Time-to-event data in the presence of competing risks has been well studied in recent years. One popular approach to this problem is to model the subdistribution of competing risks with a proportional hazards assumption. The estimator resulting from this model does not perform as expected when the covariates are measured with error, which is often the case in biomarker research. We propose a novel method which combines the intuition of the subdistribution model with risk set regression calibration, which corrects for measurement error in Cox regression by recalibrating at each failure time. We perform simulations to assess under which conditions the subdistribution hazard ratio estimator incurs a significant amount of bias in regression coefficients, and demonstrate that our new estimator reduces this bias. We show that the estimator is asymptotically normally distributed and provide a consistent variance estimator. This method is applied to Alzheimer's Disease Neuroimaging Initiative data, which examine the associations between measurement error-prone cerebrospinal fluid biomarkers and risk of conversion to Alzheimer's disease.