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 � Objectives � Research methodology � Probabilistic model � Analysis � Sensitivity analysis � Conclusions

MS&E220 Probabilistic Analysis Autumn 2008 Group 3: Medical Insurance Plan Selection Objectives � Find the probability of selecting one � Calculate overall mean expense among two different medical insurance of the employees in company plan offering based on estimated expense distribution � Perform sensitivity analysis by � Plan A (HRA): Good for low expenses considering different % change in � Plan B (PPO): Good for high expenses mean expenditure after selecting a � The probability that selected plan plan and calculate saving to the turns out to be the correct plan under company by doubling HRA incentive different scenarios Plan Elements Plan A (HRA) Plan B (PPO) E ES ESC E ES ESC � Plan coverage choices Premium ($)* 18 50 75 25 60 100 • Employee only (E) Deductible ($)** 1,000 2,000 2,000 300 600 600 • Employee, and Spouse (ES) Max out of pocket ($)** 3,000 6,000 6,000 1,500 3,000 3,000 • Employee, Spouse, Children (ESC) HRA ($)** 500 1,000 1,000 0 0 0 Plan Coverage 80% 80% 80% 90% 90% 90% * Bi‐weekly ** Yearly

MS&E220 Probabilistic Analysis Autumn 2008 Group 3: Medical Insurance Plan Selection Probabilistic Model MEDICAL INSURANCE PLAN TYPE STATISTICS � We assumed that medical expenses Mean Std Dev follow a Gaussian continuous distribution Employee (E) $7,600 $3,500 Employee plus Spouse (ES) $15,200 $7,000 � Probability Tree Prior distributions Employee, Spouse plus Children (ESC) $21,000 $7,500 • E(f1) = 0.5 • ES(f2) = 0.2 • ESC(f3) = 0.3

MS&E220 Probabilistic Analysis Autumn 2008 Group 3: Medical Insurance Plan Selection Crossover point for double HRA Analysis (plan Selection) P(plan B (selection) Crossover point for � In different cases, we calculated the for double HRA HRA 500/1000/1000 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) CROSSOVER POINT FOR DIFFEREENT HRA REIMBURSEMENT Estimated expense ($) HRA 500/1,000/1,000 HRA 1,000/2,000/2,000 P(PLAN A SELECTION) FOR DIFFERENT HRA E $1,520 $6,520 REIMBURSEMENT ES $2,000 $12,000 HRA 500/1,000/1,000 HRA 1,000/2,000/2,000 ESC $5,900 $15,900 E 4.1% 37.9% � The crossover point is used to calculate the ES 3.0% 32.4% probability of plan A selection. ESC 1.5% 23.3% Overall 3.12% 32.41% (weighted average)

MS&E220 Probabilistic Analysis Autumn 2008 Group 3: Medical Insurance Plan Selection Analysis (Selected Plan Turns Out to be the Correct Plan ) � 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) DIFFERENT HRA REIMBURSEMENT 500/1,000/1,000 1,000/2,000/2,000 Overall Saving by doubling HRA = Overall P(selected plan turned 95.5% 71.1% ($14,316 ­ $12,897) * out to be the correct plan) 3000 employees = Overall Mean of medical $14,316 $12,897 $4.26 Million expenses

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.

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

MS&E220 Probabilistic Analysis Autumn 2008 Group 3: Medical Insurance Plan Selection Conclusions � 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 even if mean is reduced by just 10% after selecting plan A.