<p>The promotion time or non-mixture cure model is a popular tool for analyzing failure time data with a cured fraction and its usefulness in survival analysis has been well recognized. Although a number of inference procedures under this model have been proposed for univariate interval-censored data, corresponding estimation methods under multivariate interval censoring are still undeveloped because of the challenges in maximizing the observed data likelihood function with complex form. In this paper, we investigate the inference procedure for a class of generalized promotion time cure models, namely transformation cure rate frailty models, with multivariate interval-censored data. The class of models is quite flexible and general and includes the proportional hazards and proportional odds cure rate frailty models as special cases. An expectation-maximization algorithm is developed to calculate the nonparametric maximum likelihood estimators, and the asymptotic properties of the obtained estimators are derived with the empirical process techniques. Extensive simulation studies demonstrate the reliable and satisfactory empirical performance of the proposed method. It is then applied to a set of sexually transmitted infection data arising from an epidemiological study for illustration.</p>