Balancing investments in federally qualified health centers and Medicaid for improved access and coverage in Pennsylvania

Abstract

Two common health disparities in the US include a lack of access to care and a lack of insurance coverage. To help address these disparities, healthcare reform will provide $11B to expand Federally Qualified Health Centers (FQHCs) over the next 5 years. In 2014, Medicaid rules will be modified so that more people will become eligible. There are, however, important tradeoffs in the investment in these two programs. We find a balanced investment between FQHC expansion and relaxing Medicaid eligibility to improve both access (by increasing the number of FQHCs) and coverage (by FQHC and Medicaid expansion) for the state of Pennsylvania. The comparison is achieved by integrating multi-objective mathematical models with several public data sets that allow for specific estimations of healthcare need. Demand is estimated based on current access and coverage status in order to target groups to be considered preferentially. Results show that for Pennsylvania, FQHCs are more cost effective than Medicaid if we invest all of the resources in just one policy. However, we find a better investment point balancing those two policies. This point is approximately where the additional expenses incurred from relaxing Medicaid eligibility equals the investment in FQHC expansion.

Appendixes

1.1 Appendix 1

In this Appendix, we present the results from the logistic regressions for general care, mental health care, and dental care.

Table 8 Results from logistic regression model predicting demand of general care

Table 9 Probability of demographic group as general disease prevalence

Table 10 Results from logistic regression model predicting demand of mental care

Table 11 Probability of demographic group as mental disease prevalence

Table 12 Results from logistic regression model predicting demand of dental care

Table 13 Probability of demographic group as dental disease prevalence

1.2 Appendix 2 – utility function

In this Appendix we show how to determine the total utility from allocating a budget to FQHC expansion and increasing the number of Medicaid enrollees. Table 14 shows satisfied demand percentages by FQHC expansion by service type for various budgets as solved by the optimization model in Section 2.2.

Table 14 Satisfied Demand (%) and (#) by service type

Griffin et al. [23] developed service type weights based on the odds ratios from a logistic regression performed on NHANES data. These are provided in Table 15. We previously described in Section 2.2 how these weights were used in the objective of the optimization model. In this Appendix we show how we use them to help develop a quality score for the utility function.

Table 15 Adjusted weights for the four service types

Among the four service types, primary care is a basic service, and as seen in Table 16, the satisfied primary care demand is larger than that from other services. Starting with the satisfied demand of primary care services (N₁), there are eight possible cases. In Table 15 we show the weight sum and proportion for each of the cases.

Table 16 Service provision cases

The weights in Table 16 are a measure of the quality levels each combination of services compared to the case where all services are provided. They are calculated by adding the related weights from Table 16 (w_j). For example, the sixth case has a 100(0.40 + 0.03) = 43 % quality level compared with the case where all services are provided. Our goal is to determine the proportion of N₁ to include in each case. Under the assumption that receiving a specific service is independent of the provision of other services, the portion of each case is calculated by multiplying the corresponding percentages of (P_j) when service j is provided or (1-P_j) when service j is not provided. For example, the portion of sixth case will be P₁ × (1 − P₂) × P₃ × (1 − P₄) since this case represents that population who receives primary and dental services but not OBGyn or mental services. The aggregated percentage is obtained by summing the weighted portions as follows:

$$ \begin{array}{c}\hfill f(y)=\left({w}_1+{w}_2+{w}_3+{w}_4\right){P}_1{P}_2{P}_3{P}_4\hfill \\ {}\hfill +\left({w}_1+{w}_2+{w}_3\right){P}_1{P}_2{P}_3\left(1-{P}_4\right)\hfill \\ {}\hfill +\left({w}_1+{w}_2+{w}_4\right){P}_1{P}_2\left(1-{P}_3\right){P}_4\hfill \\ {}\hfill +\left({w}_1+{w}_3+{w}_4\right){P}_1\left(1-{P}_2\right){P}_3{P}_4\hfill \\ {}\hfill +\left({w}_1+{w}_2\right){P}_1{P}_2\left(1-{P}_3\right)\left(1-{P}_4\right)\hfill \\ {}\hfill +\left({w}_1+{w}_3\right){P}_1\left(1-{P}_2\right){P}_3\left(1-{P}_4\right)\hfill \\ {}\hfill +\left({w}_1+{w}_4\right){P}_1\left(1-{P}_2\right)\left(1-{P}_3\right){P}_4\hfill \\ {}\hfill +\left({w}_1\right){P}_1\left(1-{P}_2\right)\left(1-{P}_3\right)\left(1-{P}_4\right)\hfill \end{array} $$

(16)

To illustrate, we use a budget of 160M. Using the solution from Table 14 we obtain:

$$ \begin{array}{l}f(y)=100(1.00)(1.00)(0.26)(0.36)\hfill \\ {}+98(1.00)(1.00)(0.26)\left(1.00-0.36\right)\hfill \\ {}+97(1.00)(1.00)\left(1-0.26\right)(0.36)\hfill \\ {}+45(1.00)\left(1.00-1.00\right)(0.26)(0.36)\hfill \\ {}+95(1.00)(1.00)\left(1.00-0.26\right)\left(1.00-0.36\right)\hfill \\ {}+43(1.00)\left(1.00-1.00\right)(0.26)\left(1.00-0.36\right)\hfill \\ {}+42(1.00)\left(1.00-1.00\right)\left(1.00-0.26\right)(0.36)\hfill \\ {}+40(1.00)\left(1.00-1.00\right)\left(1.00-0.26\right)\left(1.00-0.36\right)=96.5\hfill \end{array} $$

To compare the impact of FQHCs and Medicaid expansion using an equivalent measure, a utility function is introduced. Phillips et al. [32] showed that patients receive care in an average month depending on their access and coverage status. They examined the services used for the four possible statuses (having both insurance and a usual source of care, having only insurance, having only a usual source of care, lack of both) based on data from the Medical Expenditure Panel Survey (MEPS) [35].

