It seems that the vaccine can increase risk by more than three times, although it’s not clear if it causes MS in those prone to it, or just speeds its progress.
Suspicions were first raised 10 years ago when 200 people in France developed MS shortly after having the hepatitis B jab. But, an earlier Harvard study, published in 2001, could find no link (Neurology, 2004; 63: 838-42).