Modeling Broncho-pneumonia Status in Infants Using Discriminant and Logistic Regression Analyses

Modeling Broncho-pneumonia Status in Infants Using Discriminant and Logistic Regression Analyses

CHAPTER ONE

Aim and Objectives of the Study

The aim of this study is to investigate the broncho-pneumonia status in infants using linear discriminant and logistic regression models, and this will be achieved through the following objectives; by

1. constructing a linear discriminant and logistic regression models that are capable for predicting the Broncho-Pneumonia status in infants;
2. predicting the Broncho-Pneumonia status of some infants (random selected cases) using the developed models;
3. comparing the predictive powers of the two models for Broncho-Pneumonia;
4. determining the predictor that has the most discriminating ability among the predictions

CHAPTER TWO

LITERATURE REVIEW

Introduction

 This chapter is on the collection of relevant research works that provide a basis for the present study. It gives an overview of the prevailing theories and hypotheses and methodologies on the subject of study. A critical literature review shows how prevailing ideas fit into a particular study, and how the work agrees or differs from them.

General Review

Beki (2012) used discriminant analysis and binary logistic regression for tracking the incidence of Broncho-Pulmonary Dysplasia among infants. The researcher used three possible predictor variables i.e. weight at birth, weight four weeks later and gender and

built a discriminant model that is capable of tracking Broncho-Pulmonary Dysplasia (BPD) infants. The Discriminant models for the two locations were;

Y=-2.860+0.035X₁-0.022X₂-0.658X₃andY=-3.539+0.001X₁-0.003X₂-0.795X₃ (2.1)

The Logistic regression models for the two locations were given as;

The study predicted the BPD status of five new infants using the discriminant model in which all the five new cases were correctly predicted. The discriminant model built had a perfect classification of five new cases in Kaduna while it has misclassification of one of five new cases in Sokoto. Conversely, the study predicted the BPD status of five new infants using logistic model in which all the five new cases were correctly predicted or classified. Hence, the logistic model built has a classification of five new cases in Sokoto while it misclassified two of five new cases in Kaduna.

Danbaba et al (2013), carried out a research on low birth weight using logistic regression analysis to determine the prevalence of Low Birth Weight (LBW) and some of its risk factors in maternity hospitals in Wushishi Local Government of Niger State. Data from a sample of 200 live births were collected in the hospital from June – September 2011. The data were collected by obtaining the mother‟s age at birth, mother‟s weight at birth, mother‟s education level, mother‟s occupation, gestational age, birth interval, twin or singleton birth and parity. The study fitted the logistic regression model to the data. The analysis of variance and chi-square tests were used to know the variables or factors that have statistically significant effect on birth weight at the 95.0% confidence level. The Odds Ratio (OR) of the risk factors of LBW was found using a multivariate logistic regression.

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CHAPTER THREE

RESEARCH METHODOLOGY

Introduction

This chapter focuses on the methods and data collection from the study area. It is necessary to critically study our methods and procedures as a precondition for achieving the desired goals. The research explored the prediction powers of the discriminant function and the logistic model as regards to the proper applications of biomedical modeling and to compare same for classifying the Broncho-Pneumonia (BPn) status of infants. The variables considered in this research; baby‟s weight at birth, baby‟s weight 4 weeks after, baby‟s sex, mother‟s age and mother‟s occupation are medically adequate to elucidate the difference between a normal and Broncho-Pneumonia (BPn) patient.

In this study, the researcher shall particularly build discriminant models with prior information for predicting the Broncho-Pneumonia (BPn) status of infants using the five variables.

Assumptions of Discriminant and Logistic regression analyses

1. The predictors are not correlated with one another, e. there is no multicollinearity
2. Correlation between two predictors is constant across groups.
3. The variance-covariance matrixes of all the independent variables are
4. Independent variable with the best discriminating ability between the two groups
5. The independent variables do not need to be multivariate normal
6. The dependent variable is binary

CHAPTER FOUR

ANALYSIS, RESULTS AND DISCUSSIONS

Introduction

In this chapter, the data are fitted to the linear discriminant and logistic regression models. The results of the analyses are presented and discussed. The data were analyzed using SPSS version 21.0

CHAPTER FIVE

SUMMARY, CONCLUSION AND RECOMMENDATIONS

Summary

In this study, discriminant model and binary logistic regression were used for predicting the occurrence of Broncho-pneumonia among infants using five variables as predictor variables i.e. baby‟s weight at birth, baby‟s weight four weeks after, baby‟s sex, mother‟s age and mother‟s occupation.

The objectives of this research are to construct the discriminant and logistic regression model that is capable of tracking BPn infants based on their variables used and also to compare and contrast the predictive power of the discriminant model and logistic regression for Broncho-Pneumonia.

The transcription and experimental method of data collection was used in this study and the research was carried out in Abuja with data obtained from University Teaching Hospital, Gwagwalada and Nasarawa with data obtained from Federal Medical Centre, Keffi. The data were gathered and tabulated for 180 and 253 low birth weight infants respectively.

Discriminant analysis and logistic regression were multivariate techniques employed for the analysis of the work. Box‟s M test and Wilk‟s Lambda were used to confirm the equality of the Covariance matrices and also to confirm the significance of the canonical correlation respectively.

Conclusion

In this research, linear discriminant and logistic regression model were applied to data collected for Broncho-Pneumonia from North Central Zone taking a case study of UTH, Abuja and FMC, Keffi Nasasrawa State. The result shows that the prediction of BPn is better done with discriminant model than logistic regression model in the zone.

Ten random samples of size 10 each taken from dataset were used to test the goodness of fit of the two models developed. The models were used for the prediction of the BPn status of selected samples. In discriminant model the average of 7.6 is correctly classified, while it misclassified 2.4. The study has predicted the BPn status of selected samples using the logistic model built in which an average of 5.4 were correctly predicted.

Equations (4.3) and (4.5) are the developed linear discriminant and logistic regression models constructed in this study, while, the related reviewed linear dicriminant and logistic regression models were in equation (2.1)and 2.2) respectively.

In this research, it was observed that linear discriminant model has a perfect classification than Logistic regression model. We also discovered that „baby‟s weight at birth‟ is the predictor that is best discriminating between the two groups

Recommendations

1. The researcher recommend that the models developed in this study could assist the doctors and other health practitioners to detect and monitor the prevalence and control of BPn among infants
2. Itis recommended that the discriminant model built should be used for BPn cases in the zone particularly at University Teaching Hospital, Abuja and Federal Medical Centre, Keffi Nassarawa State.
3. It is also recommended that larger sample size and health facilities be used infurther And use of other statistical package especially those dedicated to multivariate analysis on this area in order o elucidate intensive information or results.
4. Doctors and Clinics should adopt the use of the models built in this research to discover the prevalence of BPn among infants so that adequate measures for prevention and control of Broncho-Pneumonia can be taken early enough.

Contribution to knowledge

This study used both baby and mother‟s attributes to identify the best model used in the study while previous studies only used either the baby attributes or that of the mother.

Re-sampling technique which was achieved through SPSS package was also used to validate the models.

The study also identified the predictor variable with the highest discrimination between the two (2) groups.

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