It is important to remember that the balance of probabilities standard of proof does not refer to ‘probability’ in the statistical sense, but refers to the degree of belief that must be established in relation to the fact of causation. It is a qualitative assessment that may be informed by statistical or epidemiological evidence but which ultimately must also incorporate an assessment of the reliability of the evidence and of how far it can be personalised to the individual claimant.46
The balance of probabilities is often treated as a statistical tool, where causation is proven as soon as the 51% threshold is passed. In Gregg, Lord Nicholls began his speech by stating that ‘[t]he patient could recover damages if his initial prospects of recovery had been more than 50%. But because they were less than 50% he can recover nothing’.47 This is also common in academic
commentary, for example Beever has suggested that ‘[t]he problem facing the plaintiff was that, before the defendant’s negligence, his chance of being cured was only 42%. This meant that, on the balance of probabilities, the defendant did not deprive the plaintiff of a cure’.48 Yet as Lord
Nicholls observed:
Statistical evidence, however, is not strictly a guide to what would have happened in one particular case. Statistics record retrospectively what happened to other patients in more or less comparable situations. They reveal trends of outcome. They are general in nature. The different way other patients responded in a similar position says nothing about how the claimant would have responded.49
He continued to ask,
Who can know whether Mr Gregg was in the 58% non-survivor category or the 42% survivor category? There was no evidence, peculiar to him or his circumstances, enabling
46 Epidemiology is the branch of medicine that studies the incidence and causes of disease in populations. 47 Gregg (HL) (n26) [2].
48 Beever, ‘Gregg v Scott’ (n39) 201. See also Stapleton ‘Loss of the chance of cure’ (n10) 997; Green, ‘Coherence of
medical negligence cases’ (n39) 3.
130
anyone to say whether on balance of probability he was in the former group of the latter group.50
It will be argued later that there was evidence enabling the court to say which group the claimant belonged to, but it is important to note that Lord Nicholls is right to say that raw statistics do not tell us anything about the individual. This means that if the raw statistics were reversed and 58% of patients would have survived, the court would still be unable to say whether the claimant fell into the survivor or non-survivor category if there was no information enabling them to personalise the statistics.
This tendency to map the patient’s statistical chance directly onto the balance of probabilities is perhaps more common in cases of medical negligence because a doctor explaining a patient’s prognosis will routinely refer to the statistical likelihood of recovery. A purely statistical approach may mean that where the patient’s chance of recovering is very close to 50 percent the case will be seen as being very close to the margins. But once he has suffered the harmful outcome then it is a question of fact whether the condition was treatable, and the balance of probabilities is a matter of belief in this fact and is designed to deal with the uncertainty – the court does not need to be convinced that the injury was certainly treatable, it needs only be convinced that it is more likely than not that it was treatable. It is essential to understand the role that statistical evidence can play in informing the balance of probabilities standard of proof.
The balance of probabilities is a standard of proof or persuasion, so it is a ‘belief probability’. Barnes explains that belief probability refers to ‘the credibility – the believability – of the evidence in support of a party’s factual claims’.51 He distinguishes this from ‘fact probability’ and
‘sampling error probability’.52 Fact probability refers to the likelihood of a causal relationship.
One aspect of this is the ‘risk ratio’ or ‘relative risk’:
50 Gregg (HL) (n26) [29].
51 David W Barnes, ‘Too Many Probabilities: Statistical Evidence of Tort Causation’ (2001) 64 Law and Contemp.
Probs 191, 192.
52 See also Steve Gold, ‘Causation in Toxic Torts: Burdens of Proof, Standards of Persuasion, and Statistical
131
Risk ratios measure the percentage change in the incidence of a specified harm, such as a disease. A risk ratio compares a background rate, where the stimulus in question is not present, to the rate that obtains when the stimulus is present. For example, in a routine tort case alleging that a negligent failure to light a stairway caused a fall, a risk ratio might compare the incidence of falling down stairs when the stairs are well-lit to the incidence of falling when the stairs are unlit…A risk ratio greater than one indicates that risks are increased. For instance, risk ratios of 1.5 and 3 indicate that the stimulus (for example, lack of lighting) increases the risk of falling by 50% and 200% respectively.53
The ‘sampling error probability’ refers to ‘a statistical property of data underlying evidence offered to prove a relevant fact’,54 so it aids the assessment of the reliability of a particular fact
probability. Barnes explains that:
Even when a sample is composed of randomly chosen subjects, those subjects may not represent accurately the population. That possibility means that any observed statistical relationship between acts like the defendant’s and harms like the plaintiff’s revealed by a study of a sample may be due to the happenstance of having drawn randomly an atypical sample.55
Barnes explains that in all studies based on a sample of the population there will be a sampling error and that this ‘is not an error in the design of the sample. Indeed, it is not an error attributable to any person. It is an unavoidable property of inferential statistics, the process of estimating attributes of a population by examining a sample’.56 The sampling error probability is
expressed as a ‘p-value’ ranging from 0 to 1.00, and a p-value closer to 0 indicates a smaller probability that error is due to the make-up of the sample. The greatest sampling error probability that is accepted in science is five percent, meaning that on the basis of sampling error
53 Barnes (n51) 193.
54 ibid. 55 ibid. 56 ibid 198.
