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MS&E220 Probabilistic Analysis Autumn 2008 Group 3: Medical - - PowerPoint PPT Presentation
MS&E220 Probabilistic Analysis Autumn 2008 Group 3: Medical - - PowerPoint PPT Presentation
MS&E220 Probabilistic Analysis Autumn 2008 Group 3: Medical Insurance Plan Selection Amit Chattopadhyay Ben Hernandez Vishal Kedia Yehia Khalil MS&E220 Probabilistic Analysis Autumn 2008 Group 3: Medical Insurance Plan Selection Content
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MS&E220 Probabilistic Analysis Autumn 2008
Group 3: Medical Insurance Plan Selection
Find the probability of selecting one
among two different medical insurance plan offering based on estimated expense distribution
Plan A (HRA): Good for low expenses Plan B (PPO): Good for high expenses
The probability that selected plan
turns out to be the correct plan under different scenarios
Calculate overall mean expense
- f the employees in company
Perform sensitivity analysis by
considering different % change in mean expenditure after selecting a plan and calculate saving to the company by doubling HRA incentive
Objectives
Plan A (HRA) Plan B (PPO) Plan Elements
E ES ESC E ES ESC Premium ($)* 18 50 75 25 60 100 Deductible ($)** 1,000 2,000 2,000 300 600 600 Max out of pocket ($)** 3,000 6,000 6,000 1,500 3,000 3,000 HRA ($)** 500 1,000 1,000 Plan Coverage 80% 80% 80% 90% 90% 90% * Bi‐weekly ** Yearly
Plan coverage choices
- Employee only (E)
- Employee, and Spouse (ES)
- Employee, Spouse, Children (ESC)
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MS&E220 Probabilistic Analysis Autumn 2008
Group 3: Medical Insurance Plan Selection
We assumed that medical expenses follow a Gaussian continuous distribution Probability Tree Prior distributions
- E(f1) = 0.5
- ES(f2) = 0.2
- ESC(f3) = 0.3
STATISTICS MEDICAL INSURANCE PLAN TYPE Mean Std Dev Employee (E) $7,600 $3,500 Employee plus Spouse (ES) $15,200 $7,000 Employee, Spouse plus Children (ESC) $21,000 $7,500
Probabilistic Model
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MS&E220 Probabilistic Analysis Autumn 2008
Group 3: Medical Insurance Plan Selection
Analysis (plan Selection)
- In different cases, we calculated the
expense where both plans offer same benefit (Crossover point) We also calculated new cross over point if company decides to double HRA (extra incentive to promote plan A)
Estimated expense ($)
- The crossover point is used to calculate the
probability of plan A selection.
P(plan B (selection) for double HRA Crossover point for double HRA Crossover point for HRA 500/1000/1000
CROSSOVER POINT FOR DIFFEREENT HRA REIMBURSEMENT HRA 500/1,000/1,000 HRA 1,000/2,000/2,000 E $1,520 $6,520 ES $2,000 $12,000 ESC $5,900 $15,900 P(PLAN A SELECTION) FOR DIFFERENT HRA REIMBURSEMENT HRA 500/1,000/1,000 HRA 1,000/2,000/2,000
E 4.1% 37.9% ES 3.0% 32.4% ESC 1.5% 23.3% Overall (weighted average) 3.12% 32.41%
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MS&E220 Probabilistic Analysis Autumn 2008
Group 3: Medical Insurance Plan Selection
Analysis (Selected Plan Turns Out to be the Correct Plan )
DIFFERENT HRA REIMBURSEMENT 500/1,000/1,000 1,000/2,000/2,000 Overall P(selected plan turned
- ut to be the correct plan)
95.5% 71.1% Overall Mean of medical expenses $14,316 $12,897
Users of Plan A are assumed to have a decrease in actual expenses while Plan B users are assumed to have an increase. We modeled it (for each of E, ES, and ESC case)
- 30% decrease in mean expense if plan A selected
- 10% increase in mean expense if plan B selected
P(Correct plan selection for each of E, ES or ESC Case) = P(Plan A selected) * (Plan A is the correct plan with new expense distribution) + P(plan B selected * plan B is the correct plan with new expense distribution) Overall probability of correct plan = weighted average of E, ES, and ESC case. Overall mean expense = weighted mean(shifted) of E, ES, and ESC case, and further weighted by P(plan A selection), and P(plan B selection) Overall Saving by doubling HRA = ($14,316$12,897) * 3000 employees = $4.26 Million
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MS&E220 Probabilistic Analysis Autumn 2008
Group 3: Medical Insurance Plan Selection
Sensitivity Analysis (Correct plan Selection)
Earlier we assumed
- 30% decrease in mean expense after plan A selected
- 10% increase in mean expense after plan B selected
Now we did sensitivity analysis based on different change in mean, and calculated Probability of Correct(Best) plan selection in different cases Decrease in mean expense, and hence saving to the company of size 3000. Results:
- For original HRA (500/100/2000),
probability of correct plan selection is always close to 95% (Plan B was always good)
- By Doubling HRA, Plan A becomes
competitive as well, and now showing good response by more changes in mean after plan is Selected.
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MS&E220 Probabilistic Analysis Autumn 2008
Group 3: Medical Insurance Plan Selection
Sensitivity Analysis : Overall savings
- By doubling HRA, more employees select plan A. HRA amount is also doubled.
‐ ‐ Resulting in overall $1.31 Million extra HRA to be given by company with 3000 employees . Here is the overall saving by doubling HRA in different cases Results: If there is no shift in mean after plan A/B selected, company will not save anything by doubling HRA. More the shift in mean, (According to plan) more the company will save by doubling HRA. $1.31 Million extra HRA can be easily compensated, if mean is shifted just by 10% after plan A/B selected
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MS&E220 Probabilistic Analysis Autumn 2008
Group 3: Medical Insurance Plan Selection With the given specifications of two plan, plan A is good only for very low expense
- Resulting in very few employees (only 3.12 % ) selecting plan A.
The employer is better off with more employees selecting Plan A, as it encourages less spending.
- Doubling Plan A’s reimbursement makes it more attractive for wider range of expense.
- Hence increases the probability of any employee selecting Plan A to 32.41%
For a company with 3,000 employees, doubling HRA means
- Extra $1.31 Million given in HRA reimbursement
- But results in net saving of $4.25 Million using realistic assumptions (30% decrease in
mean expense after plan A selected, and 10% increase after plan B selected)
- Sensitivity analysis shows that doubling HRA is a good bet, as it gives better return