Predicting High Need End-of-Life in Medicare Patients through Machine Learning

Abstract

Patients are often at risk of consuming significant medical resources during the last 6 to 12 months of life, without improving their life expectancy. We develop a model for predicting patients likely to die within the next 6 to 12 months based on administrative claims and demographic data. Standard statistical models as well as newer machine learning approaches are used to identify target patients. Patients identified through the model are candidates for palliative care of hospice care. Timely intervention with appropriate care has been shown to both improve the quality of life of such patients while also reducing resource consumption. We demonstrate the use of the model by incorporating in an economic model of an intervention program, showing that intervention in the highest predicted probability cohort can provide a positive return on investment, provided the program is targeted at the highest-risk patients.

1. Introduction

As the Medicare program struggles to control expenditures, there is increased focus on opportunities to manage patient populations more efficiently and at lower cost. A major source of expense for the Medicare program is beneficiaries at end of life. A recent paper by the same authors [1] concludes, using the Medicare Limited Dataset files that the full cost of Medicare decedents in 2015 amounted to 21% of Medicare’s expense in that year. A Kaiser Family Foundation study by Cubanski et al. [2] found the average cost per decedent in 2014 to be $34,500, or about 3.5 times the cost of the average Medicare beneficiary. A well-known paper by Finkelstein et al. [3] has been interpreted to imply that patients in the last year of life account for only 5% of spending. This interpretation is incorrect, because the authors were looking at the cost of patients predicted to die, rather than those who actually died. Because risk-taking entities such as Medicare Advantage plans and Accountable Care Organizations¹ (ACOs) need to reduce costs while improving the quality of care of terminally-ill patients, they should initiate programs to better manage the care of patients with serious or advanced illness [4, 5]. There is evidence in the literature that such programs both improve quality of care and provide savings to the payer [6, 7, 8]. With limited resources available to manage high-need patients, it is important to identify early those patients who are at risk of death within 6 to 12 months. Using available claims data and newer statistical methods it is possible to identify patients who are at risk of end of life and who are candidates for intervention.

2. Prior predictive models of end-of-life risk

It is important to understand the value of models for prediction either to supplement or replace the judgment of medical professionals. On the accuracy of clinician predictions, see Christakis and Lamont [9] or Selby et al. [10]. Models to identify patients at risk may be classified into three types:

• Rules-based models

An example of a rules-based model is that of Amy Kelley [11, 12]. Dr. Kelley stratifies patients merging different data sources. A challenge with such models is ranking patients according to urgency of intervention when multiple different scales are integrated.

• Parametric models

There are numerous examples of parametric models, both commercial and in the literature. A sample of publications may be found at [13, 14, 15, 16].

• Machine learning and Artificial Intelligence models

The remainder of this chapter discusses the development of Machine Learning and AI models.

3. Machine learning and AI models

There are various machine learning algorithms that can be used to solve complex problems. Using a data set, called Training Data (TD) we can look at various important characteristics behind a desired outcome. Developing a TD dataset requires subject matter knowledge so that there are fewer chances of spurious outcomes. See Duncan Chapter 3 [17] for an extensive discussion of administrative data and their use. We discuss some of the most compelling machine learning algorithms that can enhance our approach model development.

1. Decision Tree A decision tree is a non-parametric estimation procedure where the process begins with splitting choices progressively to identify the best options available for attaining the outcomes, predictions, or reduced residual noises. When splits are made progressively the process emulates tree branches and leaves. This is strictly a hierarchical model as shown in Figure 1 where the process starts from the top and then branches out along various conditional statements. Expected outcomes are measured at the end of the process by looking at the probability of each branch or node and then calculating expected outcomes. The decision tree approach is satisfactory for simplistic scenarios but fails in complex estimation problems.

   In the image above nodes indicate branching logic at which the tree splits into branches/edges. The end of the branch occurs when no further split is possible (in this case whether or not there was a Cardio diagnosis). The model uses two features/attributes from the data set, namely sex and age. The outcome is either a cardiac diagnosis or not.

