i) Prevalence of Malaria in the village in Malawi among 200 under 5 years children using a rapid diagnostic test per malaria was:
Those who tasted positiveTotal Sample Size100%= 51200 100% = 0.225 x 100%
= 25.5% prevalence level
ii) 95% confidence interval for the prevalence level estimate:
x- Za2. Sn <u < x+Za2. SnEp=0.255=pVarp= p1-pn= 0.2551-0.255200 =9.49875 10-4s=9.49875 10-4 = 0.03082
Za2 at 95% = 1.96
According to Bland (2000) the confidence interval at 95% for a large sample n>30 is:
0.255- 1.96 0.03082200 < u < 0.255+1.96 0.030822000.255- 0.00427 < u < 0.255+0.004270.25073 < u < 0.25927 Malaria prevalence is within [0.25073, 0.25927] interval at 95% accuracy level
b) 40% - slept under a net the night before the survey, 15% of the 40% tested positive for malaria.
Two way chi-square table
Malaria infection Test positive for malaria Test negative for malaria Total
Sleeping under net 12 68 80
Not Sleeping under net 39 81 120
Total 51 149 200
Estimate the odds ratio, risk ratio and risk difference.
Risk ratio: =0.150.325= 0.4615
Odd ratio: 12813968=0.3665Risk difference = 149200=0.745The x2 p-value = 0.005 and a = 0.05. We test the hypotheses:
H0:There is no association between not sleeping under a bed net and testing positive for malaria during the rapid diagnostic test.
H1:There is an association between not sleeping under a bed net and testing positive for malaria during the rapid diagnostic test.
The p-value is less than alpha at the 95% confidence level hence we fail to reject H0.
i) The appropriate test would be a chi-squared test to be used to examine the association between bed net use and malaria infection based on the participants socio-economic status. The chi-square test of association hypotheses would be:
H0: There is no difference based on socio-economic status for getting malaria infection.
H0: There is a difference based on socio-economic status for being infected with malaria.
Chi-square is a non-parametric test of independence for categorical variables in the study population of 200 under 5 years children in terms of expected proportion using a contingency table.X2=Or,c- Er,c2Er,c where: X2=chi-square, ii) The computation would give the odd ratio, Odds ratio is used when one of two possible events or outcomes are measured, and there is a supposed causative factor (Mary, 2009).
The adjusted estimate is likely to be closer to the null value since the socio-economic status of participants influences their ability to afford bed nets that reduce the risk of getting malaria infection. Furthermore, the rich have higher chance of accessing malaria treatment in time compared to their counterparts with lower socio-economic status. According to Kavita et. al., (2014), the study participants who did not use bed nets regularly reported a high occurrence of malaria infection compared to the ones who used bed nets everyday (p < 0.0001).
Kavita Y., Sunil D., Bipul R., Saikia P. K., & Vijay V., (2014). Socio-economic determinants for malaria transmission risk in an endemic primary health centre in Assam, India. PMCID: PMC4078389. 3: 19. Doi: 10.1186/2049-9957-3-19
Mary L. M., (2009). The odds ratio: calculation, usage, and interpretation. Biochemia Medica;19(2):120-6. http://dx.doi.org/10.11613/BM.2009.011Bland M. (2000) An Introduction to Medical Statistics, 3rd edition. Oxford University Press.
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