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Noncompliance or non-adherence to randomized treatment is a common challenge when interpreting data from randomized clinical trials. The effect of an intervention if all participants were forced to comply with the assigned treatment (i.e., the causal effect) is often of primary scientific interest. For example, in trials of very low nicotine content (VLNC) cigarettes, policymakers are interested in their effect on smoking behavior if their use were to be compelled by regulation. A variety of statistical methods to estimate the causal effect of an intervention have been proposed, but these methods, including inverse probability of compliance weighted (IPCW) estimators, assume that participants’ compliance statuses are reported without error. This is an untenable assumption when compliance is based on self-report. Biomarkers (e.g., nicotine levels in the urine) may provide more reliable indicators of compliance but cannot perfectly discriminate between compliers and non-compliers. However, by modeling the distribution of the biomarker as a mixture distribution and writing the probability of compliance as a function of the mixture components, we show how the probability of compliance can be directly estimated from the data even when compliance status is unknown. To estimate the causal effect, we develop a new approach which re-weights participants by the product of their probability of compliance given the observed data and the inverse probability of compliance given confounders. We show that our proposed estimator is consistent and asymptotically normal and show that in some situations the proposed approach is more efficient than standard IPCW estimators. We demonstrate via simulation that the proposed estimator achieves smaller bias and greater efficiency than ad hoc approaches to estimating the causal effect when compliance is measured with error. We apply our method to data from a recently completed randomized trial of VLNC cigarettes.