5 Finkelstein, et. al. “Subsidizing health insurance for low-income adults: evidence from Massachusetts.” National

Bureau of Economic Research. Working Paper 23668. Page 31. Finkelstein also cites three other papers with similar

estimates.

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o Individuals with directly-purchased insurance who are below 138% (i.e., those currently purchasing insurance on the individual ACA marketplace) will be prodded automatically to enroll in Medicaid (and subsidies for this population would be unavailable). We model this as a strong incentive of -$1,000.

We also use the MEPS utilization model to extract a fitted estimate of the probability of having any health care in the time period. We rescale the distribution of these estimates to match the standard deviation of the Medicaid model person-level effects and re-use these as the actual person-level estimates in the Medicaid model. This allows us to more fully incorporate the effects of adverse selection into the simulation, rather than just sorting people by demographic risk.

(3) A Wyoming-specific estimate of overall take-up from the maximum take-up percentage model (described later) is then applied to the sorted list to ‘enroll’ the specified total number of people in Medicaid. At this stage, assuming these members are all now on Medicaid, we apply the Medicaid cost model (described later) to more precisely estimate monthly Medicaid medical costs based on age, sex, and the probability of having health care expenses estimated in the MEPS model. (4) The enrollment ramp model then builds the by-month timeline of expansion (not everyone enrolls in Month 1), again assuming the highest-risk individuals are first to enroll.

We repeat this process 2,000 times to obtain the overall estimates that are shown in the enrollment summary.

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Enrollment models Because enrollment experience has varied significantly across states, these models are used to attempt to estimate Wyoming’s enrollment based on characteristics it might share with other states. The core of the two enrollment models comes from monthly state Medicaid enrollment figures from CMS, covering January 2014 to December 2016.6 These data show the enrollment trajectories for states at various stages of expansion; where some expanded Medicaid as soon as the opportunity was available (California, Colorado), others expanded later (Montana, Alaska, Louisiana). After lining up the trajectories based on when states began to show enrollment and updating maximum enrollment figures for the later-expanding States, the data for expansion states looks like Figure 6, below. Figure 6: Aligned actual enrollment trajectories; states that expanded Medicaid. Dashed lines show

maximum enrollment at plateau / ‘steady state.’

6 https://data.medicaid.gov/Enrollment/Medicaid-Enrollment-New-Adult-Group/pfrt-tr7q

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We use this trajectory data, combined with census estimates of the eligible population and various state-level characteristics, to build two enrollment models:

A “take-up percentage” model that attempts to estimate what percent of the potentially eligible population will ultimately enroll (e.g., the ‘steady-state’ total represented by the dashed lines in Figure 6, on the previous page).

An “enrollment ramp” model that estimates what the month-to-month growth trajectory will look like (the solid lines on Figure 5, but represented as a percent of the ‘steady-state’ maximum).

Maximum take-up percentage model The best-fitting model uses four main factors as predictors for take-up rate:

The percent of the underlying eligible population who might have Employer-Sponsored Insurance (ESI);

Employment by economic sector (clusters);

Geographic region of the United States; and

Whether the State is a “red” or “blue” state, politically. Figure 7, to the right, illustrates how well the predicted take-up rates (shown as shaded red density curves) fit the actual take-up rates (black squares) for Medicaid expansion states, as well as the predictions for non-expansion States. Wyoming’s predicted take-up is estimated to be relatively lower than other states, but note how the model spreads probability density more thinly (e.g. the curve is flatter), with wide uncertainty between 25% and 75%. Enrollment ramp Turning back to Figure 6 (previous page), you will note that enrollment growth varies by state — some had a substantial fraction of their maximum enrollment in the first few months, while others took longer to build to a steady state. To fit these varying growth patterns, we used a more flexible non-linear growth function (two-parameter Weibull). Figure 8, on the next page, shows how well this function (and corresponding 95% credible intervals) fits the data for expansion states.

Figure 7: Estimated (red density) vs actual (black square) take-up rates

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Figure 8: Actual (black) vs. predicted (dashed red) enrollment trajectories, with 95% credible intervals (shaded red)

Figure 9, below, shows the fitted (e.g. average) trajectory estimates for Wyoming. Note that the model predicts Wyoming to have slower-than-average enrollment growth (similar to North Dakota and Alaska), but there is, again, wide uncertainty.

