Risk Retention and Management Implications of Medical Malpractice in the Italian Health Service

Abstract

This work provides an economic exploration of the multifaceted world of medical malpractice risk. Third party liability insurance plays a central role in protecting healthcare providers and public care institutions from the financial consequences of medical malpractice claims, although in recent years, the industry landscape has been characterised by periods of distress for this type of protection, with rising litigations and reimbursement costs, resulting in a peculiarly complex market. For the Italian context, the study focuses on the financial repercussions for healthcare institutions of the growing trend towards risk retention practises, legally empowered by the introduction of Law No. 24/2017. The analysis employs Generalised Linear Models for the regressive approach to incorporate the structural and organisational characteristics of hospitals and uses quantitative simulations to explore different scenarios at a regional aggregate level. Due to the limited existing literature and data on the topic, this research aims to provide new methods for effectively understanding and managing this type of risk, thereby supporting decision-making processes in the healthcare sector.

1. Introduction

The evolution of society has led to a heightened awareness of constitutionally guaranteed rights, including an ever-growing recognition of the “Right of Health”, resulting in an increased sensitivity to medical malpractice (medmal).1 In parallel, the role of the insurance sector has become relevant to contribute indirectly to the fulfilment of the extension of this right by offering risk transfer as a safeguard to compensate patients for the physical damage suffered and to protect providers from the legal consequences of claims filed by the injured party, offering a financial buffer in return for the payment of a premium. However, with changing societal factors such as a growing and ageing population and rising expectations of healthcare treatments, there has been a concomitant increase in the number of medmal claims. This has extended the core importance of clinical risk management and patient safety within the healthcare supply chain (Greve 2002). Over the years, upward trends in both the frequency and severity components of claims have been observed, starting with the US experience (Danzon 2000; Studdert et al. 2004), but these excessive behaviours have also been recognised globally, with market crises affecting several countries, as empirical evidence from Japan, Australia, and the Eurozone shows (OECD 2006). In addition, the tightening of capital requirements for insurance companies induced by the financial crises at the beginning of the millennium contributed to a decline in the affordability and availability of policies for medmal coverage, especially in periods of hard market for the insurance cycle (Sage et al. 2020). Companies have struggled to establish competitive reserving and pricing models to cope with the long-tail nature of the business and the uncertainty in the quantification of technical provisions, further reducing the attractiveness of insurance offerings. In Italy, specifically, the risk of medmal is concentrated mainly on public hospitals, whose income is dependent on public funds, some of which are provided by the central government and some by the regional authorities. It is no coincidence that the market crisis has hit public health facilities the hardest, with a marked change in the demand and the supply of the sector. The annual survey of the Institute for the Supervision of Insurance (IVASS2) (IVASS 2021) reports that in Italy, between 2010 and 2021, the total premiums for public hospitals was reduced by more than 50%, passing from EUR 520 million to EUR 250 million, with almost two-thirds fewer insured. The same years show higher average costs per claim, higher pure premiums, higher frequency of claims and loss ratios mostly above the benchmark of 100%. Indeed, the signals posed by the insurance market and the financial restrictions on the Italian national health service—called Servizio Sanitario Nazionale (or SSN)—have been driving shifts in risk management, with the emergence of new strategies, as proactive measures to face the unsustainable premiums’ tariffs. With the advent of Law No. 24/2017 (Italian Parliament 2017), the Italian legal landscape has fuelled the changes in the organisational structures, particularly concerning the possibility for healthcare companies to cover the risk of medical negligence without resorting to insurance policies, but by retaining the risk.3 Obviously, this new attitude has non-trivial implications for the whole system, since hospitals must act consciously where they believe that this choice can be financially viable in terms of efficiency and solvency. In itself, the term risk retention refers to a mechanism whereby health care providers decide to bear all or a significant part of the risk themselves, rather than transferring it to an insurance company (Nordmann et al. 2004). It refers to the creation of capital resources earmarked for the guarantee of a subject to cover possible losses or damages. Such a possibility is accompanied by related problems of determining solutions to create forms of asset segregation, issues related to the application of legal discipline and management difficulties of claims handling. This choice clearly might depend on the specific needs and financial capabilities of a business, since it can offer greater control over how claims are managed and potentially provide cash flow advantages. The immediate expenditure savings, as payments are made over the life of the claim rather than upfront premium costs, also prevent institutions from the payment of the heavy taxation added to the policies.4 In practice, risk retention can also be more effective in resolving potential disputes between patients and the healthcare system. This is because it facilitates constructive feedback on problems and errors that have occurred which, in turn, leads to a shorter period of time for the settlement of claims. In addition, it enables the creation of internal know-how in terms of prevention mechanisms (Vetrugno et al. 2022). On the contrary, it requires the introduction of professionals with specific skills and competencies and investments in information and monitoring systems to collect and analyse data. To date, in Italy, there are only a few examples of hospitals or regional authorities having made sustained investments in professionals and infrastructure to ensure an effective clinical risk management capacity in the context of risk retention. Nevertheless, if we were to assume an adequate and effective investment capacity, which should be not taken for granted given the fragile state of the SSN (OECD, European Commission, and European Observatory on Health Systems and Policies 2021), we should first question whether insurance companies and healthcare organisations are actually comparable in terms of risk management and retention. It is necessary to evaluate the risk management practices in relation to those implemented by insurers, particularly to the assessments imposed on reserves in traditional insurance to pursue a strategy based on their own funds only.

The context in which this study moves is particularly challenging, since there are no national databases that report medical errors and incurred claims, except for non-indicative and sporadic independent reports at the regional level or aggregated data collected by competent supervisory authorities. Furthermore, the available literature on this subject is not exhaustive. Indeed, the paper aims at providing a new approach for risk retention and management, in line with an insurance coverage scheme, by highlighting the potential evaluation techniques that healthcare institutions could adopt if they wished to assume risks in a similar way to the insurance sector. To support this comparison, a simplified quantitative model is presented. This model uses a priori pricing techniques, based on the characteristics of hospitals within the SSN, and it incorporates quantitative tools for the monetary identification of probable risk exposures, in line with the European Union’s Solvency II directives. The data refer to the year 2021, as the analysis conducted by the authors provides this period as a consistent framework for the research. Similarly, the study focuses on public hospitals, as operational characteristics were available through the Ministry of Health exclusively for these institutions. The methodology involves collecting and analysing hospitals’ operational and claims data to fit GLM regression analysis, allowing for risk segmentation of hospitals in terms of frequency and severity. Subsequently, similar to the insurance market, the varying levels of risk are utilised to define potential exposures based on appropriate risk measures tailored to the study context. The quantitative analysis is then aggregated at the regional level. The findings demonstrate the applicability of these techniques in a healthcare context, highlighting the various financial liabilities influenced by regional risk factors.

