Differences in COVID-19 testing and tracing across countries, as well as changes in testing within each country over time, make it difficult to estimate the true (population) infection rate based on the confirmed number of cases obtained through RNA viral testing. We applied a backcasting approach to estimate a distribution for the true (population) cumulative number of infections (infected and recovered) for 15 developed countries. Our sample comprised countries with similar levels of medical care and with populations that have similar age distributions. Monte Carlo methods were used to robustly sample parameter uncertainty. We found a strong and statistically significant negative relationship between the proportion of the population who test positive and the implied true detection rate. Despite an overall improvement in detection rates as the pandemic has progressed, our estimates showed that, as at 31 August 2020, the true number of people to have been infected across our sample of 15 countries was 6.2 (95% CI: 4.3-10.9) times greater than the reported number of cases. In individual countries, the true number of cases exceeded the reported figure by factors that range from 2.6 (95% CI: 1.8-4.5) for South Korea to 17.5 (95% CI: 12.2-30.7) for Italy.