Comparative Study on Logit and Probit Models in the Prediction of Broncho-Pulmonary Dysplasia Status of Infants

Comparative Study on Logit and Probit Models in the Prediction of Broncho-Pulmonary Dysplasia Status of Infants

Chapter One

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;

1. fitting a Logistic Regression (Logit) model capable of tracking infants’ BPD
2. 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.
3. comparing the two symmetric binary models fitted in (i) and (ii) above in order to assess the one that predict

CHAPTER TWO:

LITERATURE REVIEW

  Introduction

In every research, the review of related literature is necessary to achieving the desired research objectives. It is pertinent to begin every research work, particularly in this kind of statistical fitting, by outlining how other relevant literatures were consulted.

Review of Related Literature

A review of only those items relevant to the dissertation work has been made in this section, which has an immediate bearing to this research at hand. Broncho Pulmonary Dysplasia (BPD) continues to be a major cause of chronic morbidity among this population. Danan (2002) observed that there are large variations in the incidence and severity of this disease.

Some Key Facts about BPD

• BPD is associated with inflammation and scarring in thelungs
• BPD is much more common among low birth weight and premature
• Most infants recover from BPD, but some may have long-term breathing
• Infants are not born with BPD; the condition results from damage to the lungs which are caused by mechanical ventilation (respirator) and long-term use of
• The severity of BPD is defined by the amount of oxygen an infant requires at time of birth and the length of use of supplemental oxygen or mechanical

According to the National Institutes of Child Health and Human Development of USA (NICHD) consensus (2001),it reported that the incidence of BPD in Latin Americacomes from the neonatal group study of a very-low birth- weight (VLBW).

Tapia et al (2006) examined that the BPD is a chronic pulmonary disease which affects premature infants and contributes to their morbidity and mortality. Despite substantial changes in incidence, risk factors and severity after the introduction of new therapies and mechanical ventilation (MV) techniques, BPD remains common, for more details refer to Tapia et al (2006). Kumar et al (2011) conducted a study to determine the prevalence risk factors of nephropathy in type-2 diabetic patients. Here, it is remarked that Kumar et al (2011) discovered that as the duration of type-2 diabetes increases, the incidence of Nephropathy also increases significantly. Hence, all the type-2 diabetic patients, especially those with increased duration should be screened for Nephropathy and be made aware of the complications.

Carlos et al (2007) conducted a research which involves the building of model for the prediction of Broncho-pulmonary dysplasia model for seven-day old infants and their aim was to develop a predictive model capable of identifying which premature infants have the greatest probability of presenting (BPD) based on assessment at the end of the first week of life. Carlos et al (2007) concluded that at the end of the first week of life, the predictive model they developed was capable of identifying newborn infants at increased risk of developing BPD with high degree of sensitivity.

Boule et al (2001) proposed that adaptive control effects of exercise on glycemic control and body mass in type 2 diabetes mellitus is generally access by clinical trials. Maja et al (2004) worked on comparison of Logistic Regression and Linear Discriminant Analysis; a simulation study and their aim was the problem of choosing between the two methods and to set some guideline for proper choice. Maja et al (2004) found out that, LDA is a more appropriate method when the explanatory variables are normally distributed. In the case of categorized variables, LDA remains preferable and fails only when the number of categories is really small (2 or 3).The

results of LR, however, are in all these cases constantly close and a little worse than those of LDA. But whenever the assumptions of LDA are not met, the usage of LDA is not justified, while LR gives good results regardless of the distribution. As the estimates for LR are obtained by the maximum likelihood method, they have a number of nice asymptotic properties as well. Shah et al (2007), Inhaled corticosteroids have long been used as a therapy for patients who have developing or established BPD, but the evidence supporting their use is mixed.

A Cochrane systematic review of randomized controlled trials revealed that there is no evidence that early-inhaled corticosteroid therapy (at <2 weeks after birth) to ventilated preterm infants decreases the incidence of BPD. According to HIFI (High Frequency Ventilation in Premature) study in 1980, high frequency positive pressure ventilation, high frequency jet ventilation, and high frequency oscillation have been developed to provide artificial ventilation and reduce barotrauma. It is unclear whether any of these techniques offer any advantages over conventional mechanical ventilation in the routine treatment of respiratory failure of preterm infants. Their use does not seems to decrease the incidence of broncho pulmonary dysplasia, and may be associated with undesirable side effects such as increased incidence of grade III or IV intracranial haemorrhage.