The paper is organised as follows: Section 2 and Section 3 provide the theoretical and mathematical background underlying the model. Section 4 presents the application of the developed methodology to the available data. Finally, Section 5 concludes and offers insights for future developments.

2. Background Literature

Despite a rich line of research mainly focused on the driving forces of medmal from a legal perspective, we document little to no academic work on this topic within the insurance literature. This is clearly due to the lack of available data on medical malpractice, which are not consistent or exhaustive, but are characterised by isolated attempts by academics (Tehrani et al. 2013), companies (see, for example, Marsh (2023)) or national institutions (IVASS 2022) to unravel the complexities of this issue. Most of research has focused on analysing the characteristics of liability and compensation systems, assessing their effectiveness in deterring negligence (Kessler 2011; Zuckerman et al. 1990), the implications in terms of behaviours and incentives induced by the justice system (Grembi and Garoupa 2013), and the impact of clinical risks on physicians’ practices (Jena et al. 2011) or their incentives to engage in defensive medicine (Osti and Steyrer 2017; Quinn 1998), resulting in substantial indirect costs’ increase for US patients (Rothberg et al. 2014). Other works have measured the impact of lawsuits in terms of costs for the health system (Liu et al. 2023), or how the expansion of the guaranteed aid provided by the government affects medical liability costs (Luo et al. 2022).

However, in healthcare risk management, the predictability of claims frequencies and severities is a non-negligible concern. Specialised studies investigating medical errors do not provide a holistic approach consistent with the insurance framework.

From an actuarial modelling perspective, the articles by Cooil (1991) and Viscusi and Born (2004) are of particular interest, providing a starting point to enhance our model for the specific context of the analysis and foundations of statistical inference in the field of investigation. In particular, Viscusi and Born (2004) analyse the impact of tort reforms that have taken place in the US with estimates of insurance losses in relation to premiums paid to insurers. Their analysis is based on multiple linear regressions, which furthermore converges in the estimation of loss ratios, with a related regression technique on their quantiles. Cooil (1991), instead, develops a Poisson model for the frequency component using Florida claims experience, taking into account the over-dispersion of the data and the effect of time, steering the research in favour of a Poisson inhomogeneous process. On the same line, Gibbons et al. (1994) aims to investigate the predictability of claims by developing a binary model to determine how the covariates chosen in the model increase the likelihood of claims and how differences in controlling variables, in terms of each physician’s speciality and its prior experience rating, induce variability in expected outcomes. For the Italian landscape, the strand of research is heterogeneous, with a variety of approaches, ranging from the interplay between the liability system and the cost of insurance (Bertoli and Grembi 2018) to the behavioural study of doctor-patient interactions in dynamic systems according to an evolutionary game (Frezza et al. 2023). The proposed model expands Boccadoro and DeAngelis (2012), which investigates the phenomenon of medmal from different perspectives and attempts to bring the typical insurance practices closer to innovative methodologies for the assessment of the risk of medical errors. However, while our model borrows the logic of risk segmentation and uses fair value as the estimation criterion for risk assessment, it diverges by employing a simulation approach at the regional aggregate level and by providing risk indicators at different confidence levels for different purposes. Nevertheless, the tool implemented is risk-based, taking the fair value of the liabilities and breaking it down into technical components. Moreover, it also includes insights of econometric studies in Italian Regions, which develop synthetic models for the frequency of claims based on the volume and the effects of the long-tail nature of medmal (Buzzacchi et al. 2016), and which confirm significant fluctuations in this type of claims (Bonetti et al. 2016). The proposal of Mazzi et al. (2024) is also of particular relevance, as it focuses on the challenge of establishing a correct allocation of capital in the event of a malpractice claim by exploiting chain-ladder methodologies and, in particular, Generalised Linear Models (GLMs) to extend the regression-based approach to the class of exponential distributions.

3. Theoretical Framework of the Model

3.1. Risk Retention and Technical Reserves

European regulations (Solvency I and Solvency II) and national regulations (Insurance Code) pay particular attention and compel insurance companies to guarantee solvency with the inaccessibility of the funds set aside as reserves. The impact of the risk fund and the reserve fund5 provided by healthcare organisations in their balance sheet to manage risk in-house is certainly not trivial, as it accounts for about EUR 2 billion in 2021 (IVASS 2022). Still, in any case, it can be stated that the most inherent limitation of relying on internal funds lies precisely in the approximate allocation of the technical component of the reserve in the balance sheet, since it is a mechanism outside the typical constraints of traditional insurance companies, dictated by several and fragmented accounting rules. It should also be borne in mind that the typical insurance company, in its specific role of risk transferor, and under the supervision of the competent authority, collects the premiums in advance, invests them in the markets from which it earns an average (positive) return, and manages the positive income in order to meet future cash needs of the insured pool. In addition, the insurance industry defines the technical component of the premium based on a large community of homogeneous risks, so that the business is set up in such a way that the positive performance earned on some indexes compensates for those assets which are performing worse. This applies to different risks and to different types of insured. In this way, policyholders are those who pay the subsidies, supporting each other in a mutualistic way. In the absence of risk transfer, the burden is borne solely by public budgets so that, in the event of miscalculations and inadequate estimates in setting up the reserves, the only instrument that can intervene is income taxation. Taxpayers act as a safety net; however, this, in turn, implies that those who subsidise are no longer the bearers of the risk, but the general public as a whole, or rather, not those who might cause the damage, but those who might suffer it. This contradicts the logic of insurance. Indeed, the possibility to utilise funds from internal provisions in their entirety or in a mixed form, through the use of SIR clauses6, should not be seen as a simple yes/no answer. The matter is rather how to implement it, as each of the issues and profiles mentioned above makes the system as a whole more or less sustainable from an economic and a social point of view.

