COMPARATIVE STUDY ON LOGIT AND PROBIT MODELS IN THE PREDICTION OF BRONCHO-PULMONARY DYSPLASIA STATUS OF INFANTS

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COMPARATIVE STUDY ON LOGIT AND PROBIT MODELS IN THE PREDICTION OF BRONCHO-PULMONARY DYSPLASIA STATUS OF INFANTS

ABSTRACT
Bronchopulmonary dysplasia (BPD) is a chronic lung illness that affects premature infants who are treated with oxygen and positive-pressure ventilation. The disease affects premature babies and increases their morbidity and death.

This study aims to fit and compare the predictive capacities of the Logistic Regression (Logit) and Probability Regression (Probit) models in tracking infants’ BPD status using gender and weight at two different time intervals.

The investigation was based on 50 newborn samples obtained from an underlying population of children with low birth weight (g) at Ahmadu Bello University Teaching Hospital in Zaria. The youngsters were admitted to a newborn intensive care unit and required intubation within the first 12 hours of life.

They survived for at least 28 days and had their weights measured four weeks later. The findings revealed that explanatory variables (weight at birth, weight at four weeks of life, and gender) were strongly associated with the occurrence of BPD in babies, suggesting that Probit fits BPD data better than Logit.

As a result, it is recommended that clinics employ the probit model fitted by this study to detect the prevalence of BPD among newborns so that effective preventative and control measures can be implemented early enough to warn the danger of the disease’s complete onset.

Chapter one

INTRODUCTION
1.1 Background of the Study
Understanding the goal of statistical science will be vital in starting this type of research. In Bivariate and Multivariate Statistical Analysis, Usman (2016) defines multivariate statistical analysis as a collection of advanced approaches for examining correlations between numerous variables at the same time.

Multivariate approaches are used by researchers in studies that incorporate more than one response variable (phenomenon of interest) and/or more than one explanatory variable (also known as a predictor).

Statistical approaches are used when we have a medical hypothesis to test or when we have a relationship in mind that is important in medical decision-making or public health policy analysis.

According to Northway (1967), Broncho-Pulmonary Dysplasia (BPD) is a chronic lung condition in newborns and children that was first reported 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 type of chronic lung disease that develops in preterm neonates treated with oxygen and positive-pressure ventilation. BPD is among the most frequent chronic lung disorders in children. According to the National Heart, Lung, and Blood Institute (NHLBI), there are between 5,000 to 10,000 cases of BPD in the United States each year.

Babies with extremely low birth weights (less than 2.2 kilogrammes) are most likely to develop BPD. In BPD, the lung and airways (bronchi) are damaged during the newborn period, resulting in the destruction (dysplasia) of the lung’s tiny air sacs (alveoli).

The pathophysiology of this illness is complex and poorly understood; nonetheless, a variety of variables can not only harm tiny airways but also interfere with alveolarization (alveolar septation), resulting in alveolar simplicity and a reduction in overall surface area for gas exchange.
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The developing pulmonary microvasculature may potentially be damaged. Many infants born with BPD show signs and symptoms of respiratory distress syndrome, such as tachypnea, tachycardia, increased respiratory effort (with retractions, nasal flaring, and grunting), and frequent desaturations.

Namasiavayam (2014) discovered that prematurely born infants, particularly those born before 28 weeks of gestation, have few alveoli at birth. The alveoli that are there are not developed enough to function properly, thus the infant needs respiratory support (a respirator) to breathe.

Babies who are born prematurely or who experience respiratory problems soon after birth are at risk of developing bronchopulmonary dysplasia, also known as chronic lung disease.

Although life-saving, these treatments have the potential to cause lung damage known as “broncho [airway] pulmonary [lung] dysplasia [destruction], or BPD. Bronchopulmonary dysplasia is a chronic lung illness that affects premature neonates, increasing their morbidity and death (Sahni, 2005).

How BPD Affects the Body
BPD has a direct effect on both the lungs and the rest of the body. In the lungs, a large proportion of alveoli become fibrotic (scarred) and stop functioning. This injury affects both existing alveoli and those that continue to develop after birth.

Because to the reduced number of functional alveoli, the affected infant will require long-term use of a breathing machine (ventilator) and/or oxygen. This oxygen may cause more damage.

