Systems, methods, and apparatus for determining whether a culture in a vessel contains a plurality of microorganisms are provided. A normalization relative value is calculated for each respective measurement of a biological state of the culture between (i) the respective measurement and (ii) an initial biological state. For each fixed interval of time points, a derivative of the normalization relative values in the interval of time points is calculated, thereby forming a plurality of rate transformation values. For each set of rate transformation values in the plurality of rate transformation values, a measure of central tendency of the values in the set is computed, thereby forming a plurality of average relative transformation values. A determination whether the culture contains the microorganisms is made based on whether any calculated average relative transformation value exceeds a first threshold or whether an extent of growth exhibited by the culture exceeds a second threshold.