3.2. A Risk-Based Approach

The long-tail nature of medmal risk leads to an increase in technical provisions, as only a small proportion of claims are settled in a short time period, due to delays in reporting incidents and prolonged litigation processes.7 This means that the provisions, recorded on the balance sheet of the insurance company, but implicitly also by the healthcare institutions, are subject to certain degrees of randomness and fluctuations in terms of timing and schedule cash-flow. In the insurance industry, this volatility translates into reserve risk, which is the risk of reserve fund deficits, for which, under Solvency II, insurance companies have to hold a capital buffer. It is not clear a priori whether medmal risk embeds a reserve risk, but its characteristics suggest that, over time, the random nature of payouts could create a deficit in the claims reserve. For this reason, healthcare facilities should devote special attention to comparative cost–benefit analyses between insurance coverage and direct assumption of risk. It is crucial to have a clear understanding of the cost definition underlying the strategic choice of risk retention, selecting according to criteria that measure the quality of the calculation models, generally evaluated by stochastic implementations (Arató and Martinek 2022). As part of the Solvency II project, the European Commission has demanded a quantitative clarification, through common standards, of the general principle of prudence contained in the Directives, in order to promote a more harmonised approach in Europe for its inclusion in technical provisions for insurance companies. The standard is defined by the fair value measurement of insurance liabilities, estimated by projecting and discounting all future cash flows on a market-consistent basis. Liabilities that cannot be marked to market (so-called “non-hedgeable” liabilities) are to be divided into two components: the Best Estimate (BE) and the Risk Margin (RM). To determine the amount of capital required, a particularly pessimistic value, reflecting the worst-case scenario for a 99.5% confidence level, with a time horizon of one year, is determined based on a prudential buffer that depends on the risk measure adopted. As identified by England et al. (2019), four elements need to be detected: a risk profile (distribution of the liabilities), a risk measure, a risk tolerance criterion, and a time horizon (one year). In the evolved Italian context, if regional authorities or healthcare companies decide to manage the risk themselves, there are no specific capital requirements to comply with; nonetheless, management is expected to estimate the capital exposure to which their company is subject to, through the selection of suitable criteria in the same spirit of what an insurance company would do.

To this end, the strategy for handling future costs in-house should systematically analyse risk using principles akin to those in financial mathematics, addressing both Expected Losses (EL) and Unexpected Losses (UL) (as illustrated in Figure 1), while considering the specific characteristics of healthcare facilities at local or regional levels. For insurance regulation, the “Black Swan”8, intended as a risk tolerance criterion, requires a high worst-case, as it underpins the solvency of the European insurance market; for Regions or healthcare entities, the requirement should ideally be lower, as it aims to identify deviations from the ELs generated by different models. This is why, in developing the model, the quantiles chosen to determine the exposures differ from those usually considered for the insurance market. In light of the above, it has been deemed appropriate to construct a methodology using a quantitative approach, which takes into account the conscious evaluation of ELs and outlines benchmarks for information gathering and risk management in the occurrence of adverse scenarios. Following standard actuarial mathematics on the expected future cash flows weighted by their respective probabilities, the BE component coincides with the EL, as the average value of the distribution of potential losses, for a given probability density function. Similarly, the RM is framed within the quantile approach as the UL, whereby the fair value of the risk, or rather the value of the chosen risk measure, is obtained by positioning itself at the $\alpha$ percentile of the probability distribution of the random total claims amount variable. From a theoretical point of view, where X is the random loss variable (i.e., the total amount of claims to be compensated), it is possible to formalise RM in terms of UL as follows:

$$RM\left(X\right)={\rho }_{\alpha }\left(X\right)-BE\left(X\right)$$

(1)

where ${\rho }_{\alpha }\left(X\right)$ is the risk measure at a given confidence level and BE(X) is the expected value of the liabilities (EL). From now onwards, solely BE and RM will be used as notations. In general, ${\rho }_{\alpha }\left(X\right)$ gives the amount of capital that must be added to a position associated with a random loss X to be acceptable for an internal or external regulator, given the loss distribution of the portfolio over a time horizon $\Delta$. In this case, Value at Risk (VaR) has been used, defined as, for $\alpha \in (0,1)$,

$${\mathrm{VaR}}_{\alpha }\left(X\right)=inf\{x\in \mathbb{R}\mid Pr[X>x]\le 1-\alpha \}$$

(2)

which corresponds to the maximum potential loss that can be incurred over a given time horizon in the $(1-\alpha )\%$ worst-case, observable on a given probability distribution. In terms of funds needed, it describes the unexpected change in the random variable that provides an estimate of the total amount of claims. For the sake of clarity, it should also be mentioned that the chosen risk measure could be problematic, in that it requires a careful choice of $\Delta$ and $\alpha$ and, furthermore, it takes into account the frequency of risk exposure, but not its magnitude.

3.3. Claim Frequency and Claim Severity

The main targets of interest for a generic non-life insurance policy rely on the frequency and severity components, expressed from now onwards by the random variables N and S, respectively. While claims frequency and severity are valuable on their own, their true significance emerges as they interact. The synergy between these components gives rise to aggregated damage scenarios, presenting a comprehensive picture of the overall risk distribution. By analysing how frequently events occur and the magnitude of each occurrence, it is possible to derive the random variable X, which expresses the total payout. X is obtained by summing up a random number of claims N and the corresponding random number of claim amount $S_i$. Indeed, for $i=1,2,\dots ,N$,

$$X=\sum _{i=1}^N{S}_i$$

(3)

Indeed, a simple model that provides an easy straightforward calculation of the mean of X can be derived, according to which

$$\mathbb{E}\left(X\right)=\mathbb{E}\left(N\right)\mathbb{E}\left(S\right)$$

(4)

where X has a compound distribution, and is obtained by assuming that:

• The random variables S and N are independent;
• The random variables $S_1,S_2,\dots ,S_N$ are mutually independent and identically distributed, with $\mathbb{E}\left(S_i\right)=\mathbb{E}\left(S\right)$ for each $i=1,2,\dots ,N$.

Theoretically, the expected value of X, $\mathbb{E}\left(X\right)$, has to be discounted to the present value, according to realistic assumptions for the number of claims N and for the claim amounts S.9 We observe that all that is required is an estimation of the expected claim frequency, denoted as $\mathbb{E}\left(N\right)$, and the expected claim severity, denoted as $\mathbb{E}\left(S\right)$. These metrics provide a statistical summary of the expected average cost for each insured risk. This approach can be conducted using estimates from an experiential model that incorporates historical data, claims dynamics, and associated costs.

In the rate-making process, allowing for risk segmentation based on the insured’s objective characteristics, a set of risk factors is necessary to customise the equivalence premium. This “customisation” tailors the expected values of the frequency and severity components constituting the model to the specific level of claims experience. In this context, for determining the measure of risk, we decompose the variable X into the product of N and S, both functions of the values assumed by various risk factors. Indeed, it is evident that

$${\mathbb{E}}_{\omega }\left(X\right)={\mathbb{E}}_{\omega }\left(N\right){\mathbb{E}}_{\omega }\left(S\right),$$

(5)

where $\omega =\left\{k_1,k_2,\dots ,k_i,\dots ,k_n\right\}$ is the set of risk factor variables selected for segmentation, and n is the number of covariates in the set. These variables and their associated parameters have been determined by implementing multivariate regressions through the use of GLMs.

