Drug Induced Injury

1
Drug Induced Injury

• The contribution of statistics to establishing
  cause

2
Statistics in Law

• Statistics is about description, estimation
  and probability / likelihood.
• Statistics play a part
• Sally Clark case ? Probability of two cot
  deaths ? 1 in 73 million
• Epidemiological evidence ? Sally Clark case,
  Gregg v Scott, McTear v Imperial Tobacco
• Prosecutors fallacy
• Probability of observing evidence given innocence
  ? Probability of innocence given observed
  evidence
• e.g. fire alarm if major fire
• balance of probabilities

3
Motivation

• To discuss issues relating to the use of
  statistics in law, with particular attention to
  the law in relation to medicine.
• Establishing causality
• Systematic experimentation
• Interpreting statistics
• Population versus Individual risk
• Examples of questionable statistics
• Vioxx (rofecoxib)
• Gregg v Scott
• Oral contraceptives case

4
Causality and Risk

• I would rather discover one causal law than be
  King of Persia
• Democritus (460-370 B.C.)
• How can causality be established?
• Observation
• Induction (Observation ? Observation)
• Correlation?
• Deduction (Theorem ? Proof)

5
Attributing causality

• 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

6
Attributing causality

• Even plausible relationships are not necessarily
  causal
• 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?

7
Systematic Experimentation

• 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)

8
Systematic Experimentation

• 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

9
Systematic Experimentation

• 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
• 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.
• Compare with balance of probabilities

10
Interpreting clinical trial data

• Data are often presented as an estimated effect
  plus a confidence interval
• 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.

11
Interpreting clinical trial data an example

• Vioxx (rofecoxib) and the risk of Myocardial
  Infarction
• Relative risk 2.24, 95 Confidence Intervals
  (1.24 4.02), P0.007 lt 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.

12
Interpreting clinical trial data - warnings

• 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
• 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

13
Interpreting clinical trial data an example
(continued)

• An example Vioxx (rofecoxib) and the risk of
  Myocardial Infarction
• Relative risk versus all controls 2.24, 95
  Confidence Intervals (1.24 4.02), P0.007
• 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)
• 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?

14
An aside Product liability for Medicines and
Medicinal Devices

• Established duties of care
• 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?
• N ????
• Time ????
• Dose ????

15
Observational experiment

• Not all experiments can be conducted optimally
• i.e. cant randomise to being male / female
• Use observational experiments
• 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.

16
Individual risk

• Even Jonny Wilkinson has a 3 in 4 chance of
  getting high cholesterol when hes older
• 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?
• ?We cannot accurately say from the population
  data alone.

17
Estimating individual risk

• 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
• 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

18
Gregg v Scott

• 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?
• E.g. 99 chance of survival ? 51 chance of
  survival no loss

19
Gregg v Scott

• Issue 2 Why 10-year survival?
• 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?

20
Oral Contraceptives

• How was the test derived? Was balance of
  probabilities used as the basis for agreeing to
  use a doubling of risk (relative risk2) to allow
  the judge to reach a decision?
• Is it appreciated that probability gt 50 and
  relative risk gt 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

21
Summary

• 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.