2. Random Forest A Random Forest is simply an extension of the decision tree approach where multiple decision trees are assembled. The final estimation is done by tracking the mean outcomes from various trees included in the model. Random Forests assume that the learning from a single tree is much weaker than when a result gathered from multiple trees of unequal size. Final outcomes are derived as an average of various trees, resulting in lower variance and better predictions of the target outcomes (Figure 2).

   Random Forest (strong learner) is built as an ensemble of Decision Trees (weak learners) to perform different tasks such as regression and classification. Unlike Decision Trees, only one tree Random Forest generates n-trees randomly from training data.

3. Gradient Boosting Trees (GBT) Gradient boosting is a machine learning technique which uses decision tree models, called weak learners, and creates a composite model. Each successive tree in this model improves its prediction from the previous one by minimizing the error residuals from previous tree. This technique is also an ensemble method which combines multiple weak models. Based on using previous constructs of trees and their weighted residuals, the models attempt to slowly build more and more trees and in that process reduce noise (residual error) from successive builds. When ultimately the marginal (gradient) reductions in error becomes small or zero, the model completes the total construct (Figure 3).

   In the example blue dots (left) plots are input (x) vs. output (y). The red line (left) shows values predicted by decision tree. Green dots (right) show residuals vs. input (x) for i-th iteration. Each iteration represents the fitting of a gradient boosting tree. With more iterations we see that the residuals become smaller and smaller. At some point we consider that the model has come up with a prediction much robust compared to the first set of iterations.

4. Logistic Regression Model (LRM) Logistic regression is the appropriate regression analysis to conduct when the dependent variable is either dichotomous (binary) or may have multinomial (multiple) outcomes but at discrete levels. Like all regression analyses the logistic regression can be used as a predictive analysis. In our approach

   • Linear Model: $y=b_0+b_{1}x$.

   • Logistic Model: $p=\frac{1}{1+e^{-b_0+b_{1}x}}$.

Figure 1.

Decision tree example (from Duncan [15]).

Figure 2.

Random Forest – Simplified [18].

Figure 3.

Gradient boosting trees [19].

When there are limited dependent variables, the appropriate technique is not to use procedures like regression estimation due to the following disadvantages.

1. Prediction of linear regression will allow the expected value to fall outside the range of 0 to 1.

2. Due to the dichotomous nature of the dependent variable, the residuals of the linear regression method will not be normally distributed.

3. Logistic regression produces predicted values which are bound between 0 and 1 range.

4. In the case where the outcome variable has more than two outcomes, multinomial logistic regression may still be applied. In that case, every outcome is assigned a probability whose sum must be between values of 0 to 1.

1. Naïve Bayes The Naïve Bayes machine language technique borrows from Bayes’ Rule, which is applied to estimate probability of certain outcomes of interest based on our a priori knowledge of certain events preceding it. The 2nd aspect of this technique is Naïve which means independence of events. Applying Naïve Bayes’ approach is to figure out probabilities of given attributes and then estimate posterior probability of various outcomes of interest.

2. Deep Learning A subset of machine learning algorithms called Deep Learning is based on artificial neural networks. Such algorithms are based on functionality similar to a human brain, learning from large amounts of data. Deep Learning algorithms perform a task repeatedly, each time tweaking it a little to improve the outcome. We refer to “deep learning” because the neural networks have various (deep) layers that enable learning.

3. Neural Net Neural Net is another AI technique which has been growing in importance. There has been many applications in various sectors but we are mostly interested as they apply to improvements in predicting target outcomes in healthcare. There are various layers in this technique—input, hidden and output. The complex model may have multiple hidden layers. When Neural Net receives data via the input layer, it passes on that input to the hidden layers. Each input node may pass that information to one or multiple hidden layer’s nodes. The hidden nodes then create weights which is then applied to various combinations of inputs based on hidden connections and correlations which have been built in the hidden part of the model. When trained data is applied to the model, it goes via the input layer to various nodes of the hidden layer and then gets transformed in its journey to the output layer. During the training process, various weights and thresholds are continuously adjusted and readjusted so that training data consistently yield similar outputs (Figure 4).

