Amer Dababneh Amjed Zraiqat

There are different sampling methods and formulas that you can use to calculate the sample size for your study. The appropriate method and formula depend on several factors, including the study design, research question, sampling strategy, and statistical analysis plan.

In your case, since you are comparing the safety and efficacy of two treatments in a specific population (transfusion-dependent thalassemia in children), a randomized controlled trial (RCT) may be an appropriate study design.

For an RCT, the sample size calculation typically involves determining the minimum sample size required to detect a clinically meaningful difference between the treatment groups with a specified level of statistical power and significance level. The sample size calculation can be done using one of several formulas, such as the formula for comparing two independent means or proportions.

One common formula for comparing two independent means is:

n = [2 (z_alpha + z_beta)^2 * s^2] / d^2

where n is the sample size per group, z_alpha and z_beta are the z-values for the desired significance level and power, respectively, s is the estimated standard deviation of the outcome variable, and d is the minimum clinically important difference between the two treatments.

For comparing two proportions, the formula is:

n = [(z_alpha/2 + z_beta)^2 * (p1 * (1 - p1) + p2 * (1 - p2))] / d^2

where n is the sample size per group, z_alpha/2 and z_beta are the z-values for the desired significance level and power, respectively, p1 and p2 are the estimated proportions in the two groups, and d is the minimum clinically important difference between the two proportions.

Both formulas assume that the outcome variable is normally distributed or that the sample size is sufficiently large to apply the central limit theorem.

As for the sampling method, you may consider using a random sampling strategy to select participants from the target population. This can help ensure that the sample is representative of the population and reduces the risk of selection bias. You can use different random sampling techniques, such as simple random sampling, stratified random sampling, or cluster sampling, depending on the nature of the population and the available resources.

The choice of sampling method and formula for sample size calculation depends on several factors, such as the research question, study design, expected effect size, level of statistical power, and desired level of precision.

In general, for a comparative study design like the one you described, a randomized controlled trial (RCT) would be an appropriate study design to compare the safety and efficacy of Thalidomide vs Hydroxyurea in Transfusion dependent Thalassemia in children. The sample size calculation for an RCT can be based on the following formula:

n = (Zα/2 + Zβ)^2 (p1q1 + p2q2) / (p1-p2)^2

where:

• n = sample size required in each group
• Zα/2 = the Z-score corresponding to the desired level of significance (usually 1.96 for a 95% confidence level)
• Zβ = the Z-score corresponding to the desired level of statistical power (usually 0.84 for a power of 80%)
• p1 and p2 = the expected proportions of the outcome in the two groups
• q1 and q2 = 1 - p1 and 1 - p2, respectively

To estimate the expected proportions of the outcome, you will need to conduct a pilot study or review the literature to identify the expected effect size. The effect size is typically expressed as a difference in means, odds ratio, or relative risk.

For a more precise sample size calculation, you may want to consult with a statistician or use a sample size calculator that takes into account the specific details of your study design and expected effect size.