132
there must be at least a 95 percent chance that the relationship is causal and not due to the chance that the sample is unrepresentative of the population. Furthermore:
A sampling error probability may as easily be calculated from a poorly designed study as from a randomized, controlled, double-masked study. The credibility of that probability and any fact probability derived from that study, however, depends on the quality of the design study.57
In other words, ‘[t]he p-value does not measure the probability that the design was perfect; rather, it assumes the design was perfect’.58
This means that in order for the court to form a rational belief in causation based on statistical or epidemiological evidence the reliability of the study must also be evaluated by addressing factors such as the experimental design and measurement. There are a range of criteria available for assessing the reliability of an epidemiological study and the statistics to which it gives rise. Barnes explains that the ‘well-known gold standard for experimental design is the randomized, controlled, double-masked study’.59
After the quality of a study has been established, epidemiologists then need to test the reliability of the causal inferences that can be drawn from the data. Miller has explained, ‘[i]n the UK, the nine criteria articulated by Professor Bradford Hill are perhaps the best known’60 criteria to test
causal inferences. These are: the strength of association, how high is the relative risk?; consistency, have the results been replicated elsewhere?; specificity of cause and of effect, does the ‘cause’ produce only one effect? Does the ‘effect’ have only one cause?; temporality, the effect must follow the cause; biological gradient, is a ‘dose relationship’ identifiable?; plausibility, is it consistent with prevailing biological knowledge?; coherence, does it conflict with any known biology of the disease?; experiment, does the frequency of the effect fall when the ‘cause’ is
57 ibid 200.
58 ibid 204. 59 ibid 200.
133
removed?; analogy, is the cause-effect relationship of any comparable disease accepted?61 These
factors relate to the question of whether there is a general causal relationship between the ‘cause’ and ‘effect’ i.e. the harmful agent for which the defendant is responsible and the type of illness suffered by the claimant. Miller notes that ‘Hill took pains not to exaggerate the claims of his criteria: “None of my nine viewpoints can bring indisputable evidence for or against the cause- and-effect hypothesis and none can be required as a sine qua non”’.62 While none of the factors
alone is determinative of the quality of the study, together they enable its reliability to be evaluated.
Furthermore, in order to form a rational belief about the causal relationship in an individual case, the court must assess the extent to which it is possible to extrapolate from the fact probability about general causation to causation in the individual case. This involves other factors, notably how closely matched the claimant is with the sample population and with the general population. So even if a study is reliable, the sampling error probability is not the same as a belief probability because it ‘would be divorced from the belief probability just where we need it – where we ask whether the particular defendant’s act was a necessary event in producing the particular plaintiff’s harm’.63 All of these factors therefore affect our overall degree of belief in the fact that the
particular defendant’s negligence was a cause of the particular claimant’s loss, the belief probability. This means that statistical evidence can provide a starting point for forming a rational belief in causation in an individual case, but it must be interrogated for reliability and for how far it is capable of informing us about the individual claimant.
It is important not only for lawyers to understand what the ‘balance of probabilities’ entails but also to ensure consistency in the discourse between lawyers and medical experts. The trial judge in Hotson noted that the claimant’s expert witness ‘speaks of likelihood as something involving a
61 ibid 548.
62 ibid 548. Citing A Bradford Hill, ‘The environment and disease: association or causation?’ (1965) 58 Proc R Soc
Med 295.
134
less than 50% chance in contradistinction to a probability as denoting more than that’.64 In other
words, the medical expert drew a significant distinction between something being ‘likely’ and it being ‘probable’. Given the importance of the ‘balance of probabilities’ in determining the outcome of a case it is essential that all parties understand the concept and use the term ‘probability’ consistently.
Indeed the pressure from the lawyers to express the chances in statistical terms seemed to go against the medical experts’ position in Gregg which was that a figure could not be put on the individual chance. With regard to the claimant’s pre-tort chance of cure, Inglis J noted:
Professor Goldstone was unable to put a percentage figure on that chance. It has to be taken as less than evens...It might be said that since neither he nor Dr Bunch put a figure on it, the court should not. I do not agree...The experts thought it possible that his individual prognosis had been reduced to less than 50% of what it would have been intrinsically at the outset.65
So since the balance of probabilities involves a qualitative assessment of the evidence it is important not only to avoid the temptation to map statistical probabilities directly onto it but also to avoid pressuring expert witnesses to quantify the risk if they are unable to.