Changes

<translate>Let us consider a number <math>n</math> of individuals including people who report Orofacial Pain who generally have bone degeneration of the Temporomandibular Joint. However, there may also be other apparently unrelated causes. We must mathematically translate the 'relevance' that these causal uncertainties have in determining a diagnosis.</translate>

<translate>Let us consider a number <math>n</math> of individuals including people who report Orofacial Pain who generally have bone degeneration of the Temporomandibular Joint. However, there may also be other apparently unrelated causes. We must mathematically translate the 'relevance' that these causal uncertainties have in determining a diagnosis.</translate>

===The casual relevance===

===<translate>The casual relevance</translate>===

To do this we consider the degree of causal relevance <math>(cr)</math> of an event <math>E_1</math> with respect to an event <math>E_2</math> where:

<translate>To do this we consider the degree of causal relevance <math>(cr)</math> of an event <math>E_1</math> with respect to an event <math>E_2</math> where:</translate>

*<math>E_1</math> = patients with bone degeneration of the temporomandibular joint.

*<math>E_1</math> = <translate>patients with bone degeneration of the temporomandibular joint</translate>.

*<math>E_2</math> = patients reporting orofacial pain.

*<math>E_2</math> = <translate>patients reporting orofacial pain</translate>.

*<math>E_3</math> = patients without bone degeneration of the temporomandibular joint.

*<math>E_3</math> = <translate>patients without bone degeneration of the temporomandibular joint</translate>.

We will use the conditional probability <math>P(A \mid B)</math>, that is the probability that the <math>A</math> event occurs only after the event <math>B</math> has already occurred.

<translate>We will use the conditional probability <math>P(A \mid B)</math>, that is the probability that the <math>A</math> event occurs only after the event <math>B</math> has already occurred</translate>.

With these premises the causal relevance <math>cr</math> of the sample <math>n</math> of patients is:

<translate>With these premises the causal relevance <math>cr</math> of the sample <math>n</math> of patients is:</translate>

<math>cr=P(E_2 \mid E_1)- P(E_2 \mid E_3)</math>

<math>cr=P(E_2 \mid E_1)- P(E_2 \mid E_3)</math>

where <math>P(E_2 \mid E_1)</math> indicates the probability that some people (among <math>n</math> taken into consideration) suffer from Orofacial Pain caused by bone degeneration of the Temporomandibular Joint, while <math>P(E_2 \mid E_3)</math> indicates the probability that other people (always among <math>n</math> taken into consideration) suffer from Orofacial Pain conditioned by something other than bone degeneration of the Temporomandibular Joint.

<translate>where</translate>

:<math>P(E_2 \mid E_1)</math> <translate>indicates the probability that some people (among <math>n</math> taken into consideration) suffer from Orofacial Pain caused by bone degeneration of the Temporomandibular Joint</translate>,

Since all probability <math>P(A \mid B)</math> is a value between <math>0 </math> and <math>1 </math>, the parameter <math>(cr)</math> will be a number that is between <math>-1 </math> and <math>1 </math>.

:<math>P(E_2 \mid E_3)</math> <translate>indicates the probability that other people (always among <math>n</math> taken into consideration) suffer from Orofacial Pain conditioned by something other than bone degeneration of the Temporomandibular Joint</translate>.

The meanings that we can give to this number are the following: we have the extreme cases (which in reality never occur) which are:

<translate>Since all probability suggest that <math>P(A \mid B)</math> is a value between <math>0 </math> and <math>1 </math>, the parameter <math>(cr)</math> will be a number that is between <math>-1 </math> and <math>1 </math></translate>.

*<math>cr=1</math> indicating that the only cause of orofacial pain is bone degeneration of the TMJ,

<translate>The meanings that we can give to this number are as follows: </translate>

*<math>cr=-1</math> which indicates that the cause of orofacial pain is never bone degeneration of the TMJ but is something else,

*<translate>we have the extreme cases (which in reality never occur) which are:</translate>

*<math>cr=0</math> indicating that the probability that orofacial pain is caused by bone degeneration of the TMJ or otherwise is exactly the same,

:*<math>cr=0</math> <translate>indicating that the probability that orofacial pain is caused by bone degeneration of the TMJ or otherwise is exactly the same</translate>,

and the intermediate cases (which are the realistic ones)

*<translate>and the intermediate cases (which are the realistic ones)</translate>

*<math>cr>0</math> indicating that the cause of orofacial pain is more likely to be bone degeneration of the TMJ,

:*<math>cr>0</math> <translate>indicating that the cause of orofacial pain is more likely to be bone degeneration of the TMJ</translate>,

 

:*<math>cr<0</math> <translate>which indicates that the cause of orofacial pain is more likely not bone degeneration of the TMJ</translate>.

*<math>cr<0</math> which indicates that the cause of orofacial pain is more likely not bone degeneration of the TMJ.