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Background When patients are admitted to an intensive care unit (ICU) their risk of getting an infection will be highly depend on the length of stay at-risk in the ICU. In addition, risk of infection is likely to vary over calendar time as a result of fluctuations in the prevalence of the pathogen on the ward. Hence risk of infection is expected to depend on two time scales (time in ICU and calendar time) as well as competing events (discharge or death) and their spatial location. The purpose of this paper is to develop and apply appropriate statistical models for the risk of ICU-acquired infection accounting for multiple time scales, competing risks and the spatial clustering of the data. Methods A multi-center data base from a Spanish surveillance network was used to study the occurrence of an infection due to Methicillin-resistant Staphylococcus aureus (MRSA). The analysis included 84,843 patient admissions between January 2006 and December 2011 from 81 ICUs. Stratified Cox models were used to study multiple time scales while accounting for spatial clustering of the data (patients within ICUs) and for death or discharge as competing events for MRSA infection. Results Both time scales, time in ICU and calendar time, are highly associated with the MRSA hazard rate and cumulative risk. When using only one basic time scale, the interpretation and magnitude of several patient-individual risk factors differed. Risk factors concerning the severity of illness were more pronounced when using only calendar time. These differences disappeared when using both time scales simultaneously. Conclusions The time-dependent dynamics of infections is complex and should be studied with models allowing for multiple time scales. For patient individual risk-factors we recommend stratified Cox regression models for competing events with ICU time as the basic time scale and calendar time as a covariate. The inclusion of calendar time and stratification by ICU allow to indirectly account f