Wipfli Health Insurance 2014 Analysis

Assumptions:

  • In-network procedures
  • Non-tobacco users
  • Family plans
  • All medical bills are paid pre-tax (via either HSAs or FSAs).

Plan Details


In [42]:
%matplotlib inline
import matplotlib
import numpy as np
import matplotlib.pyplot as plt

class Plan:
    def __init__(self): pass

p1 = Plan()    
p1.family_deductible = 1200.00
p1.individual_deductible = 600.00
p1.family_oopmax = 3600.00
p1.individual_oopmax = 1800.00
p1.family_cost_monthly = 910.00
p1.hsa_contribution = 0.00
p1.coinsurance_rate = 0.2

p2 = Plan()
p2.family_deductible = 3000.00
p2.individual_deductible = 1500.00
p2.family_oopmax = 6000.00
p2.individual_oopmax = 3000.00
p2.family_cost_monthly = 480.00
p2.hsa_contribution = 900.00
p2.coinsurance_rate = 0.2

p3 = Plan()
p3.family_deductible = 4600.00
p3.individual_deductible = 2300.00
p3.family_oopmax = 9200.00
p3.individual_oopmax = 4600.00
p3.family_cost_monthly = 186.00
p3.hsa_contribution = 900.00
p3.coinsurance_rate = 0.2

Helper functions


In [43]:
# For the purposes of this estimation, we are assuming the deductible
# is always larger than the HSA contribution amount
def apply_deductible_and_hsa(cost, deductible, hsa):
    cost_to_you = 0
    cost_remaining = 0
    
    # Apply HSA
    deductible_minus_hsa = deductible - hsa
    
    if cost <= hsa:
        cost_to_you = 0
        cost_remaining = 0
    elif cost <= deductible:
        cost_to_you = cost - hsa
        cost_remaining = 0
    elif cost > deductible:
        cost_to_you = deductible_minus_hsa
        cost_remaining = cost - deductible

    return (cost_to_you, cost_remaining)

def apply_coinsurance(cost, coinsurance_rate):
    return cost * coinsurance_rate

def apply_oopmax(cost, oopmax):
    if cost >= oopmax:
        return oopmax
    else:
        return cost
    
def setup_graph(title='', x_label='', y_label='', fig_size=None):
    fig = plt.figure()
    if fig_size != None:
        fig.set_size_inches(fig_size[0], fig_size[1])
    ax = fig.add_subplot(111)
    ax.set_title(title)
    ax.set_xlabel(x_label)
    ax.set_ylabel(y_label)

Plan cost functions


In [44]:
def individual_cost(plan, gross_cost):
    (cost_to_you, cost_remaining) = apply_deductible_and_hsa(gross_cost, 
                                    plan.individual_deductible, 
                                    plan.hsa_contribution)
    cost_to_you += apply_coinsurance(cost_remaining, plan.coinsurance_rate)
    cost_to_you = apply_oopmax(cost_to_you, plan.individual_oopmax)
    
    # Apply yearly premiums - note that the out-of-pocket max doesn't include
    # the premiums; thus, we apply them after applying out-of-pocket max.
    cost_to_you += (plan.family_cost_monthly * 12)
    return cost_to_you
    
    
def family_cost(plan, gross_cost):
    (cost_to_you, cost_remaining) = apply_deductible_and_hsa(gross_cost, 
                                    plan.family_deductible, 
                                    plan.hsa_contribution)
    cost_to_you += apply_coinsurance(cost_remaining, plan.coinsurance_rate)
    cost_to_you = apply_oopmax(cost_to_you, plan.family_oopmax)
    
    # Apply yearly premiums - note that the out-of-pocket max doesn't include
    # the premiums; thus, we apply them after applying out-of-pocket max.
    cost_to_you += (plan.family_cost_monthly * 12)
    return cost_to_you

Sanity Tests

Zero costs


In [45]:
# Should be the monthly premium times 12 (to make up the yearly premium).
family_cost(p1, 0)


Out[45]:
10920.0

In [46]:
p1.family_cost_monthly * 12


Out[46]:
10920.0

In [47]:
family_cost(p2, 0)


Out[47]:
5760.0

In [48]:
p2.family_cost_monthly * 12


Out[48]:
5760.0

In [49]:
family_cost(p3, 0)


Out[49]:
2232.0

In [50]:
p3.family_cost_monthly * 12


Out[50]:
2232.0

Cost less than HSA


In [51]:
# Should be monthly premium times 12
family_cost(p3, 500) == p3.family_cost_monthly * 12


Out[51]:
True

Cost greater than HSA and deductible


In [52]:
(p3.family_cost_monthly * 12) + \
(p3.family_deductible - p3.hsa_contribution) + \
(6000 - p3.family_deductible) * p3.coinsurance_rate


Out[52]:
6212.0

In [53]:
family_cost(p3, 6000)


Out[53]:
6212.0

Family Cost graph


In [54]:
# Calculate costs
gross_costs = range(0, 40000)
p1_costs = [family_cost(p1, cost) for cost in gross_costs]
p2_costs = [family_cost(p2, cost) for cost in gross_costs]
p3_costs = [family_cost(p3, cost) for cost in gross_costs]

# Do graph
setup_graph(title='Family costs', x_label='Gross cost', y_label='Cost to you', fig_size=(12,7))
ax = plt.subplot(1,1,1)
p1_graph, = ax.plot(gross_costs, p1_costs, label="Plan 1")
p2_graph, = ax.plot(gross_costs, p2_costs, label="Plan 2")
p3_graph, = ax.plot(gross_costs, p3_costs, label="Plan 3")
handles, labels = ax.get_legend_handles_labels()
ax.legend(handles, labels)
plt.show()


Individual cost


In [55]:
# Calculate costs
gross_costs = range(0, 40000)
p1_costs = [individual_cost(p1, cost) for cost in gross_costs]
p2_costs = [individual_cost(p2, cost) for cost in gross_costs]
p3_costs = [individual_cost(p3, cost) for cost in gross_costs]

# Do graph
setup_graph(title='Individual costs', x_label='Gross cost', y_label='Cost to you', fig_size=(12,7))
ax = plt.subplot(1,1,1)
p1_graph, = ax.plot(gross_costs, p1_costs, label="Plan 1")
p2_graph, = ax.plot(gross_costs, p2_costs, label="Plan 2")
p3_graph, = ax.plot(gross_costs, p3_costs, label="Plan 3")
handles, labels = ax.get_legend_handles_labels()
ax.legend(handles, labels)
plt.show()


Conclusion

It seems pretty clear that Plan 3 is the one to buy :) And here is how I feel about Plan 1...


In [56]:
from IPython.display import YouTubeVideo
YouTubeVideo('4F4qzPbcFiA')


Out[56]:

In [ ]: