Transcript Causality

Drug Induced Injury
The contribution of statistics to
establishing ‘cause’
Statistics in Law
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Statistics is about ‘description’, ‘estimation’ and
‘probability / likelihood’.
Statistics play a part:
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‘Sally Clark’ case  Probability of two cot deaths  1 in 73
million
Epidemiological evidence  Sally Clark case, Gregg v
Scott, McTear v Imperial Tobacco
Prosecutor’s fallacy
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Probability of observing evidence given innocence 
Probability of innocence given observed evidence
e.g. fire alarm if major fire
‘balance of probabilities’
Motivation
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To discuss issues relating to the use of statistics in
law, with particular attention to the law in relation to
medicine.
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Establishing causality
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Systematic experimentation
Interpreting ‘statistics’
Population versus Individual risk
Examples of questionable ‘statistics’
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Vioxx (rofecoxib)
Gregg v Scott
Oral contraceptives case
Causality and Risk
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“I would rather discover one causal law than
be King of Persia”
Democritus (460-370 B.C.)
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How can causality be established?
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Observation
Induction (Observation  Observation)
Correlation?
Deduction (Theorem  Proof)
Attributing causality
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Even significant correlation does not imply
causation (Fairchild v Glenhaven Funeral
Services)
Even ’significant correlation’ is not sufficient
 Folkes v Chadd, Hill v Metro. Asylum Board
e.g. Number of divorces versus importation of
tobacco
spurious correlation
Attributing causality
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Even plausible relationships are not necessarily
causal
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e.g. socioeconomic status and heart disease
 Confounded by (at least) smoking
MMR and Autism confounded by time /
improvements in diagnoses?
“Confounded”  other plausible explanations
Confounding is often an intractable problem in both
‘observational’ and ‘individual’ data
How can causality be established avoiding problems
such as confounding?
Systematic Experimentation
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“Development of Western Science is based
on two great achievements: the invention of
the formal logical system (in Euclidean
geometry) … and the discovery of the
possibility to find out causal relationships by
systematic experimentation”
(Albert Einstein, 1953)
Systematic Experimentation
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A clinical trial is a systematic experiment of a medical
intervention in human subjects
In many instances the optimal clinical trial is controlled,
adequately powered, fully pre-specified, randomised and
double-blind. The idea being to create groups of
patients almost identical (in reality and in perception)
except for the intervention of interest.
“adequately powered”  sufficient number of patients to
estimate the quantity of interest with desired precision.
Importance of control  Northwick Park
Systematic Experimentation
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If an event of interest occurs with greater frequency
in the treated group of patients, it might be argued
that the treatment causes the event.
This cannot be said with certainty, but a probability
is attached to the likelihood that two interventions
differ.
Statistics quantifies this likelihood
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Probability of observing data given a null hypothesis
If that probability is less than 5% it is common to
assume that the effect is ‘established’.
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Compare with ‘balance of probabilities’
Interpreting clinical trial data
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Data are often presented as an estimated
effect plus a confidence interval
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Essentially, all statistics based on samples are estimates.
Confidence Interval If the experiment were repeated 100 times,
95 percent of such intervals would contain the true value.
In lay terms:
 The estimated effect is our best guess at the difference in
effect between two treatments
 The confidence interval is a measure of uncertainty around
that effect, the wider the interval the less certain the estimate.
 If the confidence interval excludes the point of no difference,
the difference is said to be statistically significant.
Interpreting clinical trial data – an example
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Vioxx (rofecoxib) and the risk of Myocardial Infarction
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Relative risk 2.24, 95% Confidence Intervals (1.24 –
4.02), P=0.007 < 5%
In lay terms:
 Vioxx was estimated as more than doubling the risk
of MI compared to ‘controls’
 The probability that the risks for Vioxx and ‘controls’
were the same is 0.7%. This is ‘statistically
significant’.
Interpreting clinical trial data - warnings
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Even carefully controlled experiments can mislead.
Lack of external validity
“Lies, damn lies and statistics” – retrospective analysis
and exploration of subgroups can prove anything…..
Subgroup analyses
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Aspirin is highly effective in reducing the odds of vascular death
after acute MI…
…but not in Geminis or Libras!
Bias – a systematic deviation from the truth – can be
introduced by carefully chosen statistical methodology.
