Forward-looking serial intervals correctly link epidemic growth to reproduction numbers

The reproduction number [Formula: see text] and the growth rate [Formula: see text] are critical epidemiological quantities. They are linked by generation intervals, the time between infection and onward transmission. Because generation intervals are difficult to observe, epidemiologists often substitute serial intervals, the time between symptom onset in successive links in a transmission chain. Recent studies suggest that such substitution biases estimates of [Formula: see text] based on [Formula: see text]. Here we explore how these intervals vary over the course of an epidemic, and the implications for [Formula: see text] estimation. Forward-looking serial intervals, measuring time forward from symptom onset of an infector, correctly describe the renewal process of symptomatic cases and therefore reliably link [Formula: see text] with [Formula: see text]. In contrast, backward-looking intervals, which measure time backward, and intrinsic intervals, which neglect population-level dynamics, give incorrect [Formula: see text] estimates. Forward-looking intervals are affected both by epidemic dynamics and by censoring, changing in complex ways over the course of an epidemic. We present a heuristic method for addressing biases that arise from neglecting changes in serial intervals. We apply the method to early (21 January to February 8, 2020) serial interval-based estimates of [Formula: see text] for the COVID-19 outbreak in China outside Hubei province; using improperly defined serial intervals in this context biases estimates of initial [Formula: see text] by up to a factor of 2.6. This study demonstrates the importance of early contact tracing efforts and provides a framework for reassessing generation intervals, serial intervals, and [Formula: see text] estimates for COVID-19.