A LOGISTIC REGRESSION ANALYSIS OF MALARIA CONTROL DATA Olumoh, Jamiu. S and Ajayi, Osho. O School of Arts and Sciences, American University of Nigeria, Yola Email: jamiu.olumoh@aun.edu.ng, osho.ajayi@aun.edu.ng Abstract This study investigates the effect of various methods of malaria control including mosquito net. A logistic regression fitted to the data suggested the level of risk involves for a respondent who failed to use mosquito net. The results show the odds of contracting malaria is about 3 times higher for a person who did not use mosquito net compared to a person who used it. Also, the odd of contracting malaria in urban area is almost twice that of the rural area. Age plays little or no effect of malaria status. Keywords: Logistic Regression, Odds Ratio, Control, Dichotomy, Categorical Data. 1. Introduction Malaria is widely acknowledged as one of the world s deadliest disease especially in the developing world (WHO, 2010). On the African continent alone, it is reported to be the cause of probably as many as half the deaths of infants and children under age five. There are an estimated 100 million malaria cases with many hundreds of thousands of deaths reported per year in Nigeria and these figures by far dwarfs similar figures reported for diseases/deaths attributable to HIV/AIDS (WHO 2010) in the last several years. Malaria control is regarded as a key factor in achieving a number of the poverty-reduction MDGs by the 2015 deadline. The effectiveness of the different control methods which have been directly or indirectly advocated is critical to the achievement of a serious reduction in the level of malaria as the MDG deadline approaches. Prevention which have been advocated includes among others, insecticide treated nets (ITNS),indoor residual spraying and for pregnant women, intermittent preventive treatment using at least two doses of an effective antimalarial drug during the second and third trimesters. Health groups have spent tens of billionsof dollars deploying these and other control methods without any serious quantitative evaluation of the assumed rate of success. In this work, we use the tool of logistic regression to evaluate the level of protective coverage from malaria which may be achieved from a number of control methods. We use the data oftyndall et al 2012. 101
European International Journal of Science and Technology ISSN: 2304-9693 www.eijst.org.uk 2. Description of the Data Data from 1126 randomly selected patients including patients who visited Federal Medical Centre (where treatment is relatively free) for test/diagnosis of malaria and from outreach projects which covered some rural and urban areas of Adamawa State, Northern Eastern part of Nigeria. All 1126 patient blood samples were collected and clinically diagnosed of malaria symptoms form November to June of 2010 by Tyndall et al (5). Variables considered are; Infection status, Control methods, location of home (rural or urban), age amongst others. We employed SAS Proc Logistic to analyze logistic regression via odds ratio with the aim of modeling the influence of covariate outcomes Y=1 if patient develops malaria and Y= 0 if he/she does not develop malaria. The Table 2.1 below depicts the distribution of malaria status vise a-vis the method of control, Infection Vector control status Coil Combination Net Nil Loc.HerbSpray Total ------+----------------------------------------------------------------------------+---- 0 45 9 38 136 73 334 635 1 480 20 174 67 182 491 -----+----------------------------------------------------------------------------+----- Total 93 9 58 310 140 516 1,126 The table above shows six methods of controlling malaria: Coil, Combination (more than one method), Net, Nil (No control), Loc.Herb(locally made substance), Spraying. Almost halfof the people (45.83%) sampled used Spraying method while nonuser constitutes 27.53%. The use of mosquito net is not popular among the respondent as 5.15% claimed they used it. However, the people who used mosquito net have the list cases (34.48%) of malaria. This is closely followed by those who used Spraying with 35.27%. More than half (51.61%) of people used mosquito Coil and 56.13% of people used none of preventive methods of malaria. This descriptive statistic shows that netting for control of malaria is not popular but more effective than any of the other methods. 3. The Model Let the random variable X represents the event that a randomly selected member of a population of interest using malaria control treatment j. Then,X is Bernoulli random variable with probability density: = = where is the probability of succumbing to malaria and = 1. Due to long standing traditional believes and practices, the average Nigerian, recognizes a number of different control method with a tacit believe that efficacy is across control methods. In Figure 1, we present the likelihood curves of for distinct five control methods used in our analysis. 1 102
