ABSTRACT
Broncho Pulmonary Dysplasia (BPD) is a form of chronic lung disease that develops in preterm neonates treated with oxygen and positive-pressure ventilation. The disease affects premature babies and contributes to their morbidity and mortality. This research seeks to fit and compare the predictive powers of Logistic Regression (Logit) Modeland Probability Regression (Probit) Model in tracking infants’ BPD status using gender and weights at two different time intervals. The data used for the analysis were samples of 50 infants drawn from an underlying population of children with low birth weight (g) from Ahmadu Bello University Teaching Hospital Zaria. The children were confined to a neonatal intensive care unit, where they require intubation during the first 12 hours of life, and they survive for at least 28 days and their weights measured four weeks later. The results obtained found explanatory variables (weight at birth, weight after Four weeks of life and gender) used to be significantly associated with the occurrence of BPD in infants and suggested that, Probit fits BPD data more than Logit. It is therefore recommended that Clinics should adopt the use of the probit model fitted by this research to detect prevalence of BPD among infants so that adequate measures for prevention and control can be put in place early enough to signal the danger of the full manifestation of the disease.
TABLE OF CONTENTS
TITLE PAGE ……………………………………………………………………………………….. ………………… ……..i
DECLARATION ………………………………………………………………………………….. ………………… ……..ii
CERTIFICATION …………………………………………………………………………………………………. ……. …….iii
DEDICATION …………………………………………………………………………………………………………… .. …….iv
ACKNOWLEDGEMENT ……………………………………………………………………………………….. …… ……..v
ABSTRACT …………………………………………………………………………………………………………….. …. …….vi
TABLE OF CONTENTS …………………………………………………………………………………vii
LIST OF TABLES ……………………………………………………………………………… …………. ………. ……..ix
SYMBOLS AND ABBREVIATION …………………………………………………………………..….x
CHAPTER ONE: INTRODUCTION ……………………………………………………………. ….………… ……..1
1.1 Background of the Study …………………………………………………………………………………………………. 1
1.2 Statement of The Problem ……………………………………………………………………………………………….. 6
1.3 Aim and Objectives of The Study……………………………………………………………………………………… 7
1.4Significance of The Study ………………………………………………………………………………………………… 7
1.5 Scope and Limitation ……………………………………………………………………………………………………… 7
1.6 Brief Methodology …………………………………………………………………………………………………………. 8
1.6.1 Logistic Regression (Logit) Analysis …………………………………………………………………………………. 8
1.6.2 Probability Regression model (Probit) ………………………………………………………………………………… 8
1.7 Meaning and Definition of Terms………………………………………………………………………..9
CHAPTER TWO: LITERATURE REVIEW ………………………………………………………………… …….10
2.1 Introduction ………………………………………………………………………………………………………………… 10
2.2 Review of related Literature …………………………………………………………………………………………… 10
CHAPTER THREE: MATERIALS AND METHODS ………………………………………. ….…….. ……..16
3.1 Introduction ………………………………………………………………………………………………………………… 16
3.2 Research Design ………………………………………………………………………………………………………….. 16
3.3 Population ………………………………………………………………………………………………………………….. 17
3.4 Sample……………………………………………………………………………………………………………………….. 17
3.5 Method of Data Analysis ………………………………………………………………………………………………. 17
3.6 Logit and Probit Regression …………………………………………………………………………………………… 18
3.6.1 Logistic Regression (Logit) …………………………………………………………………………………………….. 18
3.6.2 Probability Regression (Probit) ……………………………………………………………………………………….. 26
3.6.3. Hypothesis and Confidence Interval for Logit and Probit …………………………………………………….. 30
3.6.4 Deviance (G2): A Measure of Goodness – of – Fit ……………………………………………………………….. 31
3.6.5 Log-likelihood Ratio Test ………………………………………………………………………………………………. 32
3.6.6. Akaike Information Criterion (AIC) ………………………………………………………………………………… 33
3.6.7 Model’s Performance Evaluation …………………………………………………………………………………….. 33
CHAPTER FOUR: ANALYSIS, RESULT AND DISCUSSION …………………………… ….……. …….35
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4.1 Introduction ………………………………………………………………………………………………………………… 35
4.2 Results of Model fit ……………………………………………………………………………………………………… 35
4.3The results of the logistic regression of the BPD data ………………………………………………………….. 35
4.3.1 Accuracy of Logit Model ……………………………………………………………………………………………….. 36
4.4 The results of the Probit Regression of the BPD data ………………………………………………………….. 38
4.4.1 Accuracy of Probit Model ………………………………………………………………………………………………. 38
4.5 Discussion ………………………………………………………………………………………………………………….. 40
CHAPTER FIVE: SUMMARY, CONCLUSION AND RECOMMENDATION…………….……..41
5.1 Summary ……………………………………………………………………………………………………………………. 41
5.2 Conclusion………………………………………………………………………………………………………………….. 41
5.3 Recommendation …………………………………………………………………………………………………………. 42
5.4 Contribution to Knowledge ……………………………………………………………………………………………. 42
References…………………………………………………………………………………………………………………… …….43
Appendix ……………………………………………………………………………………………………………………. …….47
CHAPTER ONE
INTRODUCTION
1.1 Background of the Study
The understanding of purpose of statistical science will play important roles to start a research of this kind. Usman (2016), in Bivariate and Multivariate Statistical Analysis, refers Multivariate statistical analysis as multiple advanced techniques for checking relationships among multiple variables at the same time. Researchers use multivariate techniques in a study that involve more than one response variable (phenomenon of interest) and more than one explanatory variable (also known as a predictor) or both. The statistical methods comes into play either when we have a medical theory to test or when we have a relationship in mind that has some importance in medical decision or policy analysis in public health.
According to Northway (1967), Broncho-Pulmonary Dysplasia (BPD)is a chronic lung disorder of infants and children and was first described in 1967. It is more common in infants with low birth weight and those who receive prolonged mechanical ventilation to treat respiratory distress syndrome (RDS).According to Namasiavayam (2014), BPD is a form of chronic lung disease that develops in preterm neonates treated with oxygen and positive-pressure ventilation. BPD is one of the most common chronic lung diseases in children. According to the National Heart, Lung, and Blood Institute (NHLBI), there are between 5,000 and 10,000 cases of BPD every year in the United States. Babies with highly low birth weight (less than 2.2 kilogram) are most at risk for developing BPD. In BPD, the lung and the airways (bronchi) are damaged in the neonatal period, causing destruction (dysplasia) of the tiny air sacs of the lung (alveoli). The pathogenesis of this condition remains complex and poorly understood; however various factors can not only injure small airways but also interfere with alveolarization (alveolar septation), leading to alveolar simplification with a reduction in the overall surface area for gas exchange.
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The developing pulmonary microvasculature can also be injured. Many infants born with BPD exhibit signs and symptoms of respiratory distress syndrome, including the following: tachypnea, tachycardia, increased respiratory effort (with retractions, nasal flaring, and grunting), frequent desaturations.Namasiavayam (2014) found that, prematurely born infants, especially those born before 28 weeks of gestation, has few alveoli at the point of birth. The alveoli that are present are not matured enough to functioning well, and the infant requires respiratory support (a respirator) for breathing. Babies who are victim of premature or who have respiratory challenge shortly after birth are at risk of developing broncho pulmonary dysplasia, sometimes called chronic lung disease. Although life-saving, these treatments can also cause lung damage, referred to as “broncho [airway] pulmonary [lung] dysplasia [destruction]”, or BPD. Broncho pulmonary dysplasia is a chronic lung disease that affects premature babies and contributes to their morbidity and mortality,Sahni (2005).
How BPD Affects Body
BPD directly affects both the lungs and the rest of the body. In the lungs, a significant number of alveoli that become fibrotic (scarred) and stop working. This damage affects not only the existing alveoli, but also those that continuously develop after birth. The low number of working alveoli means that the affected infant will need to remain on a breathing machine (ventilator) and/or receive oxygen for an extended period of time. This oxygen can cause further damage.
The damage to the alveoli also causes damage to the blood vessels around them, making the passage of blood through the lungs more difficult. In the long run, this leads to increases in the pressure inside blood vessels in the lungs and between the heart and lungs (pulmonary hypertension) and puts significant strain on the heart, which in severe cases may lead to heart
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failure. Because of the low number of working alveoli, the affected infant although needs to breathe much faster and harder than healthy infants. This work may slow early growth because the infants neither have the energy nor the time to feed properly, thus taking fewer calories in than they should, and burning most of the calories just to breathe. This leaves fewer calories for them to grow, with poor growth or “failure to thrive” that in turn may cause problems to other organs of the body.
