Modeling patient's value using a stochastic approach: An empirical study in the medical industry

Highlights

• A new model to predict patients’ value in the medical industry.

• A combination of Markov chain and data mining to model customer lifetime value.

• Enhancing profitability of health centers by using a new CLV model.

• Finding more profitable patients using computer-based methods.

• Modeling patients’ behavior using computer-based methods.

Abstract

Background and objective

The rapid growth of computer methods encourages and creates competitive advantages in the medical industry. Nowadays many health centers try to build successful and beneficial relationships with their patients using customer relationship management (CRM) methods, to recognize target patients, attract potential patients, increase patient loyalty and maximize profitability. Customer lifetime value (CLV) is a metric that can help organizations to calculate their customers’ value or group them; therefore in this research we aim to develop a new CLV model for the medical industry that groups patients using computer-based methods.

Methods

To model CLV for the medical industry, we will use two computer-based methods. First, to model patients’ behavior, a data mining approach is required: the K-means algorithm is used to cluster patients and the decision tree technique is used to analyze patient clusters. Next, Markov chain model, a stochastic approach, is utilized to predict future behavior of customers

Results

This paper proposes a new CLV model for the medical industry that has some benefits over other CLV papers. It is patient behavior based, helping us to predict the future behavior of each patient as well as helping to modify managerial strategies for each type of patient. The derived CLV model includes less than 0.08 error rates.

Conclusions

Using the derived CLV model helps health centers to group their patients by computer-based methods, which makes their decision making more accurate and trustworthy. The present research helps organizations within the health industry to group and rank their patients by a new CLV model and fit their strategies to each patient group, based on his/her behavior type.

Introduction

With the increasing competition among companies, a business may strategically focus on customers to gain more market share. Today customers are intangible assets of an organization [1], hence establishing a beneficial relationship with each customer is considerably important. Customer relationship management (CRM) is a managerial endeavor that ranks customers to enhance loyalty [2] and it is used to fulfill customer needs during their interactions [3]. In all CRM applications it is important to separate customers based on their value, to continue building the best relationship with them; to do so, customer lifetime value (CLV) is a useful concept. CLV is defined as the present value of the future stream expected given a time horizon by Kotler in 1974, where it is gaining increasing importance as a marketing metric in both academia and practice [4].Customer lifetime value plays an important role in CRM endeavors, since it enables companies to segment customers and identifies those who bring largest profit [5].

Due to the fierce competition of enterprises in many industries, using CRM has become necessary. Applying CLV can help to rank customers based on their value [6]. The growing competition in the medical industry and the increasing requirements of health care quality makes IT techniques more and more useful [7]. For example, as a cutting edge IT technique, big data analytics have been used in the medical industry [8]. As a result, many health centers have tried to build a successful CRM to recognize target and potential customers, increase loyalty and satisfaction, as well as maximize their profitability [9]; holding the view that the customers in this industry are the patients of health centers.

Loyal patients represent the competitive advantage of an organization. Loyalty follows one or repeat occasions of patient satisfaction; in particular, patient loyalty is enhanced by offering efficient and comprehensive services to patients [10,11]. In health centers it is possible to maximize profit by offering appropriate services to each group of patients.

Many studies have been undertaken in the CLV field. They can be divided into two main groups. The first comprises studies that develop a new CLV model [12], [13], [14]; the second includes papers which use CLV models to help with managerial decision making, strategy development, ranking, promotion planning and so on [15], [16], [17], [18], [19].

In this section we will explain important terms, and also describe the methods that will be utilized in paper modeling.

There are different definitions in the literature for the customer lifetime value, that we mention some of them here. Dwyer defined CLV as the present value of the expected benefits less the burdens from customers in 1997 [20], while Gupta and Lehmann defined CLV as the present value of all future profits generated from a customer [21]. Venkatesan and Kumar referred to CLV as the application of contemporary finance principles in the assessment of customer value and relationship management [23] and it was used as a metric for customer selection and marketing resource allocation, but in some researches, CLV is used as an indication or prediction of net profit attributed to the entire future relationship with a customer [22] What's more, CLV has been defined as a core customer-centric metric that is calculated as the net present value of all future profits derived from a customer over his or her lifetime with a firm [24].

To count customer lifetime value, different models were introduced in the first group of papers discussed above [12]. We will review some of them below.

