Liability exposure depends on proof of causation, proof of negligence, number of cases, degree of harm, inflation, likelihood of successful claim etc. Science can directly affect the magnitude and probability of many of these factors and, combined with experience of the civil law, some informed judgement about the likelihood and magnitude of successful claims can be made.

This brief overview presents some of the principles and tools used in exposure assessment and the formation of judgements about science and liability issues.

Basic Building Blocks

Dose Response Curve
This is a fundamental requirement for making liability exposure assessment. As the dose increases to the right, at first there is no measurable response. Then the gentle slope indicates that a small but increasing proportion of the population is vulnerable to low doses. At higher doses the frequency of response increases among the more general population. At very high doses the frequency of response might reach a plateau, meaning that some section of the population is immune from a response, or that the entire population is affected.

It should be emphasised that very few dose response curves have been completed without making some assumptions. However, a few points on the curve can be extremely informative in exposure assessment and a more complete picture can be constructed as new findings are reported.

Response is sometimes measured as relative risk (RR) as opposed to frequency, however, the two can be interconverted (see below).

Hazard Response Distribution
Once you know the dose response curve, it makes sense to identify the numbers of people in a given population who experience a given dose. The usual situation is that very many people are unexposed and very few people are exposed to high doses (i.e. doses where there is a high probability of a response.) see the solid curve below.

In this figure the dose/ frequency curve is plotted on the same x axis as the dose response curve. By multiplying and integrating these curves together, the number of people with a given response can be calculated. Dose/ frequency curves are much more likely to be complete and to make few assumptions however new data is always useful for refining exposure assessments.

The number of people with a measurable response is not the same as a liability exposure assessment. Low doses may still cause disease but if the doses are below permitted levels, shown as the "Duty of Care Threshold" in the illustration below, then there should be no liability.

By integrating the curve for all exposures above the duty of care threshold (indicated by the vertical dotted line), the total number of potential claimants can be calculated. In a sense this represents the maximum exposure if the likely value of claims is known.

The liability exposure will increase if the permitted dose is changed to a lower value or the level at which a response could be detected.

The integrated total still does not represent actual liability exposure, this will depend on the distribution of the severity of the given outcome (this could vary with dose), the degree of awareness of causation, the Court’s view of personal exposure history, the length of time between exposure and effect (i.e. inflation) and many other factors. However, provided the courts stick to the facts these factors can only reduce the exposure from the maximum estimate. Medical and heads of damages inflation should be estimated as well.

In some cases a knowledge of causation evolves to the point where new liabilities are accepted, sometimes with retrospective effect and sometimes lower degrees of response are accepted as compensable. The effect of such evolution can be modelled using scientific knowledge.

Latency
When different doses produce different effects e.g. a low dose of chromium VI produces a mild injury and a higher dose a more serious disease it is often the case that the more serious outcome is delayed. Delays (latency) can take many forms but these are usually characterised by a minimum latency combined with a most probable latency.

Knowledge of time effects can assist with estimates of the effects of inflation.

The following figure illustrates a low and a high dose. The first curve (mild injury) shows that for low doses the delay between exposure and manifestation is low. The second curve shows that for high doses there is significant latency between exposure and manifestation.

To be able to use this model of disease outcomes in response to exposure to a hazard to generate estimates of the liability exposure it is necessary to obtain information on the exposure frequency at the population level. The next section will concentrate on Epidemiology and how it may be used to provide this information.

Even with the best of scientific input there is still an element of judgement required to take account of unknowable factors.

Epidemiologists provide information on:

• Exposure frequency.
• Disease frequency among the unexposed.
• Dose/ response frequency.
• Dose/ response severity.
• Latency.
• Causation.
• Standards to apply to diagnosis.
• Prognoses.
• The definition of appropriate standards for the duty of care.

All of these factors are essential to the assessment of liability exposure and to the judgement required in challenging claims that are made.

One of the most often reported variables from epidemiology is the relative risk (RR). Relative risk is the ratio of disease rate in the exposed population to the rate of disease in the unexposed population. RR values allow us to calculate the probability that a given case is related to exposure. The formula is given by:

P = 1 – 1/RR

When RR = 2, the probability = 50%. When RR = 1.5 the probability is 33%. When RR = 3 the probability is 66%.Therefore when RR is greater than 2.0, disease would be attributed to exposure on the balance of probabilities. It is not until RR = 20 that the probability reaches 95%; the usual standard required to show “beyond reasonable doubt”. RR = 20 is almost unheard of in liability scenarios.