How Serious Is Broncho Pulmonary Dysplasia?
An estimated 10,000 newborns could develop BPD in the U.S. every year. Its severity varies from infant to infant. In mild cases, the infant may only have a faster than usual respiratory rate. In cases of moderate severity, the infant may require oxygen for several months. In uncommon but severe cases, the infant may have respiratory failure that requires not only oxygen but also prolonged need for mechanical ventilation.
BPD Symptoms, Causes and Risk Factors
Symptoms The symptoms of BPD vary depending on its severity. Several risk factors make the development of BPD more likely but do not automatically lead to BPD. The most common symptoms of BPD are:
Rapid breathing
Laboured breathing (drawing in of the lower chest while breathing in).
Wheezing (a soft whistling sound as the baby breathes out).
Bluish discoloration of the skin around the lips and nails due to low oxygen in the blood.
Poor growth.
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Repeated lung infections that may require hospitalization.
Causes
The cause of BPD is related to life saving oxygen and mechanical ventilation. While a relatively high amount of inhaled oxygen over several days may be necessary to support life, it may also cause damage to the alveoli. This is sometimes made worse when the ventilator blows air into the lung, overstretching the alveoli. Less well understood, inflammation can damage the inside lining of the airways, the alveoli and even the blood vessels around them. These effects are particularly damaging on the premature lung, and BPD is considered to be primarily a complication of prematurity.
Risk Factors
There are several conditions that do not cause but make the development of BPD more likely (risk factors) such as the following:
Degree of prematurity: The less developed the lungs, the more they are likely to be damaged and result in BPD. BPD is rare in infants born after 32 weeks of pregnancy.
Prolonged mechanical ventilation: Mechanical ventilation stretches the alveoli. When overstretched, and for longer periods of time they may be damaged.
High concentrations of oxygen: The higher the concentration of oxygen and longer duration it is given, the higher the possibility of developing BPD. In general, concentrations of less than 60% oxygen are considered to be relatively safe.
Other risk factors. These include:
o Patent ductus arteriosus: The ductus arteriosus is a blood vessel that connects the right and left side of the heart that closes shortly after birth. This vessel is
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more likely to remain open in premature infants causing lung damage when too much blood flows into the lungs.
o Intrauterine growth retardation (IUGR): Different conditions may affect the growth of the fetus during the pregnancy and may also lead to premature labour. Relatively undeveloped lungs are more likely to develop BPD.
Logit and Probit regression models are members of Generalized Linear Model (GLM) that are widely used to estimate the functional relationship between binary response variable and predictors. The binary logit and probit models can be used to model functional relationship between a dichotomous response outcome and one or more predictors, (Krzanowki, 1998). When the outcome variable is dichotomous such as the case of BPD being considered in this study, both models are suitable for estimating the functional relationship between response variable and the predictors. Both models can therefore be used to analyze same data set for the same purpose, (Alison, 1999). Since the two models can be used for the same purpose, it is necessary to determine which model performs / predicts better. Logit model is a technique for fitting a set of data when the response variable consists of proportion or binary coded data. Probit model is a type of binary classification model which is also appropriate in fitting regression curve when the response variable is a dichotomous variable and the predictors are either numerical or categorical, (Dobson 1990). Model fit can be improved by the selection of appropriate link for dichotomous data. The main focus of the research is to make comparison of the link function selection and model fits of logit and probit regression models in the fitting of BPD data.
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Usman (2016), predictive modeling is one of the techniques used in statistical methodology by using historical information on a certain attribute to identify patterns which will help in predicting / determining a future value with a certain probability attached to it. Its application is valuable in the field of pharmacy and public health, particularly in medical settings. Some questions in medical research may contain dichotomous factor; in form of a person is a male or a female; a person does or does not have a disease in question, to mention but a few. In this study, we shall particularly fit and compare the two symmetrical dichotomous model; logit and probit, with prior knowledge for predicting BPD status of infants using gender and weight at two different survival time intervals of the infant as predictor variables and to establish the difference between the two stated models. In most cases, the model is used to make predictions in either the testing of a medical theory or the study of a policy’s impact in pharmacy and public health. This kind of research demands a careful control, so we have decided to use a record of BPD in ABU Teaching hospital Shika, Zaria.
