Modelling the transmission of healthcare associated infections: a systematic review

Figure 3 shows that MRSA was the most common bacterial species studied (34%; 33 studies) [14‐46], followed by Vancomycin-resistant Enterococcus (VRE) (or glycopeptide-resistant enterococci) (16%; 15 studies) [12, 18, 28, 31, 47‐57] whereas C. difficile has rarely been the subject of a model (3%; 3 studies) [58‐60]. As several studies investigated the dynamics of more than one pathogen, the total number of infection agents (N=102) listed in Figure 3 exceeds the total number of studies (N=96).

The first model of HCAI conceptualised the spread of antibiotic resistance in bacterial populations among hospital patients [13]. This was soon followed by models evaluating the effectiveness of interventions to reduce antibiotic resistance (e.g. antibiotic cycling or mixing). Since then, most HCAI models have aimed to quantify infection control effectiveness (64%; 62 studies). The infection control measures most frequently considered among these 62 papers have been: hand hygiene (37%; 23 studies), patient isolation (24%; 15 studies), HCW cohorting (23%; 14 studies), antibiotic stewardship (21%; 13 studies), and screening (18%, 11 studies). Figure 4 provides an overview of the main interventions modelled over time, emphasising that decolonisation and vaccination are more recent subjects of study. Moreover, a wider variability of interventions has been evaluated in the later years. Table 1 illustrates the type of interventions that have been evaluated for each HCAI pathogen.

Models are often used to increase epidemiological understanding. Hospital surveillance data, which is frequently used to inform HCAI models, can lack detail in what is needed for modelling purposes. For example, information on asymptomatic carriage and timing of events (e.g. infection) are often lacking. Several studies use new statistical methods to overcome such difficulties [31, 36, 48] and to allow for estimation of important epidemiological parameters (e.g. transmission rates) from different data sources, varying from routinely collected hospital data [56, 57] to strain typing [63] or genotype data [64]. Others use modelling techniques to determine the relative importance of potential transmission reservoirs or acquisition routes (of C. difficile[58, 60], VRE [50, 53], cephalosporin-resistant Enterobacteriaceae (CRE) [65] and SARS [66].

The ecological dynamics of pathogens have also been explored using models, including antimicrobial resistance [13, 67, 68]; co-colonisation with different pathogen strain types [27, 46] and competition between strains [24]. Another more recent subject of study is the potential impact of readmission of patients from settings such as long-term care facilities (LTCFs) or the community, as well as general movement patterns between healthcare institutes and/or the community on the transmission of MRSA [19, 25, 38, 69], antimicrobial resistance [70] and HCAI in general [71].

Economic outcomes were not considered in dynamic transmission models until 2011 [14, 23, 72]. Three recent papers applied dynamic modelling techniques to estimate the economic burden of disease (MRSA) [22] and norovirus [69], and to investigate economic incentives for infection control investments [73].

A number of studies (36%, 32 studies) did not specify a particular national setting. Of the publications that did; only three studies (3%) explored transmission of HCAI in lower and lower middle income countries [22, 74, 75] and another three looked at upper middle income China [15, 66, 76]. Studies have mainly concentrated on the United States (16%; 15 studies), the United Kingdom (13%; 12 studies) and the Netherlands (10%; 10 studies).

The first HCAI models captured transmission dynamics in single wards using deterministic approaches [13, 16]. As the population size in a single ward or hospital is likely to be small, a stochastic modelling approach may often be more appropriate as it can take account of the role of chance in determining transmission patterns. In Table 2, a definition of the modelling terms used for model classification is provided. Figure 5a shows that the proportion of stochastic models has increased steadily over time, and as Figure 6 illustrates, stochasticity was soon introduced (in 1997) [77] after publication of the first (deterministic) HCAI model. Several studies developed both a stochastic and a deterministic version of a similar compartmental model to investigate whether projected intervention effects were partly a result of random fluctuation [18, 35, 40, 78‐80]. Others use a deterministic model to interpret the findings of a stochastic model [81].

Infectious disease models can have either an aggregate (or compartmental) structure (which tracks groups in the population) or an individual-based structure (which tracks individuals). The latter enables better incorporation of heterogeneity in patient characteristics such as patient demographics, contact patterns and disease history, but at the cost of increased computational burden. To date, most (73%; 70 studies) HCAI models have taken an aggregate approach, although the proportion of individual-based models has increased over time (Figure 5a). In total, 26 publications (27%) took an individual-based approach of which seven papers (8%) used both compartmental and individual-based modelling [25, 34, 60, 72, 83, 95, 96].

