Probabilities of medical risks

Question

Recently, I read a UK Supreme Court judgment Montgomery (2015), a judicial decision advocating patient's dignity and safety.

The Court held that no matter how small the percentage of a certain risk of harm/damage relating to certain clinical procedure (e.g. the risk of brachial plexus injury in case of shoulder dystocia involving diabetic mothers (delivering the baby vaginally), is just about 0.2%), if (1) the risk could, if materialised, cause serious harm to the patient, and (2) a reasonable patient, if properly warned, would attach significance to it, a healthcare provider is duty bound to disclose that risk to the patient. That risk, in legal definition, is material, even though statistically speaking, negligible (too small in terms of number/percentage).

I like this judicial decision very much as it really respect patients' dignity and care about patients' safety. After all, common sense! We used to see healthcare providers, as part of medicine culture, ordinary relying upon statistical figures to explain for their failure to disclose material risks of harm to patients, claiming that the relevant risk was just negligible (in figure), not worth mentioning. As a result, denying patients rights to make informed decisions very important to their own health, at times, resulting in some serious and sad consequences.

Now I know how the judges approach this question of healthcare providers' clinical decision making.

I want to know, on the other hand, how statisticians and mathematicians would approach the same question: statistical figures naturally lead many healthcare providers to feel confident in choosing their favorite "gold standard" clinical procedures, most if not all invasive and have the potential however small to cause serious harm (especially when the relevant published incident rate was small). Are healthcare providers correct in applying statistical figures that way in their everyday clinical decisions on individual patients?

I heard about Bayesian and Frequentist approach but I don't know if they are relevant to the question I asked cos' I'm just a sport medicine student without any training in statistics.

I would be most grateful if someone may enlighten me in this regard. Thanks in advance!

Answer 1

It basically says that patients should be told about all meaningful risks of a procedure, even if these risks are very small in statistical terms.

Now, from a stats perspective, there are two main approaches - Frequentist and Bayesian. Frequentists look at the long-term frequency of an event, so a doctor might use this to say the risk is very low based on lots of data. However, Bayesians would start with this general knowledge but then update it with specifics about the patient, like their age or health condition.

While both methods might lead to the same decision about a procedure, the key thing from the court ruling is to make sure all meaningful risks are shared with the patient. That's where technology could help! Think about a medical app that gives up-to-date, personalized risk assessments. It could help doctors explain risks and help patients make informed decisions.

Answer 2

I doubt a reasonable statistician would argue with such interpretation. This is a kind of problem you look at from decision theoretic perspective. First thing you need to do is to assign some numeric values to possible gains and harms (say monetary values). Next, you would estimate the expected "harms" of such procedure, i.e. multiply the harms by their probabilities and sum everything. Reasonable decision maker would consider such medical procedure if the amount of expected harms of such procedure is not greater then the amount of expected gains. What follows, this means that "large" harm that happens even with a small probability can have a noticeable impact on the overall expected outcome.