If there are no heavy sanctions in place to prevent it, the problem of the cancellation of appointments can lead to huge economic losses and can have a significant impact on underutilized resources of healthcare facilities. A good model to predict the appointment cancellations could be an effective solution to this problem. Therefore, a new Bayesian method is proposed to estimate accurately the probability of the cancellation of visits to healthcare institutions based on specific factors such as age. This model uses the regression for binary variables, linking the explanatory variables to the probability of appearance at a previously made appointment with a new weighted function and estimating the parameters with the Bayesian method. The goodness of the new method is demonstrated by applying it to a real case and by comparing it to other methodologies. Therefore, the advantages of the proposed method are exposed and possible real-world applications are described.