The formula cannot be used for all values of RR and the circumstances in which the RR value was calculated should be taken into account when assessing any case.

In our view, epidemiology is rarely performed to standards that could be described as definitive. There is no general rule that allows new reports to be assessed in isolation, however, when RR is 3 or greater and provided there are no glaring errors of the research methodology this is a signal that the science really should be assessed in more detail.

Most often a new association between exposure and harm is first reported with RR values between 1 and 2, in isolation it is not possible to tell if such values are purely random or if they reflect a real association with an underlying causal mechanism. Assessment of the background science and the research methodology is required and it is essential to monitor the literature and build up a picture from other studies before committing to a judgement that leads to decisions. With experience, such assessments can be made and justified to the satisfaction of a judge.

RR values vary with exposure. If such information is available (from a dose/response curve) a more general expression is required. The probability at a given exposure is:

P = P(E)(RR-1) / (1 + P(E)(RR-1))

Where P(E) is the proportion of the general population exposed to a particular agent. Using this approach, the frequency of exposure related disease can be estimated if the total frequency of disease is known for the whole population. That is the results of the above equation are multiplied by the total disease frequency to get the frequency of disease associated with a particular level of exposure.

For example:

K Jamrozik BMJ, doi: 10.1136/ bmj. 38370. 496632.8 F
Estimate of deaths attributable to passive smoking among UK adults: database analysis

Estimates based on epidemiological evidence and demographic data.

Calculations assumed relative risks (RR) as follows:
RR = 1.24 for lung cancer.
RR = 1.30 for ischaemic heart disease.
RR = 1.45 for stroke.

Chronic obstructive pulmonary disease was not included.

Total numbers of deaths from these diseases was taken from national databases.

The fraction of this total that was related to passive smoking was calculated using:

{[p.(RR − 1)]/[1+p.(RR − 1)]}

(Where p = prevalence of passive smoking at home or work and RR = relative risk).

Prevalence estimates (p) were also taken from national databases:
11% of the workforce exposed at work, 36% of adults aged 20 to 64 exposed at home.

Across the United Kingdom as a whole, passive smoking at work is likely to be responsible for the deaths of more than two employed people per working day (617 deaths per year), including 54 deaths in the hospitality industry each year. Each year passive smoking at home might account for another 2700 deaths in persons aged 20-64 years and 8000 deaths among people aged ≥ 65.

These estimates are based on the most likely value of RR in each case. The precision of these values of RR remains uncertain but values similar to these have been consistently produced over the past 5 years or so. Given the typical precision of these estimates, workplace attributable deaths could be in the range 130 to 2000.

Comment
The importance of relatively weak risk ratios becomes clear when applied to large populations with high prevalences of exposure.

The method of calculation is quite generalisable. Much of the information published in regular reports to customers can be used to make, or adjust, these kinds of estimates.

Further analysis of the importance of variation with dose is provided by the following example:

E van Wijngaarden et al. Science of the Total Environment (2004)Vol. 332 p 81– 87

The paper describes a process for converting the results of epidemiologic studies into estimates of risk.

Assumptions:
Relative Risk as a function of dose is known.
Background risk rate is known; R(0).

It is fairly standard to assume that cancer risk follows the functional form:

RR=1+β.x

Where RR = relative Risk, x = exposure level and β= increment in relative risk per unit exposure.

Given this formulation, the excess risk assigned to exposure x is given by:

ERisk = β.x. R(0)

Units need to be followed through carefully.

Comment
The approach provides ready estimates of frequencies of adverse outcome. Epidemiological evidence provides a rough guide to additional risk even in the absence of insurance experience data.

Of course, some skills are required when using epidemiological data to assess liability risks. Gaps in the evidence base would require the use of estimates or extrapolations and some judgment would be required for estimating the range of possible changes in reported risk ratios and practical changes in exposures.
The effects of time lags can also be modelled quite easily.

In combination, and given sufficient information, it should be possible to predict the overall number of attributable cases and the time profile of adverse outcomes for a given year of exposure.

Summary
Epidemiology provides the basic building blocks for liability exposure assessment and for informing judgements about the likelihood of a claim succeeding if taken to court.

Both strategic aims require a degree of judgment that can only be built up from experience and assessment of factual information.

The consultants at Re: Liability (Oxford) Ltd have over 10 years experience of providing reports to inform such judgements.