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CHAPTER THREE:

MATERIALS AND METHODS

  Introduction

In this case, we have to critically examine our methods and procedures as a precondition to achieving the desired objectives. Hence, this study will critically fit and compare the prediction of dichotomous outcome models in the classification of Infants’ Broncho-Pulmonary Dysplasia as regards to the proper applications of biomedical modeling. The methodology must be carefully outlined; as the research would be conducted in the following format.

 Research Design

In order to achieve the research objectives, this work employed cross – sectional classification as a research design. In the classification design, the researcher is not interested in a mere collection of haphazard facts but models would be used to classify the BPD status of an infant whose BPD is not known earlier.

Consider the three selected predictor variables which are capable of characterizing a BPD infant. From experience and records of medical practice, these variables are also believed to vary significantly between normal infants (π₁) and BPD infants (π₂). These variables are;

X1 = Weight at birth (g)

X 2 = Weight after four week of birth (g)

X3 = Gender

The dichotomous variables are used to represent normal infants (π₁) and BPD infants (π₂) as the case may be. As used in the model, the dichotomous variable for normal infants (π₁) is 0 and that of BPD infants (π₂) is 1.

Population

Population is a collection of a known N number of identifiable units. In this case, N is called the population size. The population of this study is somewhat infinite as infants are given birth on daily basis. Any baby at birth is a potential BPD infant; hence, the population size cannot be specified at any point in time.

CHAPTER FOUR:

ANALYSIS, RESULTS AND DISCUSSION

 Introduction

This chapter contains the analyses and results obtained using the prescribed methods in the previous chapter. We have used the sample of infants drawn from an underlying population of children with low birth weight (g) from Ahmadu Bello University Teaching Hospital Shika Zaria, Nigeria. 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 infants are denoted by (1) while normal infants by (0). The explanatory variables used for the fitted models are; weight at birth ( X1 ), weight after four

weeks of life ( X 2 ) and gender ( X 3 ). The Logistic regression (logit) and Probability regression (probit) models were fitted, the models fit and performances were carried out on both logit and probit models to check their accuracy and see the one that performs better.

CHAPTER FIVE:

SUMMARY, CONCLUSION AND RECOMMENDATION

  Summary

Our goal in this work as initially stated in our objectivesto fit symmetric dichotomous models; logit and probit models that capable of predicting infants’ BPD status using gender and weights at two different times and compare the results. The study used the data of BPD status obtained from ABU teaching hospital Shika, Zaria in Nigeria to see the performance of the two stated models. The performance of the logit and probit models were checked with AIC and the accuracy of predicting the actual patient into the normal infants or BPD infants was carried out using category evaluation metrics: accuracy, sensitivity and specificity. Stata package was used for the analysis and it was discovered that probit model is more accurate in fitting BPD data as a result of its least AIC as compare to logit model. Furthermore, the model performance which measures the performance of the classification models using the stated evaluation metrics, probit and logit models were found to have 82% accurately categorize the BPD infants and normal infants to their respective categories. It was also observed that the p-values are less than 0.05 which indicated that the explanatory variables used were significantly associated with the occurrence of BPD in infants.

 Conclusion

The results of our analysis indicated that both the logit and probit model fit BPD data and the explanatory variables were found to be significantly associated with the occurrence of BPD in infants. The probit model was found to fit the BPD data more than the logit model. As far as accuracy of the logit and probit link is concerned to categorize the normal infant and BPD infants to their respective classes, probit and logit models were found to have 82% accuracy to classify infants intotheir respective categories. We have been able to make an improvement in the field of medical diagnosis using statistical methods to detect the occurrence of the disease using the stated explanatory variables without passing through the rigour and expenses of the clinical diagnosis.

Recommendation

From the analysis and evaluation of results in the previous discussions in this study so far, the following recommendations are proffered.

1. In the light of the above it is 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
2. It is also recommended that the model should be adopted to reduce the cost of clinical diagnosis.

Contribution to Knowledge

We have been able to make an improvement in the field of medical diagnosis using statistical methods to detect the occurrence of the disease without going through the expense of medical diagnosis through;

1. Logistic Regression (Logit) modeland
2. Probability Regression (Logit) model fitted by this research

References

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• Danan C. (2002), Gelatinase activities in the airways of premature infants and development of Bronchopulmonary dysplasia. American Journal of Physiol. Lung Cell Mol  Physiol., 283: L1086- L1093,

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