4. Random Tree The Random Tree technique is similar to the Random Forest but deviates from that process by selecting attributes from a subset of trees instead of using all the trees. There are various types of stochastic processes that could be applied to randomly choose trees for an ensemble set of weak learners (trees). The model uses bootstrap sampling with replacement to generate sample data. The sample data is then used to grow a tree model. The model then proceeds to select part of the predictors and uses the best ones to split a tree node. This process is repeated in splitting various other tree nodes.

5. Generalized Linear Model (GLM) Generalized Linear Models are a family of regression models using maximum likelihood estimation techniques to generate parametric estimators including error distribution. This model can accommodate various distribution functions of the dependent variable—normal, binomial, Poisson, exponential, gamma, logistic, probit, fixed-effects, random-effects, nonlinear regression, quantile regression—to develop unbiased estimators. There is an assumption that the Link function is linearly related to the independent variables in the model. Unlike ordinary least square (OLS) or multi-variate least square (MLS), GLM uses the maximum likelihood estimator (MLE).

Figure 4.

Network diagram for a feed-forward NN model with one single hidden layer (from Duncan [17] chapter 12).

4. Objective

For the purpose of managing the utilization and cost of a population it is useful to identify those patients who, at end of life, are likely to be high utilizers of healthcare services. While in many cases such services are important and contribute to patient health, in other cases alternative treatments such as palliative care or hospice may be more appropriate and lead to higher quality outcomes.

Our objective in modeling is to identify members of an insured population that are at high risk, not just of mortality but of consuming considerable medical resources over a short time period (for example the last 6 months of life). An example of such a member might be a terminally ill cancer patient treated with certain modern biological drugs, or a patient admitted for an extended period to the ICU. We refer to these patients in the following discussion as “high need” patients. They represent a subset of patients for whom different treatment modalities exist (palliative care; hospice) that may contribute to high quality of life while reducing resource needs.

5. Data

We used CMS’s Limited Data Set (LDS)² for the years 2015–2016 to develop a data file for this analysis. In order to analyze data coded according to the same coding structure, we also restricted the analysis to the period October 1, 2015 through December 31, 2016 during which the ICD-10 coding structure was used. The mortality rate in our sample data is 4.5%, consistent with other studies of Medicare mortality rates as reported in Duncan [1]. Medicare managed care (HMO, Medicare Advantage) members are excluded because the reported data in the Medicare LDS dataset is not always complete.

We selected members who were enrolled in fee-for-service Medicare between October 1, 2015 through December 31, 2016 and those who died between April 1 and December 31, 2016. This more limited timeframe allows us to have at least 6 months of claims experience for both survivors and decedents. Starting with a sample size of 1.67 million members with both Part A (hospital) and Part B (Major Medical) coverage we revised with certain selections of conditions in order to screen members at low-risk of mortality. We required all members in our sample to have one or more of a list of conditions³ which reduces sample size slightly but improves the percentage of decedents. The selection at Step 2 in Table 1 reflects an attempt to capture members at risk of death. In Step 3 we extracted a 10% stratified random sample. These steps generated a test group consisting of 4983 deceased and 84,604 survivors and a validation group consisting of 2135 deceased and 36,027 survivors.

Sample Description	Test Sample			Validation Sample
	Deceased	Survived	% Deceased	Deceased	Survived	% Deceased
Step1: Medicare 5% FFS Sample with Parts A & B	52,194	1,116,665	4.5%	22,369	478,571	4.5%
Step2: Step1 minus Select Conditions	49,823	840,631	5.6%	21,353	360,271	5.6%
Step3: 10% Stratified Random Sample of Step2	4983	84,064	5.6%	2135	36,027	5.6%

Table 1.

Sample selection details.

5.1 Dependent variable

This model has a binomial dependent variable (survived or deceased). From the demographic data from the Medicare LDS dataset we are able to work with indicators of death and date of death.