Model parameter values can be based on existing studies, assumptions, or estimated directly from data [103]. Unknown parameters, such as infection transmission rates, can be inferred by calibrating a model to empirical data. With the increasing availability of computational power, numerically-intensive statistical methods for parameter inference have become more accessible. As Figure 5b shows, although only 35% (34 studies) of HCAIs models have incorporated some sort of calibration process to empirical data, this proportion has increased over time. Metrics used to quantify goodness of fit include the least square criterion (minimisation of sums of squares between the observed data and the model predictions) [21, 56, 57, 75], maximum likelihood estimation (identification of the parameter value(s) that makes the observed data most likely) [18, 22, 24, 35, 53, 63, 65, 66] and since 2007, Bayesian methods; frequently using Markov Chain Monte Carlo (MCMC) approaches [19, 32, 40, 41, 50, 58, 64, 76] or a combination of MCMC and maximum likelihood estimation [36, 59]. A further seven studies reported fitting their models by comparing model predictions to observed epidemiological data but did not apply any formal quantitative approach [17, 29, 43, 60, 81, 101, 104].

Infectious disease models are developed and informed using a combination of available evidence, for example on infection transmission, disease natural history and intervention effectiveness. As availability of such information is unlikely to be complete, mathematical models inherently include some degree of uncertainty. This uncertainty may relate to model parameter values, model structure (e.g. in terms of disease states incorporated and the relationship between them) or methodology used [9, 105].

Parameter uncertainty was investigated by 36% of the studies (35 publications). As Figure 5b illustrates, similar trends as seen for the application of formal model calibration apply for the inclusion of parameter uncertainty. Also the methods used for parameter uncertainty have become more complex over time (Figure 5c). Of the 35 studies that have investigated parameter uncertainty, univariate sensitivity analysis (i.e. alteration of one parameter at a time whilst holding others at their base-case value) was conducted by 43% (15 studies) [18, 28, 29, 43, 44, 46, 60, 63],[69, 77, 81, 83, 89, 91, 99]. The more computationally expensive probabilistic sensitivity analysis (formulation of uncertainty in the model inputs by a joint probability distribution, and propagating this uncertainty to the outputs [106]) is in general considered a rigorous method to account for uncertainty in the joint distribution of the parameters. This was employed by 51% (18 studies) [14, 32, 36, 40‐42, 48, 50, 57‐59, 64],[75, 76, 78, 95, 96, 98] among which Latin Hypercube Sampling (LHS) as a means of performing probabilistic sensitivity analysis was conducted by four studies [75, 95, 96, 98]. Probabilistic sensitivity analysis utilizing LHS provides a rigorous method of incorporating and representing real uncertainty surrounding parameter estimates into model-based analysis where joint probability distributions for parameters are available.

Model validation is rare in HCAI modelling. Ideally, a model should be validated by means of comparing the model predictions with observations from an alternative dataset than the one used for model fitting, although this is often difficult in practice. Four studies (5%) reported some kind of model validation based on at least two different data sets [50, 53, 75, 101]. However, only one study used a statistical approach [101], whereas the others included subjective comparison of the model predictions (on infection transmission) with genotype data [50, 53, 75].

Mathematical models of HCAIs have primarily been set in a single ward (49%, 47 studies), with the intensive care unit (ICU) being the most frequent setting modelled (26%, 25 studies) [14, 16, 22, 28, 29, 31, 32, 36],[40‐42, 45, 49, 52, 53, 55, 63, 65],[72, 79, 82, 91, 101, 107, 108] or a simplified hospital setting, lacking any further ward structure (31%, 30 studies) [12, 13, 24, 27, 33, 34, 38, 39],[45, 46, 51, 58, 60, 64, 66, 68],[69, 74, 77, 78, 83‐88, 93, 94, 97],[109]. More recent studies however, have incorporated the interaction between general wards and the ICU [23, 43, 69] or between different wards [11]. Although these ward or hospital-based models do not usually treat the hospital as a closed system (i.e. hospital admission and discharge rates from and to a 'general community' are frequently included), transfer patterns between healthcare institutes are rarely considered [19, 20, 25, 70, 71, 73], as are transmission dynamics within settings outside the healthcare facilities. The interaction between community and hospital transmission has been included for MRSA [30, 35], antimicrobial resistant bacteria as a whole [67], Severe Acute Respiratory Syndrome [76, 102] and tuberculosis [75]. Hence any possible long-term feedback between the hospital and other settings is not taken into account. Only two models concerned nosocomial transmission in a LTCF setting alone, i.e. of influenza [98] and norovirus [104] respectively.