The injury to the alveoli also damages the blood arteries around them, making blood flow across the lungs more difficult. In the long run, this leads to rises in the pressure inside blood arteries in the lungs and between the heart and lungs (pulmonary hypertension) and places enormous strain on the heart, which in severe cases may lead to cardiac
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failure. Because of the limited amount of functional alveoli, the affected infant must breathe significantly faster and harder than healthy infants. This approach may delay early growth because newborns lack the energy and time to properly feed, consuming fewer calories than necessary and expending the majority of those calories just to breathe.

This leaves less calories for them to grow, resulting in poor growth or “failure to thrive” that may create problems in other organs of the body.

How Serious is Bronchopulmonary Dysplasia?
Every year, approximately 10,000 babies in the United States are at risk of developing BPD. Its severity varies with each infant. In moderate situations, the infant may just have a faster-than-normal respiratory rate.

In cases of severe severity, the infant may need oxygen for several months. In rare but severe situations, the infant may experience respiratory failure, necessitating not just oxygen but also long-term mechanical ventilation.

BPD: Symptoms, Causes, and Risk Factors
Symptoms of BPD vary according to their severity. Several risk factors increase the likelihood of developing BPD, but they do not guarantee it. The most prevalent symptoms of BPD include:

 Rapid breathing.

 Laboured breathing involves drawing in the lower chest while breathing in.

 Wheezing (gentle whistling sound as baby exhales).

Low oxygen levels in the blood can cause bluish discoloration of the skin around the lips and nails.

 Poor growth.
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 Repeated lung infections may require hospitalisation.

Causes

The cause of BPD is linked to life-saving oxygen and mechanical ventilation. While a large amount of inhaled oxygen over several days may be required to sustain life, it may potentially harm the alveoli.

This is sometimes exacerbated when the ventilator pushes air into the lungs, expanding the alveoli. Inflammation, which is less well understood, can harm the inside lining of the airways, the alveoli,

and even the blood vessels that surround them. These effects are especially harmful to the young lung, and BPD is thought to be predominantly a consequence of preterm.

Risk Factors:
Several conditions, such as the following, do not cause BPD but increase the likelihood of its development (risk factors).
 Prematurity: Less developed lungs are more susceptible to injury, leading to BPD. Infants born after 32 weeks of pregnancy are unlikely to have BPD.

 Prolonged mechanical breathing might expand the alveoli. When overstretched for an extended length of time, they may be harmed.

 High oxygen concentrations and prolonged use increase the risk of developing BPD. In general, quantities of less than 60% oxygen are thought to be generally safe.

 Additional risk factors. This includes:

o Patent ductus arteriosus: This is a blood artery that connects the right and left sides of the heart and closes shortly after birth. The vessel is

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Premature newborns are more likely to have an open airway, which causes lung injury when too much blood flows into the lungs.
o Intrauterine growth retardation (IUGR): Various diseases can impact the fetus’s growth during pregnancy, potentially leading to premature labour. People with underdeveloped lungs are more likely to develop BPD.

Logit and Probit regression models are components of the Generalised Linear Model (GLM) and are commonly employed to assess the functional connection between binary response variables and predictors. The binary logit and probit models can be used to represent the functional connection between a binary response outcome and one or more predictors (Krzanowki, 1998).

When the outcome variable is dichotomous, as in the case of BPD in this study, both models are appropriate for assessing the functional connection between the response variable and the predictor. Both models can thus be applied to the same data set for the same objective (Alison, 1999).

Because the two models can serve the same function, it is vital to establish which model performs or predicts better. The logit model is a technique for fitting a collection of data when the response variable is proportional or binary coded.

The Probit model is a binary classification model that may also be used to fit regression curves where the response variable is a dichotomous variable and the predictors are numerical or categorical (Dobson 1990).

Model fit can be enhanced by selecting the right link for dichotomous data. The primary goal of the study is to compare the link function selection and model fits of logit and probit regression models in fitting BPD data.
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According to Usman (2016), predictive modelling is a technique used in statistical methodology that involves using historical data on a specific attribute to uncover patterns that would aid in predicting / identifying a future value with a given likelihood attached. Its application is beneficial in the fields of pharmacy and public health, particularly medical settings.

