"man,” he said to Festus, “might have been set at liberty, if he had not appealed unto Caesar.” But the case had been referred to that higher tribunal, and it was now beyond the jurisdiction of either Festus or Agrippa. AA 438.5 Chapter 42—The Voyage and Shipwreck This chapter is based on Acts 27 ; 28:1-10 . At last Paul was on his way to Rome. “When it was determined,” Luke writes, “that we should sail into Italy, they delivered Paul and certain other prisoners unto one named Julius, a centurion of Augustus’ band. And entering into a ship of Adramyttium, we launched, meaning to sail by the coasts of Asia; one Aristarchus, a Macedonian of Thessalonica, being with us.” AA 439"
"For if I be an offender, or have committed any thing worthy of death, I refuse not to die: but if there be none of these things whereof these accuse me, no man may deliver me unto them. I appeal unto Cesar."
The EGW passage directly quotes and refers to Paul's appeal to Caesar, which is the central point of Acts 25:11. The context is also the same.
"In the first century of the Christian Era traveling by sea was attended with peculiar hardship and peril. Mariners directed their course largely by the position of the sun and stars; and when these did not appear, and there were indications of storm, the owners of vessels were fearful of venturing into the open sea. During a portion of the year, safe navigation was almost impossible. AA 439.2"
"Now when much time was spent, and when sailing was now dangerous, because the fast was now already past, Paul admonished them,"
Both passages discuss the dangers of sea travel during a specific time of year, making the connection more than just a general statement about sea travel.
"The apostle Paul was now called upon to endure the trying experiences that would fall to his lot as a prisoner in chains during the long and tedious voyage to Italy. One circumstance greatly lightened the hardship of his lot—he was permitted the companionship of Luke and Aristarchus. In his letter to the Colossians he afterward referred to the latter as his “fellow prisoner” ( Colossians 4:10 ); but it was from choice that Aristarchus shared Paul's bondage, that he might minister to him in his afflictions. AA 439.3"
"Aristarchus my fellowprisoner saluteth you, and Marcus, sister’s son to Barnabas, (touching whom ye received commandments: if he come unto you, receive him;)"
EGW directly quotes Colossians 4:10 and uses it to illustrate Aristarchus's companionship with Paul.
"The Lord give mercy unto the house of Onesiphorus; for he oft refreshed me, and was not ashamed of my chain:"
Both passages refer to someone ministering to Paul in his imprisonment and not being ashamed of his chains. While not a direct quote, the theme is similar.