Frailty models are widely used to model clustered survival data. Classical ways to fit frailty models are likelihood-based. We propose an alternative approach in which the original problem of "fitting a frailty model" is reformulated into the problem of "fitting a linear mixed model" using model transformation. We show that the transformation idea also works for multivariate proportional odds models and for multivariate additive risks models. It therefore bridges segregated methodologies as it provides a general way to fit conditional models for multivariate survival data by using mixed models methodology. To study the specific features of the proposed method we focus on frailty models. Based on a simulation study, we show that the proposed method provides a good and simple alternative for fitting frailty models for data sets with a sufficiently large number of clusters and moderate to large sample sizes within covariate-level subgroups in the clusters. The proposed method is applied to data from 27 randomized trials in advanced colorectal cancer, which are available through the Meta-Analysis Group in Cancer.