Those who accept the Saviour, however sincere their conversion, should never be taught to say or to feel that they are saved. This is misleading. Everyone should be taught to cherish hope and faith; but even when we give ourselves to Christ and know that he accepts us, we are not beyond the reach of temptation. ... Those who accept Christ, and in their first confidence say, I am saved, are in danger of trusting to themselves.
Ellen G. White, Christ’s Object Lessons, p.155, written in 1900.
What does the Bible say about knowing Christians are saved? The following passages are from the New International Version, with my italic emphasis.
I write these things to you who believe in the name of the Son of God so that you may know that you have eternal life. 1 John 5:13
I tell you the truth, whoever hears my word and believes him who sent me has eternal life and will not be condemned; he has crossed over from death to life. John 5:24
I tell you the truth, he who believes has everlasting life. John 6:47
There are many more passages that can be produced to demonstrate that a believer can certainly be assured of their salvation. Once again, E.G. White has been proven to be a false teacher, and those who follow her teachings are in bondage to legalism and false representation of not only the Gospel, but of God and Jesus as well.