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The widely used joint model for this purpose is the shared random effect model. Presumably, adding more longitudinal predictors improves the predictive accuracy. However, the shared random effect model can be computationally difficult or prohibitive when a large number of longitudinal variables are used. In this paper, we study an alternative way of modeling the joint distribution of longitudinal and time\u2010to\u2010event data. Under this formulation, the log\u2010likelihood involves no more than one\u2010dimensional integration, regardless of the number of longitudinal variables in the model. Therefore, this model is particularly suitable in dynamic prediction problems with large number of longitudinal predictors. The model fitting can be implemented with tractable and stable computation by using a combination of pseudo maximum likelihood estimation, Expectation\u2010Maximization algorithm, and convex optimization. We evaluate the proposed methodology and its predictive accuracy with varying number of longitudinal variables using simulations and data from a primary biliary cirrhosis study.<\/jats:p>","DOI":"10.1002\/sim.9037","type":"journal-article","created":{"date-parts":[[2021,5,21]],"date-time":"2021-05-21T05:27:45Z","timestamp":1621574865000},"page":"4395-4409","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Backward joint model and dynamic prediction of survival with multivariate longitudinal data"],"prefix":"10.1002","volume":"40","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3549-5763","authenticated-orcid":false,"given":"Fan","family":"Shen","sequence":"first","affiliation":[{"name":"Department of Biostatistics and Data Science The University of Texas School of Public Health  Dallas Texas USA"},{"name":"Department of Biostatistics The\u00a0University of Texas MD Anderson Cancer Center  Houston Texas 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