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=='''Probabilistic language logic in medicine'''==

==Probabilistic language logic in medicine==

Every scientific idea (whether in medicine, architecture, engineering, chemistry, or any other subject), when put into practice, is subject to small errors and uncertainties. Mathematics - hrough probability theory and statistical inference - helps precisely control and thereby contain these uncertainties. It must always be considered that in all practical cases, ‘the outcomes also depend on many other factors external to the theory’, whether they be initial and environmental conditions, experimental errors, or something else.  

Every scientific idea (whether in medicine, architecture, engineering, chemistry, or any other subject), when put into practice, is subject to small errors and uncertainties. Mathematics - hrough probability theory and statistical inference - helps precisely control and thereby contain these uncertainties. It must always be considered that in all practical cases, ‘the outcomes also depend on many other factors external to the theory’, whether they be initial and environmental conditions, experimental errors, or something else.  

The casuality indicates the lack of certain connection between cause and effect. The uncertainty of a close union between the source and the phenomenon is among the most adverse problems in determining a diagnosis.  

The casuality indicates the lack of certain connection between cause and effect. The uncertainty of a close union between the source and the phenomenon is among the most adverse problems in determining a diagnosis.  

In a clinical case a phenomenon <math>A(x)</math> (such as for example a malocclusion, a crossbite, an openbite, etc ...) is randomly associated with another phenomenon <math>B(x)</math> (such as TMJ bone degeneration) when there are exceptions for which the logical proposition <math>A(x) \rightarrow B(x)</math> it's not always true (but it is most of the time). In that case it will say that <math>A(x) \rightarrow B(x)</math>it is not always true but it is probable.

In a clinical case a phenomenon <math>A(x)</math> (such as for example a malocclusion, a crossbite, an openbite, etc ...) is randomly associated with another phenomenon <math>B(x)</math> (such as TMJ bone degeneration) and when there are exceptions for which the logical proposition <math>A(x) \rightarrow B(x)</math> it's not always true (but it is most of the time). In that case it will say that <math>A(x) \rightarrow B(x)</math>it is not always true but it is probable.

{{q2|We pass from a deterministic condition to a stochastic one.|}}

{{q2|We pass from a deterministic condition to a stochastic one.|}}

#Mary Poppins is probably suffering from TMDs (qualitative term).

#Mary Poppins is probably suffering from TMDs (qualitative term).

#Mary Poppins is more likely to have TMDs than neuropathic OP (comparative term: number of diagnosed cases of TMDs versus (_nOP).

#Mary Poppins is more likely to have TMDs than neuropathic OP (comparative term: number of diagnosed cases of TMDs versus _nOP.

#The probability that Mary Poppins has TMDs is 0.15 (quantitative term, relative to the population).

#The probability that Mary Poppins has TMDs is 0.15 (quantitative term, relative to the population).

'''Objective probability'''

'''Objective probability'''

On the other hand,  events and random processes cannot be described by deterministic processes as 'if A then B'. The statistic is used to quantify the frequency of association between A and B and to represent the indeterministic relationships between them as a degree of probability that introduces the degree of objective probability. In the wake of the growing probabilization of uncertainty and randomness in medicine since the eighteenth century, the term "probability" has become a respected element of medical language, methodology and epistemology.

On the other hand,  events and random processes cannot be described by deterministic processes as 'if A then B'. The statistic is used to quantify the frequency of association between A and B and to represent the relationships between them as a degree of probability that introduces the degree of objective probability. In the wake of the growing probabilization of uncertainty and randomness in medicine since the eighteenth century, the term "probability" has become a respected element of medical language, methodology and epistemology.

Unfortunately the two types of probability, the subjective and the objective, are not accurately differentiated in medicine and also in other disciplines. The fundamental fact remains that the most important meaning that probability theory has generated in medicine, particularly in the concepts of probability in aetiology, epidemiology, diagnostics and therapy, is its contribution to our understanding and representation of biological casuality.

Unfortunately the two types of probability, the subjective and the objective, are not accurately differentiated in medicine and also in other disciplines. The fundamental fact remains that the most important meaning that probability theory has generated in medicine, particularly in the concepts of probability in aetiology, epidemiology, diagnostics and therapy, is its contribution to our understanding and representation of biological casuality.

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<br />So be it then <math>P(D)</math> the probability of finding, in the sample of ours <math>n</math> people, individuals who present the elements belonging to the aforementioned set <math>D=\{\delta_1,\delta_2,...,\delta_n\}</math>

<br />So be it then <math>P(D)</math> the probability of finding, in the sample of our <math>n</math> people, individuals who present the elements belonging to the aforementioned set <math>D=\{\delta_1,\delta_2,...,\delta_n\}</math>

In order to take advantage of the information provided by this dataset, the concept of partition of causal relevance is introduced:

In order to take advantage of the information provided by this dataset, the concept of partition of causal relevance is introduced:

The partition <math>\pi</math> in order for it to be defined as a partition of causal relevance it must have these properties:

The partition <math>\pi</math> in order for it to be defined as a partition of causal relevance it must have these properties:

#For each subclass <math>C_i</math> the condition must apply <math>rc=P(D \mid C_i)- P(D )\neq 0, </math> ie the probability of finding in the subgroup <math>C_i</math> a person who has the symptoms and elements belonging to the set <math>D=\{\delta_1,\delta_2,...,\delta_n\}</math> it cannot be identical to that which one would have in finding it 'fishin'" in the whole sample <math>n</math>. A causally relevant partition of this type is said to be '''homogeneous'''.

#For each subclass <math>C_i</math> the condition must apply <math>rc=P(D \mid C_i)- P(D )\neq 0, </math> ie the probability of finding in the subgroup <math>C_i</math> a person who has the symptoms, clinical signs and elements belonging to the set <math>D=\{\delta_1,\delta_2,...,\delta_n\}</math>. A causally relevant partition of this type is said to be '''homogeneous'''.

#Each subset <math>C_i</math> must be 'elementary', ie it must not be further divided into other subsets, as if these existed they would have no causal relevance.

#Each subset <math>C_i</math> must be 'elementary', ie it must not be further divided into other subsets, as if these existed they would have no causal relevance.

Now let us assume, for example, that the population sample <math>n</math> to which our good patient Mary Poppins belongs is a category of subjects aged between 20 and 70 years. We also assume that in this population we have those who present the elements belonging to the data set <math>D=\{\delta_1,.....\delta_n\}</math> which correspond to the laboratory tests mentioned above.

'''Now let us assume, for example''', that the population sample <math>n</math> to which our good patient Mary Poppins belongs is a category of subjects aged between 20 and 70 years. We also assume that in this population we have those who present the elements belonging to the data set <math>D=\{\delta_1,.....\delta_n\}</math> which correspond to the laboratory tests mentioned above.

Let us suppose that in a sample of 10,000 subjects from 20 to 70 we will have an incidence of 30 subjects <math>p(D)=0.003</math> showing clinical signs <math>\delta_1</math> and <math>\delta_4

Let us suppose that in a sample of 10,000 subjects from 20 to 70 we will have an incidence of 30 subjects <math>p(D)=0.003</math> showing clinical signs <math>\delta_1</math> and <math>\delta_4