1.2 Statement of the Problem
There have been reported cases of late discovery of BPD in infants which has been causing serious permanent health challenge for many people due to inability to discover it at an infancy as a result of clinical diagnosis of the disease which is rather expensive; however, a predictive model that will predict the disease could be a rare opportunity to detect the disease without passing through the rigour and expenses of the clinical diagnosis. Moreover, the model could be used to determine the prevalent rate of the diseasebased on the prior information available such as; weight at birth, weight after four weeks of birth and gender. Zysman et al (2013), discovered that gestational age and birth weight were correlated with the occurrence of BPD with each additional week of gestation. However, researches on statistical models that can appropriately
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predict the disease using some other information are quite limited. Therefore, this research seeks to address the problem of predicting BPD in infants using weights and gender with the aid of Logit and Probit Models.
1.3 Aim and Objectives of the Study
The aim of this research is to fit and compare the symmetric dichotomous models that predict infants’ BPD status using gender and weights. The following are specific objectives through which the stated aim would be achieved by;
i. fitting a Logistic Regression (Logit) model capable of tracking infants’ BPD status.
ii. fitting a Probability Regression (Probit) model that can be used to predict infants’ Broncho-pulmonary dysplasia (BPD) status based on gender and weight at two different times.
iii. comparing the two symmetric binary models fitted in (i) and (ii) above in order to assess the one that predict better.
1.4 Significance of the Study
This research will be of help to the research community especially, the medical practitioners to help them detect in time with the help of the fitted models, the prevalence of BPD among infants based on the weights and gender so as to take proper and adequate measures for controlling BPD.
1.5 Scope and Limitation
This study used samples of 50 infants drawn from an underlying population of children with low birth weight (g)from Ahmadu Bello University Teaching Hospital Zaria. These children were confined to a neonatal intensive care unit, they require intubation during the first 12 hours of life, and they survive for at least 28 days and their weights measured four weeks later. Infected
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infants are denoted by (1) while normal infants by (0). Two statistical models were fitted which
are; Logistic Regression (Logit) and Probability Regression Model (Probit) using BPD status,
gender and weights at two different time interval.
1.6 Brief Methodology
1.6.1 Logistic Regression (Logit) Analysis
The goal of logit is to find the best fitting and most parsimonious model to describe the
relationship between the outcome (dependent or response variable) and a set of independent
(predictor or explanatory) variables. The method is relatively robust, flexible and easily used,
and it lends itself to a meaningful interpretation. In logit model the link function is the logit
transform, ln
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. This research focuses on the case of a dichotomous outcome variable
(Y). The logit model that will be fitted can be expressed as
1 1 2 2 3 3
1 1 1 2 2 3 3
i i i
i i i
X X X
i X X X
e
P
e
… 1.1
Where i P
(the 𝑝s are independent Bernoulli random variables)is the probability that the ith infant
has BPD,fori= 1……n
The coefficients of this model are estimated using the maximum likelihood method. Logistic
regression model is discussed further by Hosmer and Lemeshow (1989).
1.6.2 Probability Regression model (Probit)
A Probit model (also called Probit regression), is a way to perform regression for binary
outcome variables. Binary outcome variables are dependent variables with two possibilities like
yes/no, positive testresult/negative test result or single/not single. The word “probit” is a
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combination of the words probability and unit; the probit model estimates the probability that a
value will fall into one of the two possible binary (i.e. unit) outcomes.
The Probit transformation or Probit link, is given by the inverse of the standard cumulative
normal distribution function which gives;
i 0 1 i1 2 i2 3 i3 P X X X …1.2
Where i P
is the probability that the ith infant has BPD,for i= 1……n
1.7 Meaning and Definition of Terms
1. Broncho : Airways
2. Dysplasia : Destruction
3. Alveoli : Lung
4. Ventilator : Breathing Machine
5. Ductus Arteriozus : Blood vessel that connects the right and left side of the heart that
closes shortly after birth
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