5.2 Independent variables

1. The independent variables available for analysis are:

2. Age/Sex Bands—5 bands for male and 5 bands for female

3. Race—6 flags

4. Region—5 flags

5. HCC—79 flags based on CMS Medicare risk grouper⁴

6. Additional 5 HCC conditions⁴

7. 15 comorbid conditions

8. Additional 24 clinical conditions

9. Discharge indicator to Home/Self-care

10. Hospital readmission

11. ICU before death flag in 30 days

12. ICU before Hospice admission

13. Charlson Co-morbidity Index [20]

14. Hospice Admission count 3-month and 6-month prior to death

15. Inpatient Admission count 3-month and 6-month prior to death

16. SNF Admission count 3-month and 6-month prior to death

17. Transition of Care count 3-month and 6-month prior to death

18. 30-day Readmission counts over 6-month prior to death

19. ER Visit count 3-month and 6-month prior to death

20. ER Trauma Admissions 3-month and 6-month prior to death

21. Hospital Admission via ER flag

22. Total PMPM of Patient, square root of PMPM and square of PMPM

23. Percent cost of patients in last 3-month prior to death

24. Homecare DME

6. Results

We used RapidMiner™ software⁵ to develop various models. We used the test sample to explore various relationships between the dependent variable and the list of independent variables above. The validation sample was used to score the prediction of members’ outcomes into 2 possible categories - survival and death (Figure 5).

Figure 5.

Performance of models for predicting high need members.

There are three key measures we used to determine relative performance of the model, all for predicted probabilities >0.5. Specificity is the ability of the model accurately to predict the negative outcome (in this case survival). Sensitivity is the ability of the model accurately to identify the positive outcome (in this case death). Sensitivity measures how many of the High Need members did indeed consume considerable resources prior to death. Positive Predictive Value (PPV) measures accuracy for cases where prediction >0.5, how many members were correctly identified as experiencing high need death. The higher the probability, the more accurate the prediction. The findings can be summarized below:

1. Invariably almost all the models exhibited high specificity, meaning that members who were predicted to survive, actually survived. This is unsurprising given the high frequency of survival relative to death. This observation is true for most models (specificity >90%); the exception is Naïve Bayes (87.1%) which has the lowest specificity of all the models.

2. Sensitivity shows the proportion of those members with probabilities exceeding 50% (i.e., p > 0.50) who were predicted to experience high need. Naïve Bayes’ has the best score (78.8%), followed by Deep Learning (63.2%), Logistic Regression (60.4%), GLM (58.0%), Neural Net (57.5%), and followed by Gradient Boosted Tree (53.3%) being the Top 6 models. High sensitivity score is very important because it generates a higher proportion of people for expected deaths.

3. Regarding the positive predictive accuracy (PPV), most models perform well, with a few exceeding 90% accuracy. This measure is a ratio of people predicted to die with a p > 0.50 as a proportion of all members (e.g., survivors and decedents) in that range. This measure shows the accuracy of the model in predicting high need (or deceased) people as a proportion of all members in that probability range. Some models have high PPV but low sensitivity. That reduces the model’s overall efficiency, that is, it is only accurate on a small number of people. The Top 6 models are Random Forest (97.8%), Gradient Boosted Tree (90.3%), Decision Tree (88.3%), Logistic Regression (85.5%), GLM (83.7%) and Deep Learning (77.3%).

4. We also created percentage of cost (i.e., % of Cost) measure which shows cost of high need members who were predicted (at p > 0.50) to die as a percentage of all costs for those who deceased or survived. Performance is mixed with the Naïve Bayes model doing well at 23.4%. Deep Learning and Logistic models being the other two at 19.5 and 19.2% respectively.

The appropriate choice of attribute from Sensitivity, Specificity and PPV is an art. For example, we could pick a model with high sensitivity like Naïve Bayes (78.8%) as best performer, but we have a problem because its PPV is very low (34.1%)! Since specificity is relatively high for all models, we can choose best performers based on only PPV and Sensitivity attributes.

How do we weigh sensitivity and PPV? It depends on the proposed use. For example, one may weigh PPV higher than sensitivity or vice versa. If PPV is weighed higher than sensitivity, then Random Forest and GBT could be possible candidates. However, if sensitivity is more important than PPV, then possibly Naïve Bates and Deep Learning models could be good performers.

