IMA Journal of Management Mathematics - current issue

Editorial

Utley, M., Chaussalet, T., Baker, R. — Thu, 27 Aug 2009 06:37:44 PDT

Non-homogeneous Markov models for sequential pattern mining of healthcare data

Garg, L., McClean, S., Meenan, B., Millard, P. — Thu, 27 Aug 2009 06:37:44 PDT

Sequential pattern mining has been a popular data mining technique for extracting useful information from large databases and has successfully been used for numerous industrial and commercial problems. This paper presents a new mathematical modelling application to healthcare, providing important information to health service managers and policy makers to help them identify sequential patterns which require attention for efficiently managing scarce healthcare resources and developing effective healthcare management policies. In healthcare, these sequential patterns are analogous to the patient pathways. We present a non-homogeneous Markov model for identifying not only patient pathways which have high probability but also for identifying pathways which incur high cost or time. In order to have a more realistic model, we also consider time-dependent covariates and their impact on the pathways. An algorithm based on branch and bound global optimization is presented which can efficiently extract a required number of such patient pathways of interest. The approach is illustrated using historical data on geriatric patients from an administrative database of a London hospital.

Analytical methods for calculating the distribution of the occupancy of each state within a multi-state flow system

Utley, M., Gallivan, S., Pagel, C., Richards, D. — Thu, 27 Aug 2009 06:37:44 PDT

We present analytical techniques for estimating the time-varying occupancy of each state within any multi-state flow system that can be represented as a particular type of directed graph called a rooted directed tree. Such systems have a single point of entry from which each other state within the system can be reached by exactly one directed path. The discrete-time model presented incorporates the use of time-varying and general distributions for the number of individuals entering the system and of general sojourn time distributions for each state. We illustrate the use of such analysis in the context of the delivery of mental health services in the community for people with common mental health problems and then discuss the possibility of adapting these methods with relation to systems that have a structure more complex than that of a rooted directed tree.

Modelling risk of readmission with phase-type distribution and transition models

Demir, E., Chaussalet, T., Xie, H., Millard, P. H. — Thu, 27 Aug 2009 06:37:44 PDT

A patient with frequent past readmissions may have an increased risk of future readmission. The principal objective of this paper was to determine the risk of readmission, given individual patient's history of readmissions. First, we develop a modelling approach to systematically tackle the issue surrounding the appropriate choice of a time window which defines readmission. Discharged patients can be divided into two groups: a group at high risk of readmission and a group at low risk. Using national data (England), the estimated time window for chronic obstructive pulmonary disease is 38 days. Using this time window, we classify ‘high’ and ‘low’ risk of readmission groups. We use transition models to incorporate patients’ history of readmissions along with additional covariates. Solely using patients’ history of readmissions, the model has a receiver operating characteristic c statistic of 0.71, illustrating that such a simple model with no covariates has the potential of estimating risk of readmission.

A genetic algorithm approach to the nurse scheduling problem with fuzzy preferences

Duenas, A., Tutuncu, G. Y., Chilcott, J. B. — Thu, 27 Aug 2009 06:37:44 PDT

The nurse scheduling problem (NSP) consists of generating a work schedule for nursing staff in a hospital. The approach presented in this paper considers a multi-objective NSP involving the nurses’ preferences. These preferences are modelled by fuzzy sets and aggregated to determine an overall preference cost function. The schedules are generated by a hybrid approach based on an interactive sequential multi-objective problem solving method combined with a genetic algorithm (GA). The head nurse is identified as the decision maker. Different versions of the GA are developed to test the efficiency of the approach. The results reveal that the proposed approach generates good quality solutions and due to its flexibility may be applicable in real-life NSPs.

Exploring potential consequences on mortality estimates of errors in clinical databases

Pagel, C., Gallivan, S. — Thu, 27 Aug 2009 06:37:44 PDT

Much time and energy are spent collecting and recording clinical data relating to outcomes, either within a single hospital or at a national level, in order to assess performance. Analysis of these data, particularly with respect to mortality rates, is a key part of clinical governance. However, most analyses are based on the assumption that data are accurate whereas, given the complexity of the data-gathering procedures, errors are not uncommon. Thus, it is useful to have insight into potential problems that might arise from analyses based on incomplete or erroneous data. We have developed a mathematical model that can be used to assess the effects of errors on estimates of mortality rates derived from clinical databases. Using simple assumptions about the nature of such errors, we have conducted thought experiments to investigate their potential impact. We show that there are plausible circumstances in which errors could cause systematic biases potentially leading to serious misinterpretation of clinical performance.

Equilibrium replenishment in a supply chain with a single distributor and multiple retailers

Kogan, K., Perlman, Y., Hovav, S. — Thu, 27 Aug 2009 06:37:44 PDT

This paper addresses a problem encountered by a large-scale health service supply chain operating in a periodic review mode. Due to the vital nature of the products it provides, the number and timing of urgent orders are not limited. As a result, increasingly high transportation costs are incurred and the problem is to select an inventory replenishment (review) period that minimizes the transportation cost. Moreover, the supply chain involves multiple retailers which inevitably and independently respond to any change in replenishment policy since it may affect their inventory costs. Such a relationship results in a game between a distribution centre and retailers. Since the problem is intractable due to its scale and stochastic nature, we combine a game theoretic approach with an empirical analysis. We show that this system is predictable using equilibria and that the current replenishment equilibrium of the health service supply chain is close to the Nash solution. Numerical analysis shows that the transportation costs are cut if the distribution centre implements in reality its formal (Stackelberg) leadership by reducing the replenishment period. However, this does not coordinate the supply chain and greater system-wide savings are possible by increasing the replenishment period if the supply chain is vertically integrated or the parties cooperate.