Figure 9: Wyoming’s fitted enrollment trajectories (red) vs. other states (dashed gray)

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Utilization models Both the MEPS and Medicaid models are built to model two unique features of aggregate health care costs:

A significant number of zero-cost person-periods, for people that don’t use any health care in the time period.

For those that do use care, the costs have a skewed distribution with an exceptionally-long right tail, due to the few individuals who may have extremely high costs in that period.

Structurally, therefore, they are built around similar distributional assumptions, so we use the same “hurdle lognormal” framework, where probability of any costs are modeled first (the “hurdle”), and if there are costs in the time period, those costs are modeled using a lognormal distribution. There are, however, several important differences between the two models:

The MEPS model uses more demographic predictors (e.g., insurance status, educational attainment, race) that aren’t available in the Medicaid data.

Where the MEPS model is straightforward (e.g., annual costs per person), the Medicaid model is hierarchical, in the sense that data for member-months are nested both within members (e.g., “Bob”) and months (“January”).

o The Medicaid model therefore takes advantage of this hierarchical nature to estimates varying intercepts for both individual members and for months. This effectively allows us to simulate “sicker” and “healthier” people in the data (person intercepts) while also allowing some statistical control of seasonal effects and potential Medicaid policy changes (month intercepts).

Important for the purposes of the simulation, both models produce cost predictions, not just average (conditional on predictors) costs. This allows us to fully incorporate uncertainty into the model. As noted previously, we link the two models together; we assume (a) the fitted hurdle component of the MEPS model can be rescaled and re-used as (b) the Medicaid model person-level intercepts for probability of any health care.

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TECHNICAL DETAILS All models were fit using the Hamiltonian Monte Carlo “No U-Turn” Sampler in the Stan platform7,

with R statistical software and the brms package8 as the interface. We used the data.table9 and

lubridate10 packages to clean and process data, and the ggplot211 package to create final graphics.

Output from the brms models is shown in the next few pages. The output shows the model

specification (written in lmer-like syntax), the data used, the distributional family assumed, estimates

for unobserved variables, and MCMC diagnostics. Information on priors is not included in the

output, but is available on request.

1. Enrollment ramp model Family: beta

Links: mu = identity; phi = identity

Formula: PctEnrolled ~ 1 - exp(-1 * (MonthNo/exp(lambda))^exp(kappa))

lambda ~ 1 + log(Density) + (1 | Region) + (1 | econ_cluster)

kappa ~ 1 + log(Density) + (1 | Region) + (1 | econ_cluster)

Data: expansion_dataset (Number of observations: 899)

Samples: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;

total post-warmup samples = 4000

Group-Level Effects:

~econ_cluster (Number of levels: 4)

Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat

sd(lambda_Intercept) 0.49 0.31 0.16 1.37 1561 1.00

7 Stan Development Team. 2018. RStan: the R interface to Stan. R package version 2.17.3. http://mc-stan.org 8 Paul-Christian Bürkner (2017). brms: An R Package for Bayesian Multilevel Models Using Stan. Journal of

Statistical Software, 80(1), 1-28.<doi:10.18637/jss.v080.i01> 9 Matt Dowle [aut, cre], Arun Srinivasan [aut], Jan Gorecki [ctb], Michael Chirico [ctb], Pasha Stetsenko [ctb], Tom

Short [ctb], Steve Lianoglou [ctb], Eduard Antonyan [ctb], Markus Bonsch [ctb], Hugh Parsonage [ctb] 10 Garrett Grolemund, Hadley Wickham (2011). Dates and Times Made Easy with lubridate. Journal of Statistical

Software, 40(3), 1-25. URL http://www.jstatsoft.org/v40/i03/ 11 H. Wickham. ggplot2: Elegant Graphics for Data Analysis. Springer-Verlag New York, 2016.

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sd(kappa_Intercept) 0.33 0.21 0.10 0.91 1934 1.00

~Region (Number of levels: 8)

Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat

sd(lambda_Intercept) 0.42 0.15 0.22 0.81 1511 1.00

sd(kappa_Intercept) 0.30 0.11 0.16 0.57 1986 1.00

Population-Level Effects:

Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat

lambda_Intercept 2.24 0.36 1.36 2.81 1687 1.00

lambda_logDensity -0.15 0.03 -0.21 -0.09 3471 1.00

kappa_Intercept -0.03 0.24 -0.50 0.45 1693 1.00

kappa_logDensity -0.08 0.02 -0.13 -0.03 3722 1.00

Family Specific Parameters:

Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat

phi 20.65 1.00 18.82 22.67 4938 1.00

Note: This model had 2 divergent transitions; while this is an indicator of some concern, the posterior predictive checks (Figure 7 on page 11) look OK.

