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• Option 2 – Observational Data handling and Analysis.
Answer the following questions showing any working out
where needed. All answers must be clearly labelled and
inserted as task 3 into your workbook for submission.
Task 3 Data analysis
Option 2: Observational analysis
(a)
200 children aged under 5 years were sampled from a village in Malawi using simple
andom sampling. All of the children were tested for malaria using a rapid diagnostic
test. 51 of the children tested positive. Estimate the prevalence of malaria in children
under 5 years old in the village and provide a 95% confidence interval for the estimate.
• Make sure you read the questions thoroughly
• Think about what the question is asking you to calculate first.
• Think about what is required in a CI calculation
• Summarize you findings for clarity
Prevalence
• Measure of frequency of existing cases
= the proportion of people in a defined
population that has the outcome at a specific
point in time.
• Prevalence = Number of existing cases at time (t)
Study population at time (t)
Calculating 95 % CI
In 2 parts:
1. Work out the standard first (SE)
SE – describes the precision of the sample mean
(z value for 95% confidence = 1.96)
Calculating 95 % CI
2. Calculate 95% CI
(b)
40% of children had slept under a bed net the night before the survey. Of these
15% tested positive for malaria.
• (i) Construct a carefully labeled two-way table for the data derived from the
200 children.
• Think about the layout of the table exposure vs outcome
• (ii) Estimate the odds ratio, risk ratio and risk difference for those who did
not sleep under a bed net the night before compared to those that did.
• Use your lecture notes for the equations
• (iii) A statistician performed a χ2 test and obtained a p-value of 0.005.
Interpret this result.
Exposed
Non-exposed
Cases
A
Odds Ratio calculation using a 2 x 2 Table
B
Controls
C D
A + B
C + D
Total
A + C B + D
Odds Ratio Calculation
• Ratio of the odds that the cases were exposed to the odds
that the controls were exposed
Odds Ratio
Odds that a case was exposed
OR
Odds that a control was exposed
Odds Ratio
A / C
OR
B / D
Odds Ratio
A x D
OR
B x C
Risk and odds
• Observe a lecture theatre of 200 students for 1 hou
• Outcome of interest is sneezing at least once
50 students sneeze during the lecture
Risk of sneezing: 50/200 = 0.25 (or 25%)
Odds of sneezing: 50/150 = 0.33
Rate or risk difference (RD)
• the absolute (actual) difference between two rates o
isks
• subtract the rate in unexposed (r0) from the rate in the
exposed group (r1)
Rate (risk) difference = (r1 - r0)
(c)
• It has been suggested that families of higher socio-economic status are
more likely to own bed nets and are also more likely seek malaria
treatment when they are ill. Families have been grouped into three
categories of socio economic status.
• (i) Suggest a statistical technique that would let us examine the association between bed net
use and malaria infection taking into account the differences in socio economic status.
• (ii) Which of the three measures of association mentioned in part (b) will this technique
produce?
• (iii) Is the adjusted estimate likely to be closer to or further away from
the null value than the unadjusted estimate from part (b)(ii)? Give a
ief explanation for your answer.
• Socio economic status considered a confounder here
Final Comments on task 3
• Which ever option you chose read the questions carefully.
• If you are asked to describe, comment, explain, interpret or give an example. Please do
this!
• Do NOT just calculate something and give the result without any explanation
• Careful with rounding off
• If you include tables and graphs discuss these
• do not include results that you are not prepared to comment on
• Label any graphs and tables for easy reference
Answered Same Day May 05, 2023

Solution

Mukesh answered on May 06 2023
6 Votes
To estimate the prevalence of malaria in children under 5 years old in the village, we can use the proportion of children who tested positive in the sample. In this case, 51 out of 200 children tested positive, so the sample proportion is:
p̂ = 51/200 = 0.255
To calculate a 95% confidence interval for the true population proportion, we can use the following formula:
p̂ ± z*√(p̂(1-p̂)/n)
where z is the critical value from the standard normal distribution co
esponding to a 95% confidence level, which is approximately 1.96, and n is the sample size.
lower confidence limit (LCL): p̂ - z*√(p̂(1-p̂)/n)
upper confidence limit (UCL): p̂ + z*√(p̂(1-p̂)/n)
Substituting in the values, we have:
0.255 ± 1.96√(0.255(1-0.255)/200) = (0.195, 0.315)
So the estimated prevalence of malaria in children under 5 years old in the village is 25.5% (or 0.255), with a 95% confidence interval ranging from 19.5% to 31.5%.
It is important to note that this is only an estimate based on a sample, and the true prevalence in the population may differ. Additionally, the confidence interval tells us that we are 95% confident that the true population proportion falls within the given range, but there is still a 5% chance...
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