3.4. Generalised Linear Models

GLMs represent a class of multivariate statistical models useful for severity and frequency modelling, which extend traditional linear regression by allowing for response variables, and whose error is not normally distributed (England and Verrall 1999). The primary purpose of this class is to identify the relationship between the risk factors and the response variable, by estimating parameters that can be used to predict or explain various phenomena. GLMs offer the flexibility of using a unified set of routines for both continuous and discrete outcomes and express the mean as simple linear combinations of the covariates, adding consistency and enhancing parameters’ interpretability (Frees et al. 2016). The linearity is obtained through the use of a link function.10 In the context of the proposed model, as discussed in Cooil (1991), the number of claims, related to counting data, has been represented by a Poisson distribution, and the claim sizes by a Gamma distribution, which is better suited for modelling continuous, asymmetric, and positive data.

For the Poisson distribution, the link function is typically the natural logarithm, expressing the mean $\mu$ as

$$log\left(\mu \right)={\omega }^{\prime }\beta ,$$

(6)

where the generic $\mu$ is equal to $\lambda$ in the Poisson process, $\omega$ is the set of risk factors and $\beta$ is the vector of parameters associated with each covariate. To assess the Maximum Likelihood Estimation (MLE), the Probability Mass Function (PMF) is used. For a Poisson-distributed random variable Y with rate $\lambda$ the PMF function is given by

$$P(Y=y)={\displaystyle \frac{e^{-\lambda }{\lambda }^y}{y!}},y=0,1,2,\dots$$

(7)

The likelihood function for n independent observations $y_i$, where $i\in \{1,2,\dots ,n\}$ is:

$$L(\lambda ;y_i)=\prod _{i=1}^n{\displaystyle \frac{e^{-\lambda }{\lambda }^{y_i}}{y_i!}};$$

(8)

while the log-likelihood function is:

$$\ell \left(\lambda \right)=\sum _{i=1}^n\left(-\lambda +y_{i}log\left(\lambda \right)-log(y_i!)\right)$$

(9)

The MLE of $\lambda$ is found by differentiating the log-likelihood with respect to $\lambda$, setting the derivative to zero, and solving for $\lambda$ (Ohlsson and Johansson 2010).

In contrast, the Gamma distribution employed for the claim size variable $S_i$ uses the inverse link function, leading to

$${\displaystyle \frac{1}{\mu }}={\omega }^{\prime }\beta ,$$

(10)

where the generic $\mu$ is equal to $1/\mathbb{E}\left(S_i\right)$, while $\omega$ and $\beta$ retain their previous meaning. In this case, instead of the PMF, the Probability Density Function (PDF) is used. For a Gamma-distributed random variable Z with shape $\alpha$ and rate $\theta$, the PDF is obtained as

$$f(z;\alpha ,\theta )={\displaystyle \frac{{\theta }^{\alpha }{z}^{\alpha -1}{e}^{-\theta z}}{\Gamma \left(\alpha \right)}},z>0$$

(11)

The likelihood function for n independent observations $z_i$, where $i\in \{1,2,\dots ,n\}$ is

$$L(\alpha ,\theta ;z_i)=\prod _{i=1}^n{\displaystyle \frac{{\theta }^{\alpha }{z}_i^{\alpha -1}{e}^{-\theta z_i}}{\Gamma \left(\alpha \right)}};$$

(12)

while the log-likelihood function is

$$\ell (\alpha ,\theta )=n\alpha log\left(\theta \right)+(\alpha -1)\sum _{i=1}^{n}log\left(z_i\right)-\theta \sum _{i=1}^n{z}_i-nlog(\Gamma \left(\alpha \right))$$

(13)

The MLEs of $\alpha$ and $\theta$ are obtained by taking partial derivatives of the log-likelihood with respect to $\alpha$ and $\theta$, setting them to zero, and solving the resulting system of equations. Since there is no closed-form solution, numerical optimisation techniques are employed (McCullagh and Nelder 1989).

As with any regression technique, it is important to select from the risk drivers those independent variables that influence the response variable. This is performed using the model deviance or $R^2$ as an indicator. In general, as the number of regressors increases, the deviance tends to decrease and $R^2$ tends to increase, but it is not certain that all the variables considered have a real effect on the variation of the dependent variable Ohlsson and Johansson (2010). A procedure called backward elimination is employed to identify the most relevant variables. This procedure involves iteratively removing variables from the model to determine their significance. Mathematically, this is performed by starting with a full model containing all potential predictors and calculating its deviance. In each step, a candidate predictor is removed to form a reduced model. The deviance D serves as a measure of the model’s goodness of fit. In line with McCullagh and Nelder (1989), it can be defined as

$$D=2\left(\ell \left(\mathit{saturated}\right)-\ell \left(\mathit{model}\right)\right),$$

(14)

where $\ell \left(saturated\right)$ is the log-likelihood of a perfectly fitting model, and $\ell \left(model\right)$ is the log-likelihood of the current model. Equation (14) represents the baseline allowing for comparison between full and reduced models. The change in deviance $\Delta D$ is intuitively measured by

$$\Delta D=D_{\mathrm{reduced}}-D_{\mathrm{full}},$$

(15)

where $D_{\mathrm{reduced}}$ is the deviance of the model reduced by one of the predictors and $D_{\mathrm{full}}$ represents the deviance of the model including all the parameters. The variable that causes the greatest increase in deviance, compared to the full model, is excluded (Boccadoro and DeAngelis 2012). This approach ensures that no potentially important variable is excluded initially, allowing the detection of combined effects that may only emerge when specific variables are included together. Moreover, the sequential nature of backward elimination is well-suited for a complex dataset, as it can address multicollinearity and interactions between variables while monitoring changes in model performance at each step (Mantel 1970).

4. The Structure of the Model

The model implemented is based on data from 502 public healthcare facilities, reviewed by the Ministry of Health during the annual collection of hospital statistics, specifically for the year 2021 (Direzione Generale della Digitalizzazione del Sistema Informativo Sanitario e della Statistica, Ufficio di Statistica 2021). The number of public healthcare facilities per region in Italy, as depicted in Figure 2, reveals significant variability, suggesting a potential heterogeneity in their composition, activities, and resources utilised.

As mentioned in Section 1, the choice to focus on the public sector is twofold: first, the risk of medical malpractice in Italy is predominantly concentrated in public hospitals, as the SSN is primarily public. Secondly, the operational characteristics included in the model were provided by the Ministry of Health, specifically for public hospitals.

