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The relationship between the treatment effect and the baseline risk is a recognized tool to investigate the heterogeneity of treatment effects in meta-analyses of clinical trials. Since the baseline risk is difficult to measure, a proxy is adopted, which is based on the rate of events for the subject under the control condition. The use of the proxy in terms of aggregated information at the study level implies that the data are affected by measurement errors, a problem that the literature has explored and addressed in recent years. This paper proposes an extension of the classical meta-analysis with baseline risk information, which includes additional study-specific covariates other than the rate of events to explain heterogeneity. Likelihood-based inference is carried out by including measurement error correction techniques necessary to prevent unreliable inference due to the measurement errors affecting the covariates summarized at the study level. Within-study covariances between risk measures and the covariate components are computed using Taylor expansions based on study-level covariate subgroup summary information. When such information is not available and, more generally, in order to reduce computational difficulties, a pseudo-likelihood solution is developed under a working independence assumption between the observed error-prone measures. The performance of the methods is investigated in a series of simulation studies under different specifications for the sample size, the between-study heterogeneity, and the underlying risk distribution. They are applied to a meta-analysis about the association between COVID-19 and schizophrenia.