Final answer:
Increasing the total sample size from 1500 to 3000 in a cluster randomized trial with an ICC of 0 will result in a decrease of the Minimum Detectable Effect Size (MDE), thereby allowing the trial to detect smaller effects. The MDE will decrease (Option 1).
Step-by-step explanation:
When considering a cluster randomized trial where the Intracluster Correlation Coefficient (ICC) is 0, the Minimum Detectable Effect Size (MDE) helps to determine the smallest effect that can be reliably detected by the trial. The MDE represents the smallest difference between the experimental and control groups that the trial is capable of detecting with a high level of confidence. If the total sample size in such a trial is increased from 1500 to 3000 individuals, this would generally result in a decrease in the MDE. This outcome occurs because larger sample sizes reduce variability in the estimates, allowing for more precise measurements of effect sizes. Thus, with the increased sample size, the study becomes more sensitive to finding smaller effects, making it able to detect smaller differences between groups than before. When the ICC is 0, it implies no variability is attributable to the clustering, therefore, the precision of the effect size estimate relies solely on the sample size and variability within clusters. Hence, the change in total sample size will alter the MDE without ICC contributing to the variability. Conclusion, The best description of what will happen to our MDE when increasing the sample size from 1500 to 3000 individuals is that: The MDE will decrease (Option 1).