The analysis proceeds in two distinct phases. The first phase focuses on an individual level, aiming to determine the frequency and severity of exposures for each facility. The second phase operates at a regional level, where hospitals are aggregated to quantify the expected claims costs and assess their variability. This is achieved by employing the VaR methodology at various confidence levels. The basic steps of the implementation can be summarised as follows:

• Construction of a database of risk factors useful for facilities’ customisation procedures;
• Identification of benchmarks for claims in terms of frequency and severity;
• Implementation of multivariate statistical models for risk customisation at the level of the specific structure;
• Simulation of expected annual costs at the regional aggregate level;
• Selection of the risk measure at the regional aggregate level and consequent definition of the variability of the expected costs.

The choice to operate at a regional level is based on the structure of the Italian SSN, which leaves decisions on clinical risk management to the Regions. In fact, they may choose to allocate the funds to their related healthcare organisations or centralise resources to protect against claims (Mazzi et al. 2024). So, it is on the aggregate that in principle the evaluation has to be made. Even in practice, many regions have decided to consider risk at a regional level in order to obtain a more accurate assessment of the effective loss rate.

4.1. Risk Factors

The first step in quantifying the risk is to obtain information on the structural, qualitative and organisational nature of healthcare facilities at an individual level, which makes it possible to record the parameters for measuring the volume of activity, operational capacity, effectiveness, and efficiency of the hospital system (Bonetti et al. 2016). In line with Boccadoro and DeAngelis (2012), the parameters include: Planned Bed Capacity, Number of Planned Departments, Beds Used, Number of Departments Used, Total Staff, Doctors, Nurses, Days of Hospital Stay, Available Days and Surgical Interventions, as shown at the regional aggregate level in

Table 1. Structural and operational information of public healthcare facilities (2021). Source: Direzione Generale della Digitalizzazione del Sistema Informativo Sanitario e della Statistica, Ufficio di Statistica (2021).

Region	Planned Bed Capacity	Number of Planned Departments	Beds Used	Number of Departments Used	Total Staff	Doctors	Nurses	Days of Hospital Stays	Available Days	Surgical Interventions
Piemonte	16,159	1096	11,435	942	43,252	7757	18,326	3,066,281	4,170,998	1058
Valle d’Aosta	401	28	336	26	1418	278	512	107,842	122,430	1197
Lombardia	34,862	2010	23,624	1833	114,244	19,622	46,322	6,621,389	8,603,269	1192
Prov. Auton. Bolzano	1757	109	1349	93	8875	993	3287	348,344	489,903	742
Prov. Auton. Trento	1333	91	1333	83	6465	978	2691	350,588	486,567	996
Veneto	14,532	842	13,124	784	51,723	7938	24,003	3,606,274	4,784,679	1408
Friuli Venezia Giulia	3720	251	3428	234	12,240	2965	5713	896,958	1,252,533	1187
Liguria	4901	491	4568	418	17,528	3317	8341	1,304,055	1,663,462	1093
Emilia Romagna	13,164	1098	11,873	993	47,777	8356	23,070	3,537,835	4,325,719	1554
Toscana	9347	981	8954	820	39,895	8048	17,080	2,395,335	3,260,024	940
Umbria	2890	284	2237	249	8521	1779	4061	700,340	813,023	877
Marche	4720	348	3195	319	13,553	2650	6528	957,661	1,165,276	1044
Lazio	15,578	1338	12,826	1112	50,592	11,285	24,036	3,485,379	4,672,490	1515
Abruzzo	3266	301	2929	257	8819	2070	4369	801,115	1,067,224	759
Molise	979	77	784	67	2554	513	1025	200,937	285,530	1403
Campania	11,728	1097	8732	983	34,178	8069	15,666	2,404,395	3,174,944	946
Puglia	11,440	700	8708	645	31,166	6448	14,188	2,224,033	3,171,387	1408
Basilicata	1746	132	1697	126	4726	882	2248	356,514	619,090	1333
Calabria	3498	295	2390	206	12,333	2820	5244	629,279	868,885	814
Sicilia	11,764	1108	9749	996	33,457	7819	14,752	2,601,297	3,548,121	617
Sardegna	4480	306	3902	278	13,502	3224	5911	986,022	1,422,596	1317

.

To accomplish measuring the effectiveness and efficiency of patient care delivery, a set of socio-health indicators11 commonly used in Italy has been added to the structural and organisational information dataset (

Table 2. Efficiency indicators of public healthcare facilities (2021). Source: Direzione Generale della Digitalizzazione del Sistema Informativo Sanitario e della Statistica, Ufficio di Statistica (2021).

Region	ALOS	BOR	BTR
Piemonte	12.97	53.72%	19.86
Valle d’Aosta	9.38	73.68%	28.68
Lombardia	12.82	54.00%	20.36
Prov. Auton. Bolzano	6.87	54.64%	29.16
Prov. Auton. Trento	8.06	65.48%	31.83
Veneto	13.71	62.88%	25.33
Friuli Venezia Giulia	13.27	63.49%	29.33
Liguria	10.41	74.03%	29.74
Emilia Romagna	10.76	73.79%	32.98
Toscana	10.00	66.25%	30.91
Umbria	9.47	61.18%	25.12
Marche	8.37	54.12%	24.41
Lazio	12.23	58.46%	25.31
Abruzzo	8.98	64.45%	29.76
Molise	7.81	56.96%	27.02
Campania	9.44	53.91%	26.04
Puglia	8.78	51.30%	24.10
Basilicata	20.80	47.22%	13.28
Calabria	7.29	48.48%	22.50
Sicilia	11.31	58.80%	24.45
Sardegna	10.60	48.97%	20.43

). These indicators are crucial for health policy planning and evaluation of the hospitals’ activities. In particular, the choice falls into:

• Average Length of Stay: The Average Length of Stay (ALOS) measures the average number of days a patient spends in the hospital. It is calculated using the formula

  $$\mathrm{ALOS}={\displaystyle \frac{\mathrm{Total}\mathrm{days}\mathrm{of}\mathrm{stay}\mathrm{by}\mathrm{all}\mathrm{patients}\mathrm{during}\mathrm{a}\mathrm{period}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{discharges}\mathrm{during}\mathrm{the}\mathrm{same}\mathrm{period}}}$$

  (16)
  A lower ALOS may indicate better efficiency and higher quality of care, provided that the health outcomes are satisfactory.
• Bed Occupancy Rate: The Bed Occupancy Rate (BOR) is an indicator of hospital bed utilisation. It is the ratio of occupied beds to the total available beds, usually expressed as a percentage:

  $$\mathrm{BOR}=\left({\displaystyle \frac{\mathrm{Average}\mathrm{daily}\mathrm{number}\mathrm{of}\mathrm{beds}\mathrm{occupied}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{available}\mathrm{beds}\times 365}}\right)\times 100$$

  (17)
  A higher BOR can indicate a high demand for hospital services but may also point to potential overcrowding.
• Bed Turnover Rate: The Bed Turnover Rate (BTR) reflects the frequency with which hospital beds are used by new patients. The formula for BTR is

  $$\mathrm{BTR}={\displaystyle \frac{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{discharges}}{\mathrm{Average}\mathrm{number}\mathrm{of}\mathrm{beds}\mathrm{during}\mathrm{the}\mathrm{period}}}$$

  (18)
  A higher BTR indicates a higher rate of bed utilisation, signifying efficient use of hospital resources.

