We sought to investigate whether epidemiological parameters that define epidemic models could be determined from the epidemic trajectory of infections, recovery, and hospitalizations prior to peak, and also to evaluate the comparability of data between jurisdictions reporting their statistics. We found that, analytically, the pre-peak growth of an epidemic underdetermines the model variates, and that the rate limiting variables are dominated by the exponentially expanding eigenmode of their equations. The variates quickly converge to the ratio of eigenvector components of the positive growth mode, which determines the doubling time. Without a sound epidemiological study framework, measurements of infection rates and other parameters are highly corrupted by uneven testing rates, uneven counting, and under reporting of relevant values. We argue that structured experiments must be performed to estimate these parameters in order to perform genetic association studies, or to construct viable models accurately predicting critical quantities such as hospitalization loads.