Modifiable health behaviors, a leading cause of illness and death in many countries, are often driven by individual beliefs and sentiments about health and disease. Individual behaviors affecting health outcomes are increasingly modulated by social networks, for example through the associations of like-minded individuals - homophily - or through peer influence effects. Using a statistical approach to measure the individual temporal effects of a large number of variables pertaining to social network statistics, we investigate the spread of a health sentiment towards a new vaccine on Twitter, a large online social network. We find that the effects of neighborhood size and exposure intensity are qualitatively very different depending on the type of sentiment. Generally, we find that larger numbers of opinionated neighbors inhibit the expression of sentiments. We also find that exposure to negative sentiment is contagious - by which we merely mean predictive of future negative sentiment expression - while exposure to positive sentiments is generally not. In fact, exposure to positive sentiments can even predict increased negative sentiment expression. Our results suggest that the effects of peer influence and social contagion on the dynamics of behavioral spread on social networks are strongly content-dependent.