Rigorously studying the effectiveness of individual interventions poses considerable methodological challenges. Simulation studies can explore scenarios, but they make strong assumptions that may be difficult to validate. Data-driven, cross-country modeling comparing the timing of national interventions to the subsequent numbers of cases or deaths is a promising alternative approach. We have collected chronological data on the implementation of several interventions in 41 countries between January and the end of May 2020, using independent double entry by researchers to ensure high data quality. Because countries deployed different combinations of interventions in different orders and with different outcomes, it is possible to disentangle the effect of individual interventions. We estimate the effectiveness of specific interventions with a Bayesian hierarchical model by linking intervention implementation dates to national case and death counts. We partially pool NPI effectiveness to allow for country-specific NPI effects. Our model also accounts for uncertainty in key epidemiological parameters, such as the average delay from infection to death. However, intervention effectiveness estimates should only be used for policy-making if they are robust across a range of modeling choices. We therefore support the results with extensive empirical validation, including 11 sensitivity analyses under 206 experimental conditions. In these analyses, we show how results change when we vary the data, the epidemiological parameters, or the model structure or when we account for confounders.