Fluorosis is a well-known endemic disease in many countries across the globe including Mexico, Australia, India, Africa, Thailand, China, and Sri Lanka. According to the various field surveys, it has been found that 15 States in India are endemic for fluorosis (fluoride level >1.5 mg/1 in drinking water from groundwater supply) . The presence of fluoride in the groundwater resources is due to the leaching of the fluoride-rich rocks such as Fluorspar CaF, (Sedimentary rocks, limestones, sandstones), Cryolite Na3AlFPV6 (Igneous rocks, Granite), Fluorapatite Ca,(PO), Ca(FCl),,etc., and when water percolates through these rocks, the fluoride is leached out from them. In India in the state of Rajasthan, all the 32 districts are fluorosis prone and the inhabitants are consuming water with high fluoride concentrations (8 to 10 mg/1) and some even up to 44 mg/1 . World Health Organization (WHO) has set the prescribed upper limit of drinking water fluoride concentration at 1.5 mg/1 , whereas the Bureau of Indian Standards has put down Indian standards as 1.0 mg/1 with further remarks as “lesser the better” .
PATHOPHYSIOLOGY OF FLUOROSIS
Fluorosis is normally found to have three different forms in the human body: clinical, skeletal, and dental . Until the recent times, fluorosis was described as irreversible, but Gupta et al.  reported reversal of fluorosis among children by controlled supplements of calcium, vitamin D and vitamin C. The pathophysiology of fluorosis proposed by Gupta et al.  is given in Figure 11.1, which describes how the biochemical substances within our body fluctuate after fluoride ingestion to maintain chemical homeostasis.
The data were obtained from the study carried out by Susheela and Bhat- nagar  in the hospitals of Delhi. It included 6 male and 4 female patients. Upon diagnosis of the disease, the patients were introduced to two interventions: (1) consumption of de-fluoridated water, (2) consumption of diet rich in calcium and other antioxidants for a treatment time of one year. In the present study, we derived data of drinking fluoride level, fluoride in serum, and fluoride in urine before and during their intervention.
11.3.2 STATISTICAL ANALYSIS
Data reported in the case studies have been used for model development, which was analyzed using statistical tools such as bivariate analysis, multilayer perceptron (MLP), and logistic regression analysis in SPSS.
126.96.36.199 BIVARIATE ANALYSIS
Bivariate analysis examines the relationship between two variables, which may be continuous or categorical in nature. Bivariate analysis was used to verify for a couple of associations suggested by the pathophysiology of fluorosis , first between blood fluoride and serum calcium and second between serum calcium and serum alkaline phosphatase (SAP).
Pearson product-moment coefficient (PPMC (p)) is a measure of the correlation which quantifies the strength and trend of a linear association between two variables. Value of p > 0 indicates a positive relation (or direct proportionality), while p < 0 implies a negative relation (or inverse proportionality) and p = 0 indicates that no linear relationship exists between the two variables. Further, if the numerical value of p is close to 1 or -1 it indicates a strong linear relationship. It may be noted that p is not a measure of causality, i.e., by observing the value of p, which of the two variables influences the other cannot be deduced.
11.3,2.2 MULTILAYER PERCEPTRON (MLP): A NEURAL NETWORK APPROACH
The MLP procedure produces a predictive model for a dependent/target variable, based on the values of the predictor variables. MLP was applied to interpret the change in the values of biochemical parameters; serum calcium, serum fluoride, SAP, SAA, LAA, serum GAG and fluoride in urine with respect to varying drinking fluoride levels, which is the target variable. The MLP procedure was applied using SPSS in the automatic architecture mode. This selection builds a network with one hidden layer and optimizes the number of units in the hidden layer. The frequency weights are ignored by this procedure. Automatic architecture selects hyperbolic tangent and Softmax activation function for all units in the Hidden layer and Output layer respectively. The error function is crossentropy error.
Hyperbolic tangent function takes real-valued arguments and transforms them to the range (-1, 1) and has the following form.
Softmax function takes a vector of real-valued arguments and transforms it to a vector whose elements fall in the range (0,1) and sum to 1 and has the following form.
Batch Training was used because the data set was small and the process directly minimizes the total error. Moreover, it uses information from all records in the training dataset and updates the weights many times until the stopping rule is met.
11.3,2.3 LOGISTIC REGRESSION ANALYSIS
Logistic Regression is a computational algorithm used for classifying data, i.e., to decide class membership у of an unknown data item x based on a data set:
Data item ‘x ’ is known to have class membership ‘y3 Herey. is a binary variable, i.e., a variable which can take only two values, either 0 (generally represents absence of an event) or 1 (represents presence of the event).
Logistic regression model relates the expected value of у for a given value of x by:
where, H(x) is a logit function defined by:
where, a0 and сц are the regression coefficients and odds is the ratio of number of occurrences of у = 1 to its non-occurrences. There are mainly three methods to determine these coefficients namely enter method, forward stepwise method and backward stepwise method. Logistic regression analysis was employed in this work to develop the model to predict occurrence of skeletal fluorosis in children on the basis of age, weight, and fluoride intake.