Prevalence of age-dependent diseases such as asthma is confounded not only by aging effects but also by cohort and period effects. Age-period-cohort (APC) analysis is commonly performed to isolate the effects of these three factors from two-way tables of prevalence by age and birth cohort. However, APC analysis suffers from technical difficulties such as non-identifiability problems. We isolated the effects of these three factors in a step-by-step manner by analyzing Japan's school health data collected from 1984 to 2004 focusing on asthma prevalence among school children aged 6-17 years consisting of 30 birth cohorts (entering classes). We verified the accuracy of our method showing high agreement of the observed age-, period- and cohort-specific data and the data predicted by our method. The aging effects were found to follow cubic equations whose multinomial coefficients were determined by an optimization technique. The obtained aging effect curves of age-specific asthma prevalence showed that boys reach the peak prevalence at 13 and girls at 14, declining markedly afterward. The cohort effects, defined as the arithmetic asthma prevalence means for ages 6-17 years, showed consistent upward trends for the 30 birth cohorts born in 1968-97 for both sexes. The period effects showed a consistent decline since 1984 but abruptly increased in 1999 and then declined again. We were not able to identify the exact cause of the increase in 1999, therefore, this should be examined in the future studies. Because the cohort effects show no sign of leveling off yet, asthma prevalence will likely increase in the foreseeable future.