To take into account the correlation between the efficiency indicators and the differentiation of the cases treated in each hospital, three other indicators have been analysed, such as the Case-mix Index, the Entropy Index, and the Utilisation Rate:

• The Case-Mix Index (CMI) is an index that expresses the complexity of cases treated by the operational unit (or hospital) relative to the average complexity of cases across all operational units (or hospitals) in Italy. Values greater than one indicate a case complexity higher than the reference average.
• The Entropy Index (EI) is an absolute index that measures the heterogeneity of the distribution of discharges across various DRGs.12 The minimum heterogeneity occurs when all discharged patients fall under the same DRG, while the maximum heterogeneity is achieved when discharges are evenly distributed among the various DRGs.
• The Utilisation Rate (UR) indicates the ratio between the Days of Hospital Stays and the Available Days (the number of potentially available days assuming the beds are utilised for the entire reporting period), expressed as a percentage. It can be interpreted as a reference for resource utilisation.

However, since several facilities that deal with potentially similar cases and use of resources coexist on the national scene, instead of directly adding the three indicators to the information dataset, a qualitative explanatory variable (“Healthcare Class”) was added, thus encompassing the indicators listed above and clustering the hospital facilities into homogeneous groups. This explanatory variable, therefore, takes four different values (“A”, “B”, “C”, “D”), as shown in Figure 3, based on the chosen clustering method.

The clustering method used to classify healthcare facilities into homogeneous groups is of the hierarchical-agglomerative type. That is, starting from the individual units observed, a limited number of groups or agglomerates of healthcare units must be reached by means of the aforementioned technique, which can be ordered according to increasing levels of aggregation, following a certain criterion based on the distances between the groups. The method adopted is the Ward method (Ward 1963) which, following a minimum variance principle, aggregates at each successive step of the process the two groups whose merger results in the smallest possible increase in deviance within the newly formed group (Murtagh and Legendre 2014). The choice of the number of clusters has been made by first observing the fusion distance13 that can be deduced from the dendrogram, which represents the agglomeration process on a Cartesian axis. If there is a large increase in the merging distance when moving from k clusters to k + 1, then k clusters must be cut. Then, by confuting an index proposed in the literature, such as the Silhouette Score, the optimal number of clusters was chosen. The indicator provides a measure of how similar an individual data point is to the other points in its own cluster compared to points in different clusters (Rousseeuw 1987). Theoretically, a higher score of the index indicates that the data points are, on average, closer to the other points in their cluster than to points in other clusters, suggesting that the clustering structure is robust. When using the Ward method, the Silhouette Score can be plotted for a range of cluster solutions, and the number of clusters that maximises the average Silhouette Score is often considered an appropriate choice. This approach to determining the number of clusters can be more informative than simply relying on visual assessment of a dendrogram (Figure 4a), especially in complex datasets where the increase in merging distance may not be as apparent, such as the one used. As Figure 4b shows, the number of optimal clusters is therefore four, which is the value according to which the Silhouette Score reaches its peak (i.e., the maximum value).

Finally, in order to complete the set of information of the risk factors, another qualitative variable, “Geographical Area”, has been added, which divides the healthcare facilities on the basis of their geography in the territory. For this purpose, the values “North”, “Centre”, and “South” have been assigned to healthcare organisations, according to their location. The distribution of this variable is visualised in Figure 5.

4.2. Frequency and Severity Indicators

The second step is the identification of the typical indicators of traditional insurance that underlie the estimation of the expected annual costs of each facility, namely the frequency and severity of claims. In the absence of a database containing claims experience, it was necessary to consult various industry reports to derive information and incorporate into the model those values that could best represent the general picture. Benchmarks were extracted from the report of Marsh (2023), describing frequencies and weighted average cost indicators for the errors performed in the activities of healthcare facilities. To determine the appropriate values for each facility in the information set, an a priori classification is performed.14 In particular, these indicators relate to hospital admissions with respect to the type of the facility considered (I Level, II Level, III Level) and make the different institutions comparable, so as to ensure variability at least in the frequency of claims. However, considering the influence of the initial database on the results, it is appropriate to make some observations on the structure of these data. In particular, with regard to the distribution of the number of claims, a careful evaluation of the time-series of the reference benchmarks does not reveal a Poisson distribution influenced by a mixing variable. Therefore, in developing the model, instead of using an overdispersed Poisson distribution (Buzzacchi et al. 2016; Cooil 1991; Mazzi et al. 2024), it has been considered more appropriate to use a standard Poisson distribution (Equation (7)).15 From the industry study, as summarised in

Table 3. Benchmark indicators for frequency and severity. Source: Marsh (2023).

Level	Category	Frequency (×1000 Admissions)	Severity (EUR)
I	Directly managed hospitals	0.73	EUR 141,095.8904
II	Independent hospitals	1.46	EUR 151,304.3478
III	University hospitals	1.15	EUR 110,958.9041

, it was initially only possible to obtain three reference values for the average costs, although this homogeneity is mitigated by the use of GLMs.

4.3. GLMs Linkage for the Response Variables

To fit the different levels of risk and derive the expected costs for each facility, several GLMs have been implemented. Prior to conducting the multivariate statistical analysis, the final step has been the identification, through the process of backward elimination, of the risk factors with actual power in the estimation, both for the frequency model and the severity model.

Table 4. Risk factors chosen for the GLMs models. Source: own elaboration.

Risk Factors	Frequency Model	Severity Model
Planned Bed Capacity	x	x
Beds Used	x
N° of Planned Departments	x	x
N° of Departments Used	x	x
Total Staff	x	x
Doctors	x	x
Nurses		x
Days of Hospital Stays	x	x
Available Days	x	x
Surgical Interventions		x
ALOS	x	x
BOR	x
BTR	x	x
Healthcare Class	x	x
Geographical Area	x	x

shows the result of this process, highlighting the risk factors used for the two models, implemented using Poisson and Gamma distributions.