Finally, if we assume equal weights for both sensitivity and PPV from the list of all models, then the following rankings could be made (with the top 4 performers all clustered just above 70%): Logistic Regression (73.0%), GBT (average 71.8%), GLM (70.9%), Deep Learning (70.3%), Random Forest (68.7%), Neural Net (67.1%), Decision Tree (66.9%) and Naïve Bayes (56.5%). Random Tree model has zero sensitivity and thus not included for any consideration.

Lastly, if we take product of PPV and Sensitivity, the ranking remains in favor of logistic regression (51.6%), followed by Deep Learning (48.9%), GLM (48.5%), Gradient Boosted Tree (48.1%) and Neural Net (44.0%). The new ranking based on the product of sensitivity and PPV measures the dual impact of accuracy and how much of an impact it can have on the underlying eligible population, especially those who were predicted to be of high need (deceased). Table 2 shows various measures of model efficiency. Product of PPV and Sensitivity changes the ranking compared to equal weights placed on PPV and Sensitivity measures although Logistic Regression model comes out on the top of both considerations.

Models	Accuracy (PPV)	Sensitivity	Specificity	% of Cost	Equal Weight PPV, Sensitivity	Product of PPV and Sensitivity
Logistic Regression	85.5%	60.4%	95.6%	19.2%	73.0%	51.6%
Deep Learning	77.3%	63.2%	95.4%	19.5%	70.3%	48.9%
GLM Model	83.7%	58.0%	96.1%	18.0%	70.9%	48.5%
Gradient Boosted Tree	90.3%	53.3%	96.7%	17.1%	71.8%	48.1%
Neural Net	76.6%	57.5%	95.8%	17.7%	67.1%	44.0%
Decision Tree	88.3%	45.4%	97.1%	14.1%	66.9%	40.1%
Random Forest	97.8%	39.5%	97.7%	12.5%	68.7%	38.6%
Naïve Bayes	34.1%	78.8%	87.1%	23.4%	56.5%	26.9%
Random Tree	0%	0%	100.0%	0%	0%	0%

Table 2.

Summary of model PPV, sensitivity and specificity at p > 0.5.

7. Application to population management

7.1 Program development

The development of a model such as that developed in this chapter, while interesting theoretically, has important practical applications. The ability to identify early in an insured member’s course of illness that the patient is likely to be a high need, end-of-life patient allows care managers to begin discussions about palliative care earlier. This section develops a simple economic model to demonstrate the application of the model in the context of care management programs.

We were able to estimate the impact of identifying members who are predicted to die within a period of 6–12 months and moving those members to palliative care. Based on the 2021 Medicare budget of $829 billion dollars [21] the potential of savings as a percent of total cost is provided in Figure 6 below. Given that the Naïve Bayes model has a low PPV, we would prefer to apply either the Logistic model or the Deep Learning model, or other models like GLM, Neural Net or GBT to identify members at risk of high need death. Figure 6 basically shows potential costs associated with the high need population that could be targeted for end-of-life planning. The cost estimate shows the proportion of total cost (excluding pharmacy) at risk. The extent of savings depends upon the early target and providing palliative care for the willing patients.

Figure 6.

Predicted impact of EOL model on cost of Care for Medicare Population in 2021.

7.2 Using the model for program planning

Table 3 shows the application of the model in combination with program economics to plan an intervention program.

