A higher drop-out rate can reduce the power of a study, as it leads to a smaller sample size and potentially less reliable results. To maintain the statistical significance and power of the study, a larger sample size must be enrolled initially to account for the expected number of participants who will not complete the study. Other factors that influence sample size include the incidence of the disease, the significance level, and the size of the expected treatment effect, but the question specifically asks about the impact of an increasing drop-out rate.