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A goodness-of-fit test for left-, right-and interval-censored data, assuming random censorship is proposed and studied. In the first step of the test, the null model is extended to a series of nested alternative models for censored data as in Zhang and Davidian (2008). Then a modified AIC model selection is used to select the best model to describe the data. If a model with one or more extra parameters is selected, then the null hypothesis is rejected. This new goodness-of-fit test procedure is based on the order selection test as described in Aerts, Claeskens and Hart (1999). The applicability of the test is illustrated in the context of microbial agents, and its performance characteristics are demonstrated through simulation studies.

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