RFM is an applicable CLV model used in various industries [25], [26], [27], [28], [29], [30] which tries to count customer lifetime value by three parameters containing Recency, Frequency and Monetary. Recency (R), as days since last purchase, identifies how many days ago the last purchase occurred. Frequency (F), as total number of transactions, denotes how many times the customer has purchased a service or product from the firm. Finally, Monetary (M), as total money spent, shows how much a customer has spent in the firm. To get M value, simply total the money from all transactions. As mentioned in the literature review of the RFM model, M refers to the revenue created by each customer during their lifetime. Weighted RFM is another model weighing R, F and M based on their effectiveness in the related industry. Extended RFM is used to count CLV too. In extended RFM models, other effective parameters are added to R, F and M [28], [31], [32], [33].

Another useful approach to count CLV is stochastic approach. Take for example, Markov chain model which can help researchers to predict the future value that will be created by customers [13], [34], [35], [36].

Data mining techniques are used in numerous CLV papers. Clustering and classification help grouping customers based on their similarities or value and help to better manage them [18], [37], [38], [39].

Due to the important of using CRM concept in the medical industry in this section we are going to review papers which studies CRM in the medical industry.

In 2003, Etheron highlighted the importance of patients’ differentiation to optimize the costs of an organization; he used CLV to count the value of dental patients [40]. Yeh in 2011 attempted to predict the hospitalization of hemodialysis patient's data to develop a decision-making support system [38]. Also in 2012, Chen sought to identify target patients to appropriately allocate resources for them in health care centers [7]. He integrated RFM and data mining approaches to optimize health care services. In 2016, Zare's research sought to learn more about patient's behavior via data mining techniques and CLV models in a public health care service. The CLV model utilized in that research was eRFM, an extension to RFM [9].

Based on the importance of calculating customers’ value in enterprises, many CLV studies have been conducted in recent decades; some were mentioned in the background section and an overview is provided in Table 1.

Two techniques of data mining containing clustering and classification are used in this research. Clustering is an unsupervised method which is the process of organizing objects into groups whose members are similar in some way [8], and classification is a supervised method which entails assigning labels to existing situations or classes. K-means is a popular clustering algorithm, partitioning n observations (data) into K clusters in which each observation belongs to the cluster with the nearest mean. Decision tree algorithm solves classification problems by using tree representation. Knowledge extracted from the resulting decision tree can help to better understand the data.

The basic concept of Markov chain model was introduced in 1970 by Andrey Andreyvich Markov. Markov chain is a stochastic process with the Markov property. Markov chain refers to the sequence of random variables such a process moves through, with the Markov property defining serial dependence only between adjacent periods.

$$\mathrm{Pr}\left(X_{n+1}=x|X_1=x_1,X_2=x_2,\dots ,X_n=x_n\right)=\mathrm{Pr}\left(X_{n+1}=x|X_n=x_n\right)$$

$$\mathrm{Pr}\left(X_1=x_1,X_2=x_2,\dots ,X_n=x_n\right)>0$$

The stochastic process contains a set of random variables that all special values that the random variables take on are named as a state (X_i). The set that each state accepts is called state space. The state space of the desired Markov chain in this research will be types of customers’ behaviors. The probabilities of moving from one state to another in a single period are called transition probabilities [36]. There will be a (one-step) transition probability matrix that describes the probability of each transition among two states, named as P. The t-step transition matrix is defined to be the matrix of probabilities of moving from one state to another in exactly t periods (P^t). It is a well-known property of Markov chain modeling that the t-step transition matrix is simply the matrix product of t one-step transition matrices [36]. In fact the (i,j) element of matrix P^t is the probability that the customer will have behavior j at the end of time t given that he started at behavior i.

$$P^t=P^1\times P^{t-1}$$

In this paper we seek to predict value of a dental clinic's patients. We develop a CLV model using Markov chain model and data mining techniques. A RFM model is used to model revenue vector of patients with similar behaviors.

Each group of patients shows different behavior types. Each type needs different attention and capital allocation in order to increase profitability.

Using patients’ data and data mining techniques, we become able to model patients’ behaviors. Utilizing Markov chain model, we can predict future behavior of patients, therefore in this paper we will become able to segment customers based on their behavior types.

In the next section of this paper we will explain the research methodology. Section 3 describes the experiment in detail. Section 4 presents the results and Section 5 contains the discussion and conclusion is represented in Section 6.