The number of confirmed COVID -19 cases, relative to the population size, has varied greatly throughout the United States and, even, within the same city. In different zip codes in New York City, the epicenter of the epidemic, the number of cases per 100,000 residents has varied between 437 and 4227, i.e., in a 1:10 ratio. To guide policy decisions regarding containment and reopening of the economy, schools, and other institutions, it is vital to identify which factors drive this large variation. This paper reports on a statistical study of the incidence variation across New York City, conducted with data at zip code granularity. Among many socio-economical and demographic measures considered, the average household size emerges as the single most important explanatory variable: an increase of the average household size by one member accounts, in our final model specification, for at least 876 cases, a full 23% of the span of incidence numbers, at a 95% confidence level. The percentage of the population above the age of 65, as well as that below the poverty line, are additional indicators with a significant impact on the case incidence rate, along with their interaction term. Contrary to common belief, population density, per se, fails to have a significantly positive impact. Indeed, population densities and case incidence rates are negatively correlated, with a -33% correlation coefficient. Our model specification is anchored on a basic and established epidemiological model that explains the importance of household sizes on R0, the basic reproductive number of an epidemic. Our findings support implemented and proposed policies to quarantine pre-acute and post-acute patients, , as well as nursing home admission policies.