0.0 0.2 0.4 0.6 0.8 1.0 Nill Spray Net(Control) Coil Loc Herb 0.2 0.4 0.6 0.8 1.0 p-hat Figure 1: curves for the Bernoulli Probability of malaria infection for the five different treatment methods whose names are indicated. To contrast the effectiveness of the control methods across group, we used the logistic regression.consider the two treatments outlined in the 2 2tablebelow, Table 3.1 Treat-j Treat-0 Total Sick x (m-x) m Not sick y (n-y) n Total ( x + y) [ (m-x)+(n-y)] n+m Assuming the n by pmatrix X is the explanatory variable which influences the probability of infection = 1 or lack of it = 0, then we have: P(Y = 1)= [ ] (2) where the coefficients are of interest and most importantly, the coefficient is the generalized linear model representation of the popular log odds ratio, defined as: = log! (3) 103
European International Journal of Science and Technology ISSN: 2304-9693 www.eijst.org.uk with the odds ratio!itself given by:! = # $ $ % 4 for contrasting between two treatments of interest in which the effectiveness of a particular treatment is contrasted with the control-treatment. It is not too difficult to note that one canre-write the above log equation as: $ ' =log+ # $, 5 hence log odds ratio: =log. / 0 log. 1 21 0 In this work, we consider five distinct treatments:coil, Net, Nil, Loc.herb, and Spray.For the purpose of the logistic model, we usednet as the control-treatment. The result obtained from a fit of the model is in table 3.2. The standard errors which can be used for generating the confidence interval values for the estimated parameters are also tabulated. Analysis of Maximum Estimates Parameter DF Estimate Standard Error Wald Chi-Square Pr>ChiSq Intercept 1-1.0338 0.3292 9.8588 0.0017 Vector control Coil 1 0.9129 0.3521 6.7212 0.0095 Vector control Combination 1-13.5564 407.1 0.0011 0.9734 Vector control Nil 1 1.0190 0.3032 11.2960 0.0008 Vector control Otapiapi (loc Herb) 1 0.7586 0.3303 5.2761 0.0216 Vector control Spraying 1 0.0940 0.2933 0.1027 0.7486 Location Urban 1 0.4943 0.1339 13.6272 0.0002 Age 1 0.00572 0.0570 0.0101 0.9201 Table 3.2. Parameter estimates from a logistic fitting of the data. We evaluated the likelihood function for the parameters to determine the accuracy of the standard errors. Figure 2 shows the contour for Nets and Coil while Figure 3 shows the profile likelihood curve of from where the assumption of normality for the distribution of MLE estimate 3for generating the standard errors may be considered acceptable. Figures 4, shows the contours and profile likelihoods of several other treatments. 104
contour κ -1.2-1.0-0.8-0.6-0.4-0.2 0.0 0.3 0.5 0.1 0.7 0.9 0.5 1.0 1.5 Figure 2. Contour for the log oddsratio of Coil as a malaria control against Net malaria control as a controltreatment. Profile likelihood 0.0 0.2 0.4 0.6 0.8 1.0 0.5 1.0 1.5 Figure 3. The Profile likelihood of the MLE of the log odds ratio 3 of Coil as a malaria control agent against Net as malaria control agent as a control-treatment. 105
European International Journal of Science and Technology ISSN: 2304-9693 www.eijst.org.uk contour -Spray Profile likelihood -Spray κ -0.9-0.7-0.5-0.3 0.1 0.5 0.9 0.7 0.3 0.0 0.4 0.8-0.5 0.0 0.5-0.5 0.0 0.5 contour -Herb Profile likelihood -Herb κ -0.4-0.2 0.0 0.2 0.1 0.5 0.9 0.7 0.3 0.2 0.6 1.0-1.0-0.5 0.0-1.0-0.5 0.0 Figure 4. On the left side are the likelihood contours for Spray and Local herb (Herb) while on the righthand side are the profile likelihood curves for the two different values of 3 obtained when each of the identified treatments are contrasted against the Net treatment-control. Interpretation of Results The Logistics regression model fitted shows significance of vector controls and location but, age of respondents is not significant. There is statistical evidence in the data obtained that the non-use of mosquito nets significantly increases the risk of contracting malaria and the odd of contracting malaria is about 2.788 times higher for a respondent who did not use mosquito net than for a respondent who did use mosquito net. The covariate locality also has effect on the status of malaria as it can be seen on the table below. And from fig 5, the risk of having malaria in urban area is almost twice that of the rural area. The age has little or no effect on the risk of contracting malaria, since the Wald statistic is not significant. 106
Fig 5 Conclusion The use of mosquito net is not popular among the people sampled but very effective compared with the other methods of malaria control. The risk of contracting malaria is higher for people who did not use mosquito net than people who used mosquito net. Similarly, the risk of contracting malaria is higher for people in the urban area than the rural area. References 1. Agresti, A(1996): An Introduction to Categorical Data Analysis. John Wiley and Sons. 2. Chan Y. H, Biostatics 202: Logistic Regression Analysis. Med J 2004; Vol 45(4): 149-153. 3. Kleinbaum, D.G,Kupper, L.L, Muller, K.E, and Nizam, A (1998): Applied Regression Analysis and Multivariate Methods. Third Ed. Duxbury press. 4. Lawal, H.B(2003): Categorical Data Analysis with SAS and SPSS applications. Lawrence Erlbaum Associates, New Jersey, London. 5. Tyndall, J. A, Olumoh, J.S, Oborkhale, L, Apari, E, Nyitiba I, and Bwala, JA(2012): The dilemma of Flaciparum Malaria and Telecommunications in Northeastern Nigeria. Am. J. Sci. Ind. Res, 2012, 3(3): 157-165. 6. United Nation Report (2010): http://www.africasia.com/news/newsite.php? 7. World Health Organization (2010): Word Malaria Report. http://www.who.int/malaria/world_malaria_report_2010/en/index.html. 107