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When demand exceeds supply, sales are lost, often resulting in the excess demand being censored, particularly when no backordering system is in place. The performance of a data-driven newsvendor model will be distorted when estimated with observed censored demand. The actual effect of censoring on the model varies with patterns and distributions. A comparative simulation study examines the effect of censoring on data-driven approaches to the newsvendor model with price-dependent demand. A modified approach using a Tobit model is introduced and a comparative study with recommended approaches illustrates the effect of commonly censored data on data-driven newsvendor approaches.