2. Maximum take-up model Family: beta

Links: mu = logit; phi = identity

Formula: Takeup ~ 1 + PctESI + BlueRed + (1 | Region) + (1 | econ_cluster)

Data: max_enrollment_dataset (Number of observations: 28)

Samples: 4 chains, each with iter = 3000; warmup = 1500; thin = 1;

total post-warmup samples = 6000

Group-Level Effects:

~econ_cluster (Number of levels: 4)

Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat

sd(Intercept) 0.38 0.47 0.01 1.62 1532 1.00

~Region (Number of levels: 8)

Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat

sd(Intercept) 0.71 0.33 0.22 1.52 1591 1.00

Population-Level Effects:

Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat

Intercept 2.86 0.88 1.12 4.57 2859 1.00

PctESI -6.91 2.96 -12.57 -1.17 5251 1.00

BlueRedRed -0.60 0.32 -1.21 0.04 3345 1.00

Family Specific Parameters:

Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat

phi 16.78 5.65 8.02 29.70 2650 1.00

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3. MEPS utilization model Family: hurdle_lognormal

Links: mu = identity; sigma = log; hu = logit

Formula: UScore ~ 1 + AGE16X + Male + AGE16X * Male + Race + Education +

INSURANCE + (1 | VARSTR)

sigma ~ 1

hu ~ 1 + AGE16X + Male + AGE16X * Male + Race + Education +

INSURANCE + (1 | VARSTR)

Data: model_dataset (Number of observations: 3164)

Samples: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;

total post-warmup samples = 8000

Group-Level Effects:

~VARSTR (Number of levels: 165)

Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat

sd(Intercept) 0.15 0.06 0.02 0.26 1499 1.00

sd(hu_Intercept) 0.33 0.07 0.19 0.45 2382 1.00

Population-Level Effects:

Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat

Intercept 6.67 0.37 5.95 7.41 3340 1.00

sigma_Intercept 0.22 0.02 0.18 0.26 9781 1.00

hu_Intercept 0.10 0.62 -1.07 1.37 2916 1.00

AGE16X 0.02 0.00 0.01 0.03 7747 1.00

Male -0.39 0.21 -0.81 0.01 6731 1.00

RaceAsian -0.69 0.36 -1.39 0.03 3145 1.00

RaceBlack -0.41 0.35 -1.11 0.27 3020 1.00

RaceHispanic -0.65 0.34 -1.33 0.02 3007 1.00

RaceOther -0.21 0.38 -0.96 0.56 3458 1.00

RaceWhite -0.15 0.34 -0.82 0.52 3015 1.00

EducationGraduate 0.23 0.20 -0.17 0.63 9253 1.00

EducationHSDGED 0.09 0.10 -0.12 0.30 5425 1.00

EducationNodegree 0.15 0.12 -0.09 0.38 5552 1.00

EducationOther 0.18 0.15 -0.11 0.47 6792 1.00

EducationUnknown 0.14 0.31 -0.47 0.76 10120 1.00

INSURANCEESI -0.09 0.08 -0.25 0.07 8659 1.00

INSURANCETRICAREVA 0.04 0.19 -0.33 0.41 11444 1.00

INSURANCEUninsured -0.07 0.09 -0.23 0.10 8502 1.00

AGE16X:Male 0.00 0.00 -0.01 0.01 6940 1.00

hu_AGE16X -0.02 0.00 -0.03 -0.01 6285 1.00

hu_Male 1.31 0.26 0.80 1.84 5972 1.00

hu_RaceAsian -0.58 0.60 -1.83 0.56 2752 1.00

hu_RaceBlack -0.40 0.58 -1.58 0.71 2601 1.00

hu_RaceHispanic -0.34 0.57 -1.53 0.75 2624 1.00

hu_RaceOther -0.95 0.63 -2.24 0.29 2922 1.00

hu_RaceWhite -0.94 0.57 -2.12 0.16 2594 1.00

hu_EducationGraduate 0.42 0.29 -0.16 0.99 8646 1.00

hu_EducationHSDGED 0.39 0.15 0.08 0.69 5160 1.00

hu_EducationNodegree 0.53 0.16 0.21 0.85 5327 1.00

hu_EducationOther 0.27 0.21 -0.16 0.68 6502 1.00

hu_EducationUnknown 1.65 0.33 1.01 2.32 8551 1.00

hu_INSURANCEESI 0.06 0.12 -0.18 0.29 9475 1.00

hu_INSURANCETRICAREVA -0.73 0.33 -1.42 -0.09 11038 1.00

hu_INSURANCEUninsured 0.84 0.11 0.63 1.06 9514 1.00

hu_AGE16X:Male -0.01 0.01 -0.03 -0.00 5427 1.00

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4. Medicaid claims model: probability of any health care cost in a month Family: bernoulli

Links: mu = logit

Formula: AnyCost ~ 1 + Male + zAge + Male * zAge + zTotalMMs +

zMonthsOnMedicaid + (1 | IDnum) + (1 | MonthNo)

Data: base_sample[, .(IDnum, AnyCost, Male, zAge, zMonth (Number of

observations: 205942)

Samples: 4 chains, each with iter = 6000; warmup = 4000; thin = 1;

total post-warmup samples = 8000

Group-Level Effects:

~IDnum (Number of levels: 14626)

Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat

sd(Intercept) 1.93 0.02 1.89 1.96 2055 1.00

~MonthNo (Number of levels: 36)

Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat

sd(Intercept) 0.18 0.02 0.14 0.23 1623 1.00

Population-Level Effects:

Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat

Intercept 0.84 0.05 0.75 0.94 952 1.00

Male -0.72 0.07 -0.85 -0.59 1172 1.00

zAge 0.50 0.04 0.43 0.58 1270 1.00

zTotalMMs 0.66 0.02 0.63 0.70 980 1.00

zMonthsOnMedicaid 0.18 0.02 0.15 0.21 1197 1.00

Male:zAge 0.43 0.08 0.28 0.58 1321 1.00

5. Medicaid claims model: monthly cost | non-zero cost in month Family: lognormal

Links: mu = identity; sigma = log

Formula: Cost ~ 1 + Male + zAge + Male * zAge + zTotalMMs + zMonthsOnMedicaid

+ (1 | IDnum) + (1 | MonthNo)

sigma ~ 1 + zAge

Data: base_sample[AnyCost == 1, .(IDnum, Cost, Male, zAg (Number of

observations: 110747)

Samples: 4 chains, each with iter = 6000; warmup = 4000; thin = 1;

total post-warmup samples = 8000

Group-Level Effects:

~IDnum (Number of levels: 11595)

Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat

sd(Intercept) 0.89 0.01 0.88 0.91 2243 1.00

~MonthNo (Number of levels: 36)

Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat

sd(Intercept) 0.12 0.02 0.09 0.16 1669 1.00

Population-Level Effects:

Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat

Intercept 5.47 0.03 5.41 5.53 1347 1.00

sigma_Intercept 0.28 0.00 0.27 0.29 14201 1.00

Male -0.05 0.04 -0.13 0.02 2078 1.00

zAge 0.20 0.02 0.16 0.24 1951 1.00

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Wyoming Department of Health | Director’s Unit for Policy, Research, and Evaluation | Page 17

zTotalMMs 0.03 0.01 0.01 0.05 1859 1.00

zMonthsOnMedicaid 0.12 0.01 0.11 0.14 2686 1.00

Male:zAge -0.13 0.05 -0.22 -0.04 2060 1.00

sigma_zAge -0.01 0.00 -0.02 -0.00 16079 1.00

6. Medicaid claims model: correlation between probability individual intercepts and cost individual intercepts Family: gaussian

Links: mu = identity; sigma = identity

Formula: costIntercept ~ 1 + anyCostIntercept

Data: prob_cost[sample(.N, 10000)] (Number of observations: 10000)

Samples: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;

total post-warmup samples = 8000

Population-Level Effects:

Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat

Intercept -0.04 0.01 -0.05 -0.02 8097 1.00

anyCostIntercept 0.10 0.01 0.09 0.11 9272 1.00

Family Specific Parameters:

Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat

sigma 0.87 0.01 0.86 0.89 8570 1.00