At this point, for each model, for each structure belonging to the data set, the estimated frequencies and estimated severities have been calculated using the algorithms of GLMs, thus reducing the homogeneity limits resulting from the structure of the data. As depicted in Figure 6, each hospital therefore differs from the benchmark indicators used at the outset on the basis of risk factor drivers expressed by quantitative and qualitative variables. This customisation, indeed, encompasses a priori characteristics, allowing for risk segmentation.

4.4. Extending and Validating the Model via Simulations

From this point on, the proposed analysis aims at providing a regional aggregate level of observation, in order to have a general framework that could be useful for decision-making and policy purposes. Therefore, the various structures involved in the model have been gathered at the regional level, and then risk measures have been derived for each region in terms of BE and RM. To give consistency to the results, as the sole use of only the sample composition on a regional basis did not allow the construction of risk measures capable of incorporating the correct exposure to the risk itself, a granular simulation approach has been constructed based on the newly estimated frequencies and the newly estimated severities, as summarised in Figure 7.

For each hospital, a vector of random numbers $N=\left\{n_1,n_2,\dots ,n_{1000}\right\}$ has been simulated with a Poisson distribution, representing the number of claims that occurred in a period of time, starting from the specific estimated frequency of each hospital. For each value belonging to the vector N, the amount of each claim $s_i$ corresponding to the number of claims has been simulated according to a Gamma distribution based on the estimated severity and then summed up to associate a vector X of the same length with the vector N. Thus, $X=\left\{x_1,x_2,\dots ,x_{1000}\right\}$ represents the vector with the total amount of claims for each hospital. For each region, at the aggregate level, a vector of the same length has been then generated. For each trajectory of the simulation for each hospital, the corresponding values have been summed up to obtain the regional total of the cost of claims. Thus, for the first trajectory of the simulation, each value at position $x_1$ of each hospital is associated with the corresponding $x_1$ value of the other regional healthcare facilities to obtain the regional total costs of claims. The same aggregation process takes place for $x_2,x_3,\dots ,x_n$ until $x_{1000}$ is reached. Once the vectors corresponding to the total costs have been defined for all of the regions, to quantify the risk measure (VaR), the data have been rearranged in ascending order and the numerical values displayed according to the quantile chosen have been selected.

Since, unlike insurance companies, healthcare institutions do not have to take into account the compulsory prudential measures asked by the Regulator for insurance companies, the VaR has been set at three confidence levels, lower than those adopted in the European Directives. The confidence intervals chosen are 75%, 80%, and 85%. These references should be understood as benchmarks in the case of adverse events, where the RM measure can intuitively be recorded as a sort of technical deficit in relation to the reserves set aside for the risks to be borne.

4.5. Simulation Results

Table 5. BE and VaR at different confidence levels for each region. Source: own elaboration.

Region	Best Estimate	VaR at 75%	VaR at 80%	VaR at 85%
Abruzzo	14,347,751.80 €	15,250,462.88 €	15,469,428.45 €	15,727,842.15 €
Basilicata	4,248,873.40 €	4,783,328.15 €	4,927,072.32 €	5,069,457.86 €
Calabria	9,655,479.76 €	10,430,847.58 €	10,609,656.12 €	10,849,452.37 €
Campania	39,631,329.06 €	41,131,435.31 €	41,512,208.14 €	41,942,238.21 €
Emilia Romagna	58,327,859.75 €	60,203,182.94 €	60,851,469.61 €	61,500,790.57 €
Friuli Venezia Giulia	12,863,054.34 €	13,730,479.77 €	13,953,114.71 €	14,287,149.27 €
Lazio	60,375,481.62 €	62,415,642.72 €	62,885,810.64 €	63,454,822.60 €
Liguria	18,119,556.05 €	19,224,361.21 €	19,453,447.95 €	19,744,373.46 €
Lombardia	81,918,954.21 €	84,086,318.67 €	84,563,455.12 €	85,234,076.82 €
Marche	12,275,778.25 €	13,089,214.72 €	13,355,585.97 €	13,606,954.95 €
Molise	3,357,539.14 €	3,840,721.60 €	3,931,005.25 €	4,041,910.32 €
Piemonte	44,086,719.68 €	45,746,297.08 €	46,119,461.07 €	46,662,440.22 €
Prov.Auton.Bolzano	4,598,686.52 €	5,131,175.06 €	5,272,883.72 €	5,433,287.21 €
Prov.Auton.Trento	6,291,155.16 €	6,880,833.11 €	7,060,490.23 €	7,217,566.85 €
Puglia	32,158,048.71 €	33,557,479.87 €	33,874,114.70 €	34,408,841.76 €
Sardegna	16,320,742.96 €	17,343.056.20 €	17,594,673.51 €	17,882,057.88 €
Sicilia	47,015,432.29 €	48,741,993.65 €	49,259,785.16 €	49,741,630.57 €
Toscana	42,565,884.97 €	44,266,292.16 €	44,677,910.78 €	45,244,574.22 €
Umbria	9,937,500.63 €	10,753,085.76 €	10,974,791.89 €	11,190,409.42 €
Valle d’Aosta	1,226,688.50 €	1,481,310.16 €	1.555,104.13 €	1,621,907.17 €
Veneto	52,413,813.29 €	54,127,096.41 €	54,633,082.85 €	55,174,856.15 €

shows the experimental results, distinguishing between the BE and the VaR clustering at the Region-level. The BE is obtained as a combination of the values from the frequency and severity components of the individual hospitals included in the analysis, for each region, and serves as a baseline for expected future liabilities. VaR data at different confidence levels, instead, provide a spectrum of possible outcomes, giving an idea of the buffer to cover claims payouts in more adverse scenarios.

It is no coincidence that the BE data show significant variations between regions, indicating different levels of expected liabilities. This reflects differences in population densities, healthcare utilisation rates, and overall patient care activities. Therefore, the size of the healthcare system and the activity of the related hospitals belonging to the regional health service influence the numerical estimates. The national average for the BE component is around EUR 27 million, with a standard deviation of EUR 23.3 million. The most interesting aspect, however, is the assessment of the RM as a component that allows the uncertainty associated with each region to be captured with a higher degree of probability. The first feature to notice is whether we should expect to observe increasing values as the level of the chosen quantile increases. Even in this case, the values for the three levels are not constant but vary according to the specific regional riskiness. If the comparison is made as a percentage of BE, lower values are found in Lombardy at around 3%, while the highest were in Valle d’Aosta, at over 30%. In particular, greater uncertainty is observed where the BE component is lower, with a more significant incremental variation as the confidence level increases. However, this does not imply a greater exposure in terms of cash-flow, since it is the regions with increasing BE values that present a higher RM when measured in euros. In fact, Lombardy, Lazio and Emilia Romagna, measured at the 85-th percentile, have an RM of more than EUR 3 million, which is quite remarkable given the potential impact on public budgets. The clear trend where Regions with higher BE also have higher RM in absolute terms is expected as the uncertainty and potential for deviation from the mean estimate typically grows with the size of the liabilities. In any case, once again, it should be pointed out, also with reference to the different degrees of uncertainty found on the RM, that the final results are strongly influenced by the robustness of the data sample.

