System and Method for Medical Predictive Models Using Likelihood Gamble Pricing

A method for predicting survival rates of medical patients, said method comprising the steps of:

• providing a set D of survival data for a plurality of medical patients having a same condition;
• providing a regression model, said model having an associated parameter vector β;
• providing an example x0 of a medical patient whose survival probability is to be classified;
• calculating a first parameter
• l
• 1
• =
• max
• β
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• l
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• (
• β
• |
• D
• ⋃
• {
• (
• 1
• ,
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• ♦
• ,
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• )
• that maximizes a log-likelihood function of β over the set of survival data, l(β|D) augmented by a data point (1,x0,1), wherein the log likelihood l(β|D) is a strictly concave function of β and is a function of the scalar xβ;
• calculating an second parameter
• l
• 0
• =
• max
• β
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• l
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• (
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• D
• ⋃
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• that maximizes a log-likelihood function of β over the set of survival data, l(β|D) augmented by a data point (0,x0,1);
• calculating a fair log likelihood ratio λƒ from λƒ=l0−l0;
• and
• mapping the fair log likelihood ratio λƒ to a fair price y0ƒ, wherein said fair price is a probability that class label y0 for example x0 has a value of 1.

A method for classifying medical patients based on survival rates, said method comprising the steps of:

• providing a set D of survival data for a plurality of medical patients having a same condition;
• providing a regression model, said model having an associated parameter vector w;
• providing an example x0 of a medical patient whose survival probability is to be classified;
• defining a first quantity ln(α*) as
• max
• w
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• ∑
• i
• =
• 1
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• {
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• 1
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• (
• -
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• +
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• (
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• x
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• ;
• defining a second quantity ln(β*) as
• max
• w
• 
• ∑
• i
• =
• 1
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• {
• (
• y
• i
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• ,
• wherein xi is an element of D, and yi is a label assigning xi to one of two classes;
• using a Newton-Armijo method to evaluate said maximums;
• and
• calculating a probability that class label y0 for example x0 has a value of 1 from α*/(α*+β*).

A program storage device readable by a computer, tangibly embodying a program of instructions executable by the computer to perform the method steps for predicting survival rates of medical patients, said method comprising the steps of:

• providing a set D of survival data for a plurality of medical patients having a same condition;
• providing a regression model, said model having an associated parameter vector β;
• providing an example x0 of a medical patient whose survival probability is to be classified;
• calculating a parameter vector {circumflex over (β)} that maximizes a log-likelihood function of β over the set of survival data, l(β|D), wherein the log likelihood l(β|D) is a strictly concave function of β and is a function of the scalar xβ;
• calculating a weight w0 for example x0;
• calculating an updated parameter vector β* defined as the parameter vector β that maximizes a function l(β|D∪{(y0,x0,w0)}), wherein data points (y0,x0,w0) augment said set D;
• calculating a fair log-likelihood ratio λƒ from {circumflex over (β)} and β* using λƒ=λ(β*|x0)+sign(λ({circumflex over (β)}|x0)){l({circumflex over (β)}|D)−l(β*|D)};
• and
• mapping the fair log likelihood ratio λƒ to a fair price y0ƒ, wherein said fair price is a probability that class label y0 for example x0 has a value of 1.