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Case-crossover designs have been widely applied to epidemiological and medical investigations of associations between short-term exposures and risk of acute adverse health events. Much effort has been made in literature on understanding source of confounding and reducing systematic bias by reference-select strategies. In this paper, we explored the nature of bias in the ambi-directional and time-stratified case-crossover designs via simulation using actual air pollution data from urban Edmonton, Alberta, Canada. We further proposed a calibration approach for eliminating systematic bias in estimates (coefficient estimate, 95% confident interval, and p-value). Bias check for coefficient estimation, size check and power check for significance test were done via simulation experiments to show advantages of the calibrated case-crossover studies over the ones without calibration. An application was done to investigate associations between air pollutants and acute myocardial infarction hospitalizations in urban Edmonton. In conclusion, systematic bias in a case-crossover design is often unavoidable, leading to an obvious bias in the estimated effect and an unreliable p value in the significance test. The proposed calibration technique provides an efficient approach to eliminating systematic bias in a case-crossover study. [ABSTRACT FROM AUTHOR]