Decile	No. Members	Death Probability	Expected Deaths	Actual Deaths	Nurse Case-load (annual)	No. Nurses	Nurse cost (fully-loaded)	Program Cost	Est. Cost/Patient 2023; 90 days)	Expected Total Cost of sub-set	Estimated engagement (40%)	Estd. Cost Avoided (40%)	ROI
1	3817	0.2%	7.6	6	360	10.60	$550,000	$ 5,831,528	$ 19,435	$ 74,182,506	1527	$46,643	0.01
2	3817	0.3%	11.5	10	360	10.60	$550,000	$ 5,831,528	$ 19,435	$ 74,182,506	1527	$77,739	0.01
3	3817	0.4%	15.3	10	360	10.60	$550,000	$ 5,831,528	$ 19,435	$ 74,182,506	1527	$77,739	0.01
4	3817	0.5%	19.1	7	360	10.60	$550,000	$ 5,831,528	$ 19,435	$ 74,182,506	1527	$54,417	0.01
5	3817	0.6%	22.9	13	360	10.60	$550,000	$ 5,831,528	$ 19,435	$ 74,182,506	1527	$101,061	0.02
6	3817	0.8%	30.5	32	360	10.60	$550,000	$ 5,831,528	$ 19,435	$ 74,182,506	1527	$248,765	0.04
7	3817	1.2%	45.8	36	360	10.60	$550,000	$ 5,831,528	$ 19,435	$ 74,182,506	1527	$279,861	0.05
8	3817	1.8%	68.7	68	360	10.60	$550,000	$ 5,831,528	$ 19,435	$ 74,182,506	1527	$528,626	0.09
9	3817	4.0%	152.7	213	360	10.60	$550,000	$ 5,831,528	$ 19,435	$ 74,182,506	1527	$1,655,842	0.28
9.5	1908	14.4%	274.8	336	360	5.30	$550,000	$ 2,915,000	$ 19,435	$ 37,081,536	763	$2,612,033	0.90
10	1900	77.8%	1478.2	1404	360	5.28	$550,000	$ 2,902,778	$ 19,435	$ 36,926,058	760	$10,914,565	3.76
			2127.0	2135						$ 741,650,151

Table 3.

Economic model for planning EOL intervention program.

We first divide the population by decile according to predicted deaths (we further divide the top decile into sub-cohorts in order to illustrate the method). Applying the probability of death to the population by decile allows us compare predicted and actual deaths. The model performs well overall in terms of total predicted deaths; by decile the model also performs reasonably accurately with members identified with a high predicted score dying at a high rate. Importantly, the model allows the program planner to identify that cohort of members in which there is likely to be a high probability of death, and other cohorts with a low probability that are not as likely to justify an intervention program. Said differently, focusing on the highest predicted risk members captures the largest proportion of members.

The question that we address: if the model is to be used for planning an intervention program, how should this be done? We incorporate some data into the decile table about the number of nurses required to intervene with patients in a palliative care and hospice program, the cost of the program and the likelihood of patient engagement. Combined with a “success” rate (actual number of deaths from the model together with likelihood of cost avoidance) we are able to estimate a Return on Investment (ROI) in such a program. For more information about program design, operation and outcomes see Yosick et al. [6].

Noticeably the program returns a positive ROI only in the top sub-population. The ROI in this sub-population is, however, substantial. It is sufficiently high that if a program sponsor were interested in total savings rather than ROI, it would be economically efficient to manage a larger cohort of patients. If, for example the program sponsor were to manage the top 2 cohorts (top decile in total) the total savings would be $13.5 million at an ROI of 2.325, vs. total savings of $10.9 million at an ROI of 3.76 in the top cohort.

8. Conclusion

In this chapter we have discussed the development of different machine learning and AI models to predict a specific outcome, the likelihood of high need death in a senior population (U.S. Medicare Fee-for-Service members 2015–6). We find that different models perform better on certain measures and that the choice of model depends on a balance of statistical tests and practical application. We combine the predictive model with assumptions about nursing costs and program efficiency to build an economic model for use in planning an intervention program. The economic model shows that a palliative care and hospice program could save substantial cost if applied to the right population.

Acknowledgments

Ian Duncan PhD FSA FIA FCIA FCA CSPA MAAA is Adjunct Professor of Actuarial Statistics at the Dept. of Statistics & Applied Probability, University of California, Santa Barbara, and President, Santa Barbara Actuaries Inc., Santa Barbara CA USA.

Tamim Ahmed is Director of Analytics, Santa Barbara Actuaries Inc. Santa Barbara CA USA.

RapidMiner™ is used with permission of Altair Engineering Inc. Altair is a global leader in computational science and artificial intelligence (AI) that provides software and cloud solutions in simulation, high-performance computing (HPC), data analytics, and AI. Altair enables organizations across all industries to compete more effectively and drive smarter decisions in an increasingly connected world – all while creating a greener, more sustainable future. For more information, visit https://www.altair.com/.