Multi-gene panel testing allows efficient detection of pathogenic variants in cancer susceptibility genes including moderate-risk genes such as ATM and PALB2. A growing number of studies examine the risk of breast cancer (BC) conferred by pathogenic variants of these genes. A meta-analysis combining the reported risk estimates can provide an overall estimate of age-specific risk of developing BC, that is, penetrance for a gene. However, estimates reported by case-control studies often suffer from ascertainment bias. Currently, there is no method available to adjust for such bias in this setting. We consider a Bayesian random effect meta-analysis method that can synthesize different types of risk measures and extend it to incorporate studies with ascertainment bias. This is achieved by introducing a bias term in the model and assigning appropriate priors. We validate the method through a simulation study and apply it to estimate BC penetrance for carriers of pathogenic variants in the ATM and PALB2 genes. Our simulations show that the proposed method results in more accurate and precise penetrance estimates compared to when no adjustment is made for ascertainment bias or when such biased studies are discarded from the analysis. The overall estimated BC risk for individuals with pathogenic variants are (1) 5.77% (3.22%-9.67%) by age 50 and 26.13% (20.31%-32.94%) by age 80 for ATM; (2) 12.99% (6.48%-22.23%) by age 50, and 44.69% (34.40%-55.80%) by age 80 for PALB2. The proposed method allows meta-analyses to include studies with ascertainment bias, resulting in inclusion of more studies and thereby more accurate estimates.