A 14-year-old girl with no previous psychiatric history is brought by her parents for psychiatric evaluation because of irritability, poor motivation and weight loss. The patient is now failing in school, unable to get along with friends and family, and often refusing to get out of bed. On interview, she admits to sometimes wishing she were dead but denies active suicidal ideation. The psychiatrist diagnoses major depression and recommends starting psychotherapy and an SSRI. The parents express concern about news reports of increased suicidal risk with antidepressants. Which of the following would be the most accurate information on antidepressants and suicidal behavior that the psychiatrist could give the parents?