56 Matched Case-Control
56.1 Objective
To determine if being HIV positive (exposure) is associated with malnutrition (outcome) in children on admission at a specialized nutritional rehabilitation center. A researcher intends to conduct a matched case-control study he selects children with malnutrition and matches them to controls of children without malnutrition at a ratio of 1:2.
56.2 Hypothesis
\(H_0\): There is no association between being malnourished and being HIV positive
56.3 Formula
We use the formula below by Wang and Ji (2020).
\[ n = (\frac{Z_{\alpha/2} + Z_\beta}{P_1 - P_2})^2 \times (1 + \frac{1}{k}) \]
Where:
- \(n\) is the number of matched pairs needed
- \(Z_{\alpha/2}\) is the critical value of the standard normal distribution at the desired significance level such that a 95% confidence level will correspond to 1.96
- \(Z_{\beta}\) is the critical value of the standard normal distribution at the desired power such that an 80% power will correspond to a value of 0.84.
- \(P_1\) is the proportion of exposure in cases. This can be obtained from similar prior studies
- \(P_0\) is the proportion of exposure in controls, This can be obtained from similar prior studies
- \(k\) is the number of controls per case such that for a 1:1 match \(k\) =1
56.4 Determination
Assuming in the literature the proportion of HIV positive in non-malnourished children ( \(P_0\)) was 0.25 and that for malnourished children (\(P_1\)) was 0.3. Also, the investigator decides the use a 95% confidence interval and a power of 80%. The sample size is determined as below
\[ n = (\frac{1.96 + 0.84}{0.3 - 0.25})^2 \times (1 + \frac{1}{2}) \]
Thus a minimum total of 4710 study subjects will be included. This will consist of 3140 controls and 1570 cases.