Some medical research questions may include a dichotomous component, such as whether a person is male or female, or whether or not a person has the disease in question, to name a few examples. In this study, we will fit and compare two symmetrical dichotomous models, logit and probit,

with prior knowledge for predicting BPD status of infants using gender and weight as predictor variables at two different infant survival time intervals, and we will determine the difference between the two models.

In most cases, the model is used to create predictions in either medical theory testing or policy impact studies in pharmacy and public health. This type of research necessitates meticulous control, hence we chose to use a BPD record from ABU Teaching Hospital Shika, Zaria.

1.2 Statement of the Problem
There have been reports of late discovery of BPD in infants, which has caused serious permanent health challenges for many people due to the inability to detect it at an early age as a result of clinical diagnosis of the disease,

which is rather expensive; however, a predictive model that predicts the disease could be a rare opportunity to detect the disease without going through the rigour and expense of clinical diagnosis.

Furthermore, the model may be used to calculate the disease’s prevalence rate based on previously accessible information such as birth weight, weight after four weeks after delivery, and gender. Zysman et al. (2013)

discovered that gestational age and birth weight were associated with the development of BPD with each additional week of gestation. However, research into statistical models that may suitably
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Predicting the disease based on other information is extremely restricted. As a result, the purpose of this study is to use Logit and Probit models to solve the problem of predicting BPD in babies based on weight and gender.

1.3 Goals and Objectives of the Study
The purpose of this study is to fit and compare symmetric dichotomous models that predict BPD status in babies using gender and weights. The following are specific objectives that would be used to attain the stated goal:

i. Fitting a Logistic Regression (Logit) model to track infants’ BPD status.

ii. Fitting a Probability Regression (Probit) model to predict newborns’ Broncho-pulmonary dysplasia (BPD) status using gender and weight at two separate dates.

iii. Comparing the two symmetric binary models described in (i) and (ii) above to determine which one predicts better.

1.4 Significance of the Study
This study will assist the research community, particularly medical practitioners, in detecting the prevalence of BPD among newborns based on weight and gender in real time using fitted models, allowing them to adopt appropriate and effective steps to control BPD.

1.5 Scope and Limitation.
This study employed 50 newborn samples from an underlying population of children with low birth weight (g) at Ahmadu Bello University Teaching Hospital in Zaria.

These youngsters were admitted to a neonatal intensive care unit, where they required intubation during their first 12 hours of life. They survived for at least 28 days and had their weights measured four weeks later. Infected
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Infants are represented by (1), and normal infants by (0). Two statistical models were fitted,
Logistic Regression (Logit) and Probability Regression Model (Probit) based on BPD status,
Gender and weight at two separate time intervals.

1.6 Brief Methodology
1.6.1 Logistic Regression (Logit) Analysis.
The objective of logit is to develop the best fitting and most parsimonious model to describe the

The relationship between the outcome (dependent or response variable) and a group of independent
(Predictor or Explanatory) variables. The approach is generally robust, adaptable, and easy to use.

It lends itself to significant interpretation. In logit models, the link function is the logit.
transform, ln 
 
1
 



. This study examines the scenario of a dichotomous outcome variable.
(Y). The logit model to be fitted can be stated 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 is P?
(The 𝑝s are independent Bernoulli random variables), is the probability that the ith newborn
has BPD, fori = 1……

The coefficients in this model are estimated using the greatest likelihood technique. Logistic
Hosmer and Lemeshow (1989) provide additional information on the regression model.

1.6.2 Probability Regression Model (Probit).
A Probit model (also known as Probit regression) is a method for doing binary regression.

Variables that influence the outcome. Binary outcome variables are dependent variables that have two options, such as
Yes/No, positive/negative test results, or single/not single. The term “probit” is an
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The probit model is a mix of the words probability and unit; it predicts the likelihood that
The value will fall into one of two binary (i.e. unit) outcomes.

The inverse of the standard cumulative yields the Probit transformation or Probit link.
The normal distribution function yields:

 i 0 1 i1 2 i2 3 i3 P    X  X  X …1.2
Where is P?
What is the likelihood that the ith infant has BPD for i= 1……n?

1.7 Meaning and Definitions of Terms

1. Broncho: Airways.

2. Dysplasia: Destruction.

3. Alveoli: Lung.

4. Ventilator: A breathing machine.

5. Ductus Arteriozus: A blood vessel that links the right and left sides of the heart.

Closes quickly after birth.
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