"None are so vile, none have fallen so low, as to be beyond the working of this power. In all who will submit themselves to the Holy Spirit a new principle of life is to be implanted; the lost image of God is to be restored in humanity. COL 96.1"
"Not by works of righteousness which we have done, but according to his mercy he saved us, by the washing of regeneration, and renewing of the Holy Ghost;"
Both passages discuss the renewing work of the Holy Spirit. Titus 3:5 speaks of regeneration and renewal by the Holy Ghost, while the EGW quote speaks of a new principle of life implanted by the Holy Spirit and the restoration of God's image. The connection is more than thematic; it's a direct principle of spiritual renewal.
"For all have sinned, and come short of the glory of God;"
While Romans 3:23 speaks of the universal sinfulness of humanity, the EGW quote builds upon this by stating that no one is beyond redemption. The connection is thematic, focusing on the scope of God's grace in light of human sinfulness.
"But man cannot transform himself by the exercise of his will. He possesses no power by which this change can be effected. The leaven—something wholly from without—must be put into the meal before the desired change can be wrought in it. So the grace of God must be received by the sinner before he can be fitted for the kingdom of glory. All the culture and education which the world can give will fail of making a degraded child of sin a child of heaven. The renewing energy must come from God. The change can be made only by the Holy Spirit. All who would be saved, high or low, rich or poor, must submit to the working of this power. COL 96.2"
"Jesus answered and said unto him, Verily, verily, I say unto thee, Except a man be born again, he cannot see the kingdom of God."
Both passages emphasize the necessity of divine intervention for spiritual transformation. John 3:3 highlights the need to be 'born again,' while the EGW quote stresses that humans cannot transform themselves and need God's grace and the Holy Spirit. The 'born again' concept is directly related to the 'renewing energy' from God.