Lack of statistical significance does not automatically
imply similarity
Interpreting clinical trial data – an example
(continued)
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An example: Vioxx (rofecoxib) and the risk of Myocardial Infarction
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Relative risk versus all controls 2.24, 95% Confidence Intervals (1.24
– 4.02), P=0.007
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The controls were a mixture of placebos, non-naproxen NSAIDs and
naproxen, thought to potentially have a cardioprotective effect.
Relative risk versus placebo 1.04 (0.34, 3.12)
Relative risk versus non-naproxen NSAIDs 1.55 (0.55, 4.36)
Relative risk versus naproxen 2.93 (1.36, 6.33)
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Can we say from these data alone whether rofecoxib causes an
increase in incidence of MI?
Major implications for drug regulation, continual assessment of Risk:
benefit even in the post-marketing setting?
An aside – Product liability for Medicines
and Medicinal Devices
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Established duties of care
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‘reasonable care in researching the properties of a
product’
‘liability … for unknown risks will generally be
assessed on whether sufficient research or testing
was undertaken’
What is reasonable / sufficient?
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N = ????
Time = ????
Dose = ????
Observational experiment
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Not all experiments can be conducted
optimally
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Use observational experiments
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i.e. can’t randomise to being male / female
Case / control studies, cohort studies,
epidemiological database studies
These are useful, sometimes necessary, but
arguably, less reliable because sources of
confounding are harder to control.
Individual risk
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“Even Jonny Wilkinson has a 3 in 4 chance of
getting high cholesterol when he’s older”
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paraphrased from a commercial for Zocor Heart Pro
(simvastatin) sponsored by Boots
This is drawn from the population risk of a male over
55 having ‘high’ cholesterol.
However, simply because 3 in every 4 males
experience the event does not imply that the risk for
an individual male is 3/4.
Similarly if risk of MI is doubled for population taking
rofecoxib, what does this imply for the individual?
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We cannot accurately say from the population data
alone.
Estimating individual risk
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Individual risk may be attributable to many factors,
including, but not limited to, gender, family history, genetics,
socioeconomic status, smoking, exercise, diet…..
We can model this risk by estimating the weight to be given
to each relevant factor according to its relationship to
outcome.
Use epidemiological evidence to model
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e.g. Framingham to relate LDL to risk of cardiac event.
Probability of high cholesterol = (age) + (gender) +
(history) + (smoking) + (smoking) + ……
However, we can rarely specify the model with sufficient
precision to ‘prove’ merely to ‘inform’
Gregg v Scott
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On balance of probability was 10-yr survival
affected?
Delay in treatment estimated as reducing
survival from 42% to 25%
Therefore, on balance of probabilities, he
would have died anyway.
Issue 1: Does this really measure the ‘loss’ to
the patient?
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E.g. 99% chance of survival  51% chance of
survival = no loss
Gregg v Scott
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Issue 2: Why 10-year survival?
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Probability of 5-year survival would perhaps have
been estimated as being over 50% before, but not
after, the delay.
Probability of 1-year survival almost certainly over
50% both before and after the delay
Has the outcome been determined by the
(arbitrary) choice of ‘statistical’ cut-off?
Issue 3: Was the epidemiological model
applicable to Mr Gregg?
Oral Contraceptives
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How was the test derived? Was ‘balance of probabilities’ used
as the basis for agreeing to use a doubling of risk (relative risk=2)
to allow the judge to reach a decision?
Is it appreciated that probability > 50% and relative risk > 2 are
not related?
There is a difference between saying:
 The risk is increased two-fold by 3G OCs compared to 2G OCs
 The probability that 3G OCs increase risk compared to 2G OCs is
greater than 50%
 The probability that 3G OCs increase risk by two-fold compared
to 2G OCs is greater than 50%
What was the most important question to answer?
Is relative risk of 2 also arbitrary?
Aside: BMJ criticisms
Summary
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Systematic experimentation on a large population is arguably
the most reliable way to establish ‘cause’, but one cannot
necessarily draw inferences for a given individual because of
confounding factors.
Even optimally designed experiments can give rise to
misleading statistics and should be expertly interpreted
A clear understanding of statistical principles would appear to
be necessary for those relying on statistics in law.
It is not argued that statistics should be used as the final
arbiter of causation, but that the subject should be sufficiently
well understood to be able to weigh the statistical evidence
appropriately when deliberating.