A Study of the Prevalence of HIV/AIDS Using Canonical Correlation Analysis (a Case Study of General Hospital Minna)
Chapter One
Aim and Objectives
The aim of this research work is to fit a canonical correlation model that is capable of determining whether literacy level and gender are risk factors for HIV /AIDS in Niger State.
The above aim is achieved through the following objectives;
- To determine the contribution of the risk factors to the prevalence of HIV/AIDS using canonical
- To determine the level of association between the canonical variates using Wilk’s Lambda
- To test for homogeneity of variances among the risk factors using Bartlet’s test.
CHAPTER TWO
REVIEW OF LITERATURES
In canonical correlation analysis (Hotelling, 1936), linear combinations of two sets of variables are obtained in such a way that the correlation between the linear combinations is a maximum. Generalizations to a similar approach for more sets of variables have been the topic of several studies (Horst 1961; Carroll 1968; Kettenring 1971).Consequently, several different approaches have been proposed. Kettenring (1971) provides an overview of four different generalizations. In the framework of homogeneity analysis Van der Burg (1988) and Gifi (1990) introduced nonlinear canonical correlation analysis, also referred by the algorithm name OVERALS, which takes Carroll (1968) generalized canonical correlation analysis as a special case. Using generalized canonical correlation analysis, a graphical representation, sometimes referred to as a perceptual map, can be made on the basis of the individuals’ observation matrices. Note that, the observation matrices do not necessarily contain the same attributes. Steenkamp and Wittink (1994) focused on this flexibility in their analysis of idiosyncratic sets of attributes.
Another type of application, considered by Green and Carroll (1988), concerns the derivation of a composite configuration from a set of configurations. For example, multidimensional scaling solutions (perceptual maps) for the same objects from different countries can be used as input data. Generalized canonical correlation analysis can then be applied to the coordinate matrices to obtain a composite configuration. Finally, generalized canonical correlation analysis can be used when, for the same set of subjects, we have data on sets of variables. For example, in their analysis of socio- economic determinants of HIV pandemic and nations efficiencies, Zanakis et al. (2007) used a set of 50 explanatory variables which could be divided into different sets (e.g. economic indicators, education related variables, etc.). For such multiple set data, generalized canonical correlation analysis can be used to obtain a configuration depicting the cases. Since generalized canonical correlation analysis deals with possibly large sets of data, the possibility of the occurrence of missing values is significant. Some procedures to deal with missing in generalized canonical correlation analysis have been proposed, however, no attempt has been made to compare and evaluate the alternatives .In this dissertation .We shall only concern ourselves with methods specifically aimed at dealing with missing values in generalized canonical correlation analysis. General methods (e.g. multiple imputation, Rubin 1987) that require distributional assumptions, are beyond the scope of this dissertation. The performance of the proposed methods under various conditions will be assessed by means of a simulation study. The results of this simulation study clearly indicate the validity and, in some cases, superiority of the new methods.
The Human immunodeficiency virus infection / acquired immunodeficiency syndrome (HIV/AIDS) is a disease of the human immune system caused by infection with human immunodeficiency virus (HIV). During the initial infection, a person may experience a brief period of influenza-like illness. This is typically followed by a prolonged period without symptoms. As the illness progresses, it interferes more and more with the immune system, making the person much more likely to get infections, including opportunistic infections and tumors that do not usually affect people who have working immune systems. HIV is transmitted primarily via unprotected sexual intercourse(including anal and even oral sex), contaminated blood transfusions, hypodermic needles, and from mother to child during pregnancy, delivery, or breastfeeding. Some bodily fluids, such as saliva and tears, do not transmit HIV. Prevention of HIV infection, primarily through safe sex and needle-exchange programs, is a key strategy to control the spread of the disease. There is no cure or vaccine; however, antiretroviral treatment can slow the course of the disease and may lead to a near-normal life expectancy. While antiretroviral treatment reduces the risk of death and complications from the disease, these medications are expensive and may be associated with side effects.
CHAPTER THREE
SOURCES OF DATA
The data used in this study is classified under the secondary source of data having been obtained from the Heart to Heart Centre, General Hospital Minna, Niger state on the 11th Jun, 2013.
Definition
Canonical correlation analysis can be defined as the problem of finding two sets of basic vectors, one for x and the other for y, such that the correlations between the projections of the variables onto these basis vectors are mutually maximized. Canonical correlation analysis (CCA) can also be defined as a way of measuring the linear relationship between two multidimensional variables. It finds two bases, one for each variable, that are optimal with respect to correlations and, at the same time, it finds the corresponding correlations. In other words, it finds the two bases in which the correlation matrix between the variables is diagonal and the correlations on the diagonal are maximized. The dimensionality of these new bases is equal to or less than the smallest dimensionality of the two variables.
An important property of canonical correlations is that they are invariant with respect to affine transformations of the variables. This is the most important difference between CCA and ordinary correlation analysis which highly depend on the basis in which the variables are described.
CHAPTER FOUR
ANALYSIS AND DISCUSSIONS
Introduction
This chapter deals with the analysis and discussion of the studied data considered in the research work. The analysis of canonical correlation was adopted. An initial step in canonical correlation is an inspection of the correlation matrix of the given data.
Let S denote the data such that:
CHAPTER FIVE
SUMMARY, CONCLUSION AND RECOMMENDATION
Introduction
This chapter shows the summary, conclusion and recommendations reached in the analysis of canonical correlation used on the entire variables / data.
Summary
The aim of the study is to fit a canonical correlation model that is capable of determining whether literacy level and gender are risk factors for HIV/AIDS in Niger State and hence to predict future occurrence.
The canonical correlation analysis generated two correlation coefficients, which are tested. It was found that both of the correlations were statistically different from zero.
The first canonical pair captured the variability of about 50.7%, and the second canonical pair captured the variability of about 49.3%. Hence the total variability captured by two canonical pairs is 100%. The 50.7% variability is due to the individual contribution given by the risk factors (literacy level, gender, age, marital status and weight); showing that there is a slight relationship among listed factors.
Considering the first canonical variate pair U1 and V1 with canonical correlation coefficient r1=0.2972, that the proportion of variance common to the first canonical variate pair is r12 = 0.0883 showing about 8.83% of the proportion of variance captured by the first canonical variate.
Similarly r2=0.1412 is the canonical correlation coefficient between the second canonical variate pair and so r22= 0.0199 which indicates about 1.99% of the proportion of variance captured.
Although; canonical correlation analysis has many table for interpretation, further interpretation of the canonical correlation coefficient will be done as suggested by Dunn and Deokson, (1997), using canonical loadings and canonical cross loadings.
Conclusion
It can be seen that set-A and set-B are slightly correlated as sought for. Canonical correlation analysis measured the strength of relationship of the canonical pair and the factors that strongly contributed. The first pair has a measure of correlation 0.2972 with the proportion of variability of about 50.7% and the second pair has a measure of correlation of 0.1412 with the proportion of variability of about 49.3%.
The model shows that marital status and gender are the risk factors with higher contribution for the prevalence of HIV/ AIDS. Conclusively, by combining the results of the two major risk factors, the prevalence of HIV/AIDS is higher among married men.
Recommendation
I finally recommended that there is a need for the government to enact a Law that will make it mandatory for the two partners to undergo the HIV/AIDS test.
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