Large percentages, such as the 20.76% seen for Valle d’Aosta at the 75% confidence level in

Table 6. Risk Margins in % of BE and in EUR. Source: own elaboration.

Region	Risk Margin 75% (BE)	Risk Margin 80% (BE)	Risk Margin 85% (BE)	Risk Margin 75% (EUR)	Risk Margin 80% (EUR)	Risk Margin 85% (EUR)
Abruzzo	6.29%	7.82%	9.62%	902,711.08 €	1,121,676.65 €	1,380,090.35 €
Basilicata	12.58%	15.96%	19.31%	534,454.75 €	678,198.92 €	820,584.46 €
Calabria	8.03%	9.88%	12.37%	775,367.81 €	954,176.36 €	1,193,972.61 €
Campania	3.79%	4.75%	5.83%	1,500,106.25 €	1,880,879.08 €	2,310,909.14 €
Emilia Romagna	3.22%	4.33%	5.44%	1,875,324.18 €	2,523,610.86 €	3,172,931.82 €
Friuli Venezia Giulia	6.74%	8.47%	11.07%	867,425.43 €	1,090,060.37 €	1,424,094.93€
Lazio	3.38%	4.16%	5.10%	2,040,161.10 €	2,510,320.02 €	3,079,340.98 €
Liguria	6.10%	7.36%	8.97%	1,104,805.16 €	1,333,891.90 €	1,624,817.41 €
Lombardia	2.65%	3.23%	4.05%	2,167,364.46 €	2,644,500.91 €	3,315,122.61 €
Marche	6.63%	8.80%	10.84%	813,436.47 €	1,079,807.72 €	1,331,176.18 €
Molise	14.39%	17.08%	20.38%	483,182.46 €	573,466.11 €	684,371.18 €
Piemonte	3.76%	4.61%	5.84%	1,659,577.41 €	2,032,741.39 €	2,575,720.54 €
Prov.Auton.Bolzano	11.58%	14.66%	18.15%	532,488.54 €	674,197.20 €	834,600.69 €
Prov.Auton.Trento	9.37%	12.23%	14.73%	589,677.94 €	769,335.06 €	926,411.69 €
Puglia	4.35%	5.34%	7.00%	1,399,431.16 €	1,716,065.99 €	2,250,793.05 €
Sardegna	6.29%	7.81%	9.57%	1,022,313.24 €	1,273,930.55 €	1,561,314.92 €
Sicilia	3.67%	4.77%	5.80%	1,726,561.35 €	2,244,352.87 €	2,726,198.28 €
Toscana	3.99%	4.96%	6.29%	1,700,407.19 €	2,112,025.81 €	2,678,689.25 €
Umbria	8.21%	10.44%	12.61%	815,585.13 €	1,307,291.27 €	1,252,908.79 €
Valle d’Aosta	20.76%	26.77%	32.22%	254,621.67 €	328,415.63 €	395,218.68 €
Veneto	3.27%	4.23%	5.27%	1,713,283.12 €	2,219,269.57 €	2,761,042.87 €

, are particularly noteworthy, as they imply a significant discrepancy relative to the region’s expected liabilities. This is likely to be caused by unique regional risk factors, although it must also be recognised that a smaller sample size leads to greater relative variability, which affects the results as there is only one health facility in that region.

It is also interesting to highlight graphically how the sample size in each region affects the distribution (Figure 8): where there is a larger number of institutions in the region, the dispersion is smaller around the average, and the distribution records more observations around the reference value.

The fact that the distributions are almost symmetrical, with a small hint of a tail to the right, is because the simulations assumed a Poisson distribution in the generation of the random numbers when modelling the frequency of claims. In reality, what we might expect when observing a phenomenon with the characteristics of medmal is a Poisson distribution with the presence of mixing variables in the frequency of claims, with data overdispersed around the mean, so that the resulting distributions are strongly skewed to the right, with a consequent shift in the position of the risk measures.

5. Conclusions

Even if there is room for a desirable in-depth study of a theoretical nature, the proposed model represents a different approach to quantify medmal risk. In a context where the literature is not extensive and there is limited data availability, it is of fundamental importance to define managerial guidelines and practices that provide a comprehensive view of potential risks emerging from medical errors. The analysis, despite making assumptions, provides mechanisms for creating interesting insights for benchmarking. This includes a practice of risk segmentation based on the characteristics of the hospitals embedding the risk sensitivity of each hospital included in the sample. A classification is then extrapolated to the regional aggregate level, revealing differences in terms of risk exposure and expected values. It is important to underline that for an accurate estimation of the expected frequency and severity values, a rich and well-founded database describing the historical dynamics of claims is necessary to avoid selection bias, which undermines representativeness. One suggestion could be to overcome information gaps by working on shared data collection schemes on a national scale. To ensure data accessibility, a mandatory database for reporting claims could be a valuable initiative to enrich and stimulate research in this field. At the modelling level, this work advances the discipline in two significant ways. First, it proposes clear and intuitive practices for evaluating medmal risk exposure. By using quantitative models for validation, it enables healthcare organisations to make informed decisions regarding risk retention, thereby facilitating more accurate management of expected future cash-flows. Second, the model introduces prudent risk measures, akin to those used in the financial and insurance sectors, to enhance awareness and understanding of potential risks. Nevertheless, the study could be refined by the use of different distributions than the Poisson, which may not fully capture the complexity of risk profiles. Additionally, the model’s accuracy depends on having a comprehensive and reliable dataset on historical claims. Without such data, there is a risk of biased sampling, which could undermine the reliability of the findings.

Future research should focus on several areas. Exploring and validating alternative statistical models that better address risk variability could enhance the robustness of risk assessment. Then, developing standardised criteria for prudential measures across healthcare organisations will be essential for the effective application of the proposed risk indicators, with reference to the RM identified by the model. Additionally, it should examine the impact of including such indicators in hospitals’ financial statements.

In conclusion, approaches like the one used can stimulate management in healthcare facilities to use financial models more frequently, with the expectation that this behaviour could pose a challenge to the insurance sector, potentially generating positive externalities in terms of know-how for all the players involved. Additionally, investigating methods to identify and benchmark claims distribution could enhance risk transfer strategies to the insurance market and improve risk management practices at various scale and operational levels.