ANALYSIS OF ISCHEMIC HEART DISEASEDATA USING LOGIC REGRESSION

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Nadeem Shafique ButtMuhammad Qaiser Shahbaz

Asif Hanif

27 Nov 2010

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Many observational studies establish whether certainrisk factors are associated with a disease.

In some situations it is important to study higher orderinteraction but with commonly available methods it isdifficult to study higher order interactions specifically incase of binary covariates.

We describe “Logic Regression” method proposed byRuczinski et al. (2003).

For illustration we use data collected from January 2006 to December2008 from patients admitted in cardiology department at MayoHospital Lahore

Many observational studies establish whether certainrisk factors are associated with a disease.

In some situations it is important to study higher orderinteraction but with commonly available methods it isdifficult to study higher order interactions specifically incase of binary covariates.

We describe “Logic Regression” method proposed byRuczinski et al. (2003).

For illustration we use data collected from January 2006 to December2008 from patients admitted in cardiology department at MayoHospital Lahore

Regression is most important tool in field of Statistics to

analyze data and make inference about associations

between predictor and response.

However, in most regression problems a model is developed

that only relates the predictors as they are main effects to

response. Interactions between predictors are considered as

well but usually kept very simple (2-way or 3-way at

maximum)

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Regression is most important tool in field of Statistics to

analyze data and make inference about associations

between predictor and response.

However, in most regression problems a model is developed

that only relates the predictors as they are main effects to

response. Interactions between predictors are considered as

well but usually kept very simple (2-way or 3-way at

maximum)

Logic Regression:Given a set of binary predictors X, “Logic Regression” try tocreate new and better predictors for the response byconsidering Boolean combination of those binary predictors:

Example:If the response variable is binary as well, the methodattempt to find decision rules such as if X1, X2,X3 and X4 aretrue, or X5 or X6 but not X7 then response is more likely to beclose to zero

The method try to find Boolean statements involving the binarypredictors that enhance the prediction for the response variable

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lry y X x

Logic Regression:Given a set of binary predictors X, “Logic Regression” try tocreate new and better predictors for the response byconsidering Boolean combination of those binary predictors:

Example:If the response variable is binary as well, the methodattempt to find decision rules such as if X1, X2,X3 and X4 aretrue, or X5 or X6 but not X7 then response is more likely to beclose to zero

The method try to find Boolean statements involving the binarypredictors that enhance the prediction for the response variable

The aim of this technique is to find thosecombinations of binary variables that have thehighest predictive power for the response.

These combination are Boolean Logic Expressionand since the predictors are binary, anycombination of predictors will be binary.

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The aim of this technique is to find thosecombinations of binary variables that have thehighest predictive power for the response.

These combination are Boolean Logic Expressionand since the predictors are binary, anycombination of predictors will be binary.

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This can be easily seen from thetable that higher orderinteraction will have all zeros.

Solution in this case is to find outa classification rule that correctlyassign a case to either Y=0 or Y=1using Boolean Equation

This can be easily seen from thetable that higher orderinteraction will have all zeros.

Solution in this case is to find outa classification rule that correctlyassign a case to either Y=0 or Y=1using Boolean Equation

Search Algorithms:

Given a fixed number of predictors, there are only finitemany Boolean expression that yield differentpredictions. If there are “k” predictors then there are2^2^k different prediction scenarios. And if there are“n” cases and “k” predictors then there might be up tok^n different logic trees.

Greedy search algorithm is used find out the bestBoolean Combination of the predictors that maximizethe predictability

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Search Algorithms:

Given a fixed number of predictors, there are only finitemany Boolean expression that yield differentpredictions. If there are “k” predictors then there are2^2^k different prediction scenarios. And if there are“n” cases and “k” predictors then there might be up tok^n different logic trees.

Greedy search algorithm is used find out the bestBoolean Combination of the predictors that maximizethe predictability

In this paper we have used Logic Regressiontechnique to model ISCHEMIC HEART DISEASEDATA as proposed by Ruczinski et al. (2003)using “LogicReg” package of “R”

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In this paper we have used Logic Regressiontechnique to model ISCHEMIC HEART DISEASEDATA as proposed by Ruczinski et al. (2003)using “LogicReg” package of “R”

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Details of DataData Collection Duration: Jan 2006 – Dec 2008

Venue: Cardiology Department, Mayo Hospital Lahore

Patient Definition: Under treatment of chest pain, cardiac failure and Syncope.Patient Definition: Under treatment of chest pain, cardiac failure and Syncope.

History Recorded: Clinical features, cardiovascular risk factors such ashypertension, DM, smoking habits and dyslipidaemic.

Exclusion criteria: contained sever liver disease, CLD, acute and chronicinflammatory diseases, immunological diseases and severanemia.

Finally coronary angiography was done on all patients by Judkin’s technique.

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Variable Label CodesHD CHD 0=Normal, 1=CHD

Gender Gender 0=Female, 1=Male

DM Diabetes Mellitus 0=No, 1= Yes

HTN Hypertension 0=No, 1= YesHTN Hypertension 0=No, 1= Yes

IHDF Family history ischemic heart disease 0=No, 1= Yes

FH Family history of hypertension 0=No, 1= Yes

DF Family History of Diabetes Mellitus 0=No, 1= Yes

Smoking Smoking History 0=No, 1= Yes

Viral Viral ailment 0=No, 1= Yes

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Logic Regression Model

L1:+4.15 * ((((not DM) or (not Gender)) or (HTN or (not

IHDF))) and ((Smoking or DF) and ((not DF) or (notHTN))))

L2:-2.35 * (((DM or (not DF)) and IHDF) or ((Gender and

(not DF)) or (FH and (not Gender))))

L3:+3.6 * (((IHDF and (not DM)) or ((not Gender) or (not

Smoking))) and ((DF or Smoking) or (FH or Gender)))

Logic Regression Model

L1:+4.15 * ((((not DM) or (not Gender)) or (HTN or (not

IHDF))) and ((Smoking or DF) and ((not DF) or (notHTN))))

L2:-2.35 * (((DM or (not DF)) and IHDF) or ((Gender and

(not DF)) or (FH and (not Gender))))

L3:+3.6 * (((IHDF and (not DM)) or ((not Gender) or (not

Smoking))) and ((DF or Smoking) or (FH or Gender)))

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• Logic Trees

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