A.1.2 Other Modelling Approaches
There are five major modelling methodologies presented in the previous healthcare predictive modelling studies: simulation, formula-based, statistical, probabilistic and queueing. Methods like formula-based and queueing theory are not practical for this research. Formula-based models derived from empirical data based on observed pat- terns in variables, like crowding, are generally poor regarding predictability power. Moreover, queueing-theory modelling has poor predictability performance and has lim- itation due to assumptions, which in a dynamic system this must be relaxed and tested by data from the actual system (e.g. stationary arrival time) (Wiler et al.,2011). In the following, firstly, the main regression methods in the modelling are outlined. Next, the Markov modelling is presented. Afterwards, the pros and cons of applying simulation modelling on healthcare problems are discussed.
A.1.2.1 Regression Modelling
Regression methods such as LR, LMMs1, GLM(GLMs), Generalised Linear Mixed Models (GLMMs) have been popular methodologies for modelling pathways and cor- relations (Garson,2012).
The LMM is a broad name for Hierarchical Linear Models (HLMs) and Multilevel Models, and it is used in the analysis of variance correlation, regression and factor analysis. The LMM is suitable for modelling problems with dependent observations with correlated errors. TheLMMsupports analysis of three types of variables: random effects, hierarchical effects and repeated effects. TheGLMM is an extension of LMM, which supports a variety of link functions. The fundamental importance of theGLMM
is that it supports continuous and ordinal features with non-normal distributions (Gar- son,2012).
Kulinskaya et al.(2005) provided a comparison betweenGLMmethod against a robust method such as truncated maximum likelihood for a LoS problem. The comparison was carried out on the Nervous System classification of Health Resource Groups (HRG) of the NHS. Although the robust model produce a better fit regarding variance, the differences between the two models were not significantly high in overall. Also, the
GLMmodel did outperform the robust models for a subset of factors.
1Mixed Models are also known as Mixed Effects Models, Random Coefficient Regression Models, Multilevel Models or Covariance Components Models.
A.1.2 Other Modelling Approaches 156
Adeyemi et al.(2013) presented aGLMMfor detecting stage-wise transitions in patient pathways modelling with excluding the clinical flow pathway. The solution modelled the serial independence of the readmission using continuous ratio logit model. The con- tinuous ratio logit model was used on Chronic Obstructive Pulmonary Disease (COPD) patients, to compare the categorisation factors for frailties. The method was effective in detecting the most critical threshold for readmissions.
The advantage of mixed modelling in regression is that it can account for the un- certainty in models and small evidence data. But, the major shortcomings of the mentioned regression methods are the linearity assumption. Moreover, the regression methods ignore the prior distributions and are very dependent on the subject of design; therefore, it is very hard to generalise or re-use them on similar problems.
A.1.2.2 Markov Modelling
In stochastic state-space modelling, Markov Model (MM) (Norris,1998,Ross,1993) is one of the most powerful tool. Markov modelling is simplistic approach; however, it becomes very complex, when there are a large number of states, or multiple events are modelled.
In the area of survival analysis, the PHD modelling (Neuts, 1974,1981) is a popular approach for modelling systems with state-space and latent parameters and is a way of modelling Markov stochastic process. Coxian phase-type distributions (C-PHD) (Cox,
1955) is a special type of PHD with an initial and an absorbing state, which avoids over parametrisation of the model (Fackrell,2009,Marshall and Zenga,2009).
Altman(2007) presented an extension to theHMMcalled MixedHMMwhich accounts for two sources of heterogeneity: time constant unit-specific effects and serial correla- tion. Maruotti(2011) provides two case studies for analysis of longitudinal data using
MHMM. The time-series that were studied are patent data and financial economet- rics; however, there is no library available for it and the estimation step is complex particularly for parametric models.
Length-of-Stay (LoS) models of is another research area which is highly associated to hospital readmission (Kelly et al.,2012). Xie et al. (2005) develops aMM to predict
LoS in continuous time for elderly patients. The proposed continuous time MM uses home care to model movement of elderly in residential, nursing homes and discharge to community or hospital, with two possible states: short-term and long-term stays. The model provides a good fit to the data and can capture the movement of patients
A.1.2 Other Modelling Approaches 157 between care facilities.
A.1.2.3 Simulation Modelling
There are three main approaches in simulation modelling in healthcare: Discrete Event Simulation (DES), System Dynamics (SD) and Agent-Based Simulation (ABS) mod- elling. Simulation modelling techniques provide a better understanding of the interac- tions and flows. However, most reported studies are limited by the parameters bounds, problem domains, lack of scalability and reusability. The reason behind these shortcom- ings is partly because of models complexities and the amount of data they depend on. Also, another reason stems from the weak economic and political support of projects.
DES modelling techniques generally have been used for planning healthcare services, economic modelling and disease intervention. Moreover, SD modelling techniques mainly have been used for policy evaluation, economic modelling, system and infras- tructure modelling. Finally, the applications of ABSmodelling is not yet widespread, because it is a newly developed methodology, and modelling the agents is highly com- plex. ABShas the potential to model the quality of care and used to study the scale and granularity of system behaviour. TheDESand SDcan be considered as a compliment to each other, sinceDESmodels look at the detailed level, andSDuses the aggregated level. Therefore, depending on the problems, these two approaches alone can impose some limitations in model development (Gunal and Pidd, 2010, Kanagarajah et al.,