We use these results to set a service quality score for each case, and transform these scores through the use of a utility function that we define later in the Appendix. Table 17 shows the differences in how patients receive care depending on their status.

Table 17 Difference between groups from MEPS (out of 1000 people in an average month)

Assuming that all the visit types have the same effect on increasing service quality, the number of total visits represents the quality level that the population in a group receives. In order to determine the quality score, the number of total visits is compared to the first group’s 321 total visits. For example, the quality score for second group is 100(156/321) = 49.

Fig. 5

Service quality scores for four possible statuses

Figure 5 shows the resulting service quality scores for the four possible statuses. The possible improvements obtained by either locating a new FQHC or expanding Medicaid are shown by the arrows between status groups. For example, if a person is in status 4 (quality score of 25), there are two possible improvements. If FQHC service becomes available, the individual receives a usual source of care and will change to the third status (57 quality score). Therefore, this movement is worth 32 points of improvement. If the individual becomes eligible for Medicaid service, they move to status 2, and this change will be worth 24 points of improvement.

Table 18 shows how four types of improvements can be matched with the population groups (g ₁, g ₂) described earlier, along with the corresponding adjusted improvement weight α.We set this weight by scaling the improvement values to make 100 % the largest improvement (from status 2 to status 1).

According to Table 18, when we serve the population that has insurance but no access with a newly located FQHC, the health care quality shows the largest improvement, so we set that weight to 100 %. If we serve the population that has access but no insurance with Medicaid, the improvement would be 84 %. For the population lacking both, there could be 63 % improvement by an FQHC, and 47 % by Medicaid coverage.

Table 18 Improvement type and weight α

The components are now in place to develop an equivalent measure for Medicaid and FQHCs. For Medicaid, we define the utility of a budget increase by the total number of new Medicaid enrollees multiplied by the corresponding improvement rate. For the FQHC case, we first transform the demand using Eq. 16. We then multiply this satisfied demand by the corresponding improvement rate. Therefore, we can define the total utility U(x,y) by:

$$ U\left(x,y\right)={\displaystyle \sum_{g1=3,g2}{\alpha}_{g1g2}^M{x}_{g1g2}}+{\displaystyle \sum_{i,z,j,g1,g2}{\alpha}_{g1g2}^Ff\left({y}_{izjg1g2}\right)} $$

(17)

where α ^M _g1g2 is the improvement weight for Medicaid for group (g ₁, g ₂) and α ^F _g1g2 is the improvement weight for FQHCs. Note that since a potential Medicaid beneficiary should currently be uninsured, it is not necessary to define α ^M _g1g2 for the insured group (g ₁=1, 2). Similarly, for those patients that have a usual source of care, adding an FQHC would not necessarily increase their quality score. In this case, we would not need to define α ^F _g1g2 for g ₂=1. However, if it was found that adding an FQHC increased the services provided for some individuals in the service region, the α ^F _g1g2 would be strictly positive for the group that has a usual source of care (g ₂=1).

For the example used in this Appendix we will assume that α ^F _g1g2 = 1 is 0.05. This would imply that an insured individual having access to a new FQHC would increase their number of service encounters by 5 %. The resulting weights for this example are given in Table 19.

Table 19 Weights α ^F _g1g2 and α ^M _g1g2   by coverage and access group

We now illustrate how total utility is computed for the example of Pennsylvania when a budget of 160M is used for FQHC expansion and 150M for Medicaid expansion (total budget = 310M). First, the FQHC optimization model defined in Section 2.3 is solved. The solution provides the number served by FQHCs for each service type and group. The results are given in Table 20. The number served for general health is then transposed by f(y) for the FQHC budget of 160M. This was computed earlier in the Appendix and found to be 96.5 %. Converting this to a transposed number served is done by multiplying the general health number served by f(y). For example, for g ₁=1 (private insurance) and g ₂=1 (served area), the transposed number served equals 0.965(972862) = 842312. Multiplying this value by the corresponding α ^F _g1g2 gives the utility for that group. In this case for g ₁=1 and g ₂=1, utility equals 0.05(842312) = 42116.

For the 150M budget used for Medicaid expansion, the number of new enrollees for g ₂=1(served area) would be 26038 and for g ₂=2 (not served area) would be 2264 assuming an average cost per enrollee of $5,300. Applying the appropriate α ^M _g1g2 to each gives the utility. For example, for g ₂=1, utility equals 0.84(26038) = 21872.

The overall utility for this case is computed by summing the individual utilities and equals 181002. The results for this example are shown in Table 20.

Table 20 Utility results for a 310M budget (160M for FQHC and 150M for Medicaid)