Recently, deep neural network (DNN) has provided a major breakthrough to enhance prediction in various areas (LeCun et al., 2015; Goodfellow, 2016). The DNN models allow extensions of Cox proportional hazards (PH) models (Kvamme et al., 2019; Sun et al.,2020). Recently, subject-specific prediction of the DNN models has been studied by including random effects in neural network (NN) predictor (Tran et al., 2020; Mandel et al., 2022). However, these DNN random-effect models have been studied for only complete data. In this paper we propose a new DNN-FM. To the best of our knowledge, there is no literature on the DNN-FM for censored survival data. Lee and Nelder (1996) introduced the h-likelihood for the inference of general models with random effects and Ha, Lee and Song (2001) extended it to the semi-parametric frailty models. We reformulate the h-likelihood to obtain maximum likelihood estimators (MLEs) for fixed unknown parameters and best unbiased predictors (BUPs; Searle et al., 1992; Lee et al., 2017) for random frailties by a simple joint maximization of the profiled h-likelihood, which is constructed by profiling out 1