Bayesian statistics and management of cracks
This is a discussion paper i.e. there’s no strong evidence supporting the ideas behind this paper. Nor am I saying that this is the right and only way to manage cracks. I hope that this essay would generate more discussion about the topic.
Bayes’ rule, which was first postulated by the Reverend Bayes in a posthumously published 1763 manuscript, can be so computationally complex that for century most statisticians essentially ignored the work because they lacked tools to perform their calculation it demanded. Starting in the 1950s however as computer became more powerful, scientists found they could use bayesian approaches to forecast events that were previously thought unpredictable, such as the likelihood of a war, or the odds that a drug will be broadly effective even if it has only been tested on a handful of people. Even today, though, calculating a bayesian probability curve can, in some cases tie up a computer for hours. At the core of Bayes’ rule is the principle: even if we have very little data, we can still forecast the future by making assumptions and then skewing them based on what we observe about the world. For instance, suppose your brother said he’s meeting a friend for dinner. You may forecast there’s a 60% chance he’s going to meet a man, since most of your brothers friends are males. Now, suppose your brother mentioned his dinner companion was a friend from work. You might want to change your forecast, since you know that most of his co-workers are females. Bayes’ rule can calculate the precise odds that your brother’s dinner date is female or male based on just one or two pieces of data and your assumptions. As more information comes in-his companion name is Pat, he or she loves adventure movies and fashion magazines- Bayes’ rule will refine the probability even more. (from Smarter Faster Better by Duhigg)
Learn more about Bayesian vs standard statistics here.
Management of cracks
For the sake of simplicity and brevity, conceptually, we can divide cracks in to three groups based on where the cracks end in relation to bone level. This is the case where we can clearly see crack in the pulp chamber under microscope.
Shallow crack-above the bone level. Deep crack-below the bone level. These two scenarios are quite clear from management point of view. The first, crown after endo should be able to seal and prevent new bacterial ingress. The latter, crown wouldn’t be able to prevent reinfection therefore extraction would be recommended. The third scenario is where the discussion becomes interesting and is the point of this discussion paper. The so called border-line crack, where the cracks end around bony crest.
Standard statistic thinking - frequentist
Comparative clinical outcome studies (which is considered gold standard in health science) on different types of crack management are few and far between. Clinical studies of rare diseases or conditions are difficult to conduct because of prohibitively long recruitment period (which leads to inadequate sample size). Cracks are infrequent and difficult to diagnose. Management of cracks, therefore, is not based on well-design, adequate power clinical studies, which means that standard statistic thinking is not applicable here.
“An unwanted result doesn’t make our decision wrong if we thought about alternatives and probabilities in advance and allocated our resources accordingly.”
Bayesian statistic thinking - (combination of prior beliefs, evidence and posterior beliefs), approach or decision is modified after new information emerges. Learn more about Bayesian thinking here.
What we know:
How deep is the crack;
Patients, what they are like;
easy going (cope well with uncertainty i.e. give endo a try),
uptight (may prefer predictability i.e. extraction/replacement),
cost sensitive (extraction may be cheaper) etc.
Thinking in bets suggests how to determine patient cost sensitivity and how they handle uncertainty with the following question.
“If you know that this tooth would be lost eventually, how long this tooth would need to last to (be considered) worth (treatment fee)?”
If the answer was a few year, we may give endo a try. If ten years, then the patient might not be a good candidate for endo.
What we don’t know:
If the crack will propagate, how deep it will go, if symptoms will develop.
Marry what we know with what we don’t and allocate resources accordingly. That’s Bayesian thinking.
When dealing with scenarios with high degree of uncertainty, it’s imperative that patients drive the treatment plan, not clinicians. Evidence-based concept holds the view that patients are the expert in deciding which symptoms are bearable, which economic costs are acceptable and which risks/uncertainties are worth taking. To that end, we may offer patients two options and let them choose. One, if patients value predictability, extraction/replacement would be recommended. Two, if patients value natural tooth and would like to hang on to it. They could consider the following;
Instead of finishing endo and a crown in short period of time (and the patient will bear the full treatment fee on a treatment with uncertain prognosis) what if we clean and medicate (partial fee) and review in six months gather more information. As in if surrounding tissues deteriorated, pocket developed, tooth became symptomatic, we’d give up. If, however, everything was good, we’d obturate and overlay, leave it for another six month, gather more info. Would that be conservative operatively and financially? What do you think?