A Statistical Study on Risk Factors for Low Birth Weight Using Logistic Regression & Roc Curve

Birth weight is a potent predictor and indicator of infant growth and existence. One of the commonest causes of neonatal mortality in the world is prematurity and low birth weight. Low Birth Weight defined by WHO as a birth weight less than 2500 g, since below this value birth-weight-specific infant mortality begins to rise rapidly. Epidemiological research often seeks to identify a causal relationship between the risk factors and the disease. Mechanisms of mother lifestyle characteristics on her neonate weight are intricately

Secondary data is used to study the behavioural characteristics of mother. Data was collected as part of a large study at Baystate Medical Centre in Springfield, Massachusetts during 1986. Data was collected on 189 women, 59 of which had low birth weight babies and 130 of which had normal birth weight babies. This is a complete data set from Applied Logistic regression written by Hosmer and Lemeshow. The goal of the current study was to

Source: Hosmer and Lemeshow (2000) Applied Logistic Regression; Second Edition. These data are copyrighted by John Wiley & sons Inc. and must be acknowledged and used accordingly. Data were collected at Baystate Medical Centre, Springfield, Massachuselts, during 1986. Study variables: The outcome variable y was defined as a binary response variable conforming to the risk of an infant born with low birth weight (LBW). That is, There are two sets of independent variables, qualitative and quantitative. Six independent variables (coded low birth weight, mother race, her smoking status during pregnancy, history of premature labour, history of hypertension, presence of Uterine cancer) are qualitative, two are continuous (mother age and her weight at the last menstrual period) and one is discrete (number of physician visits during the first trimester) variables. The present study has neglected the coded low birth weight as an independent variable, as the original neonate birth weight is treated as the response variable.

Logistic Regression model is used to identify the significant factors which contributes for LBW by assessing the odds ratios (OR) and their 95% confidence interval (CI). The goal of model is to describe the relationship between the dichotomous characteristic of interest (dependent variable = response or outcome variable) and a set of independent (predictor or explanatory) variables. Logistic regression generates the coefficients (and its standard errors and significance levels) of a formula to predict a logit transformation of the probability of presence of the characteristic of interest: where p is the probability of presence of the characteristic of interest. The logit transformation is defined as the logged odds: that maximize the likelihood of observing the sample values. The Receiver Operating Characteristics (ROC) plot is a popular measure for evaluating classifier performance. The ROC plot is a model-wide evaluation measure that is based on two basic evaluation measures (1-specificity) and sensitivity. Specificity is a performance measure of the whole negative part of a dataset, whereas sensitivity is a performance measure of the whole positive part. The ROC plot uses (1-specificity) on the x-axis and sensitivity on the y-axis. False positive rate (FPR) is identical with 1-specificity, and true positive rate (TPR) is identical with sensitivity. A ROC point is a point with a pair of x and y values in the ROC space where x is 1-specificity and y are sensitivity. A ROC curve is created by connecting all ROC points of a classifier in the ROC space. Two adjacent ROC points can be connected by a straight line, and the curve starts at (0.0, 0.0) and ends at (1.0, 1.0). When we are dealing with logistic regression, there are two classes coded as 1 and 0. Then we can compute probabilities that given some explanatory variables an individual belongs to the class coded as 1. If we choose a probability threshold and classify all individuals with a probability greater than this threshold as class 1 and below as 0, In most of the cases we will make some errors because usually two groups cannot be discriminated perfectly. For this threshold we can now compute our errors and the so-called sensitivity and specificity. If we do this for many thresholds, we can construct a ROC curve by plotting sensitivity against 1-Specificity for many possible thresholds. The area under the curve comes in play if we want to compare different methods that try to discriminate between two classes. After fitting a model to the observed data, one of the next essential steps is to investigate how well the proposed model fits the observed data. One method which is used to determine the suitability of the fitted logistic model is a goodness of fit test statistic. A model is said to be fit poorly if either the model's residual variation is large, systematic, or does not follow the variability postulated by the model. In the case where important predictor variables or interaction terms are omitted from the postulated model, the resulting logistic model fit would be poor due to an incorrect linear component. If the predicted values produced by the logistic model accurately reflect the observed values, then the logistic model may be a good fit for the given data.

There were 189 births to women seen in the obstetrics clinic. 39% of the baby had low birth weight. Low birth weight babies mothers mean age is 22.3(4.51). Table 1 shows that univariate analysis for socio demographic variables and clinical variables results. Out of them 50.8% were smoker and 49.2% were non-smoker had low birth weight, which is statistically significant premature Labor one or more and 69.5% of who did not had history of premature Labor, which is statistically significant (<0.001). Which are the variables being significant in the univariate analysis at 0.1 levels were included in the multivariate analysis. In Table 2: Logistic regression Multivariate Analysis The variables that were significant at the univariate analyses were considered as potential variables for multivariable logistic regression analyses. In the multivariate analysis, as compared to non-smoker, smoker mother had 2.45(95%CI: 1.12 -5.34) times higher risk for getting low birth after adjusting for other variables (p=0.024). Similarly, mother who had presence of hypertension 3.91(95%CI: 1.12-13.66) times higher risk for getting low birth weight babies as compared to patients with absence of hypertension (p=0.032). Who had Race, white and black had less risk as compared to others after adjusting for other variables, which was statistically significant(p<0.051). mother who had presence of Uterine Cancer 2.15(95%CI: 0.87-5.33) times higher risk for getting low birth weight babies as compared to patients with absence of Uterine Cancer (p=0.097). Similarly, mother who had History of premature Labor 3.73 (95%CI: 1.52-9.14) times higher risk for getting low birth weight babies as compared to patients with absence of history of premature Labour, which is statistically significant (p=0.004). ROC Curve: The ROC curves were plotted based on the model Predicted values with low birth weight (Low/Normal). ROC for Model based Sensitivity was (74.5, 95%CI: 61.6 – 85.0, Specificity (52.3, 95%CI: 43.4 – 61.1). AUC was 0.73 (95%CI: 0.66, 0.81)

that is linked to multiple factors. To reduce the infant mortality due to low birth weight this study suggests that a mother should be non-smoker, free of hypertension, free of Uterine cancer and without any premature labor. Therefore, counselling and vital assortment should be carried out for the pregnant women during pregnancy to prevent and reduce preterm deliveries and births of low birth weight infants. The fitted logistic regression model could be implied to categorize the high-risk group of pregnant mothers in the future aspects and some strategies and effective efforts can be emphasized to control the percentage of delivery in low birth weight infants.

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Department of Statistics, Madras Christian College, Chennai, India