The analysis of panel data with non-monotone nonresponse often relies on the critical and untestable assumption of ignorable missingness. It is important to assess the consequences of departures from the ignorability assumption. Non-monotone nonresponse, however, can often make such sensitivity analysis infeasible because the likelihood functions for alternative models involve high-dimensional and difficult-to-evaluate integrals with respect to missing outcomes. We develop an extension of the local sensitivity method that overcomes computational difficulty and completely avoids fitting alternative models and evaluating these high-dimensional integrals. The proposed method is applicable to a wide range of panel outcomes. We apply the method to a Smoking Trend dataset where we relax the standard ignorability assumption and evaluate how smoking-trend estimates in different groups of US young adults are affected by alternative assumptions about the missing-data mechanism. The main finding is that the standard estimate in the black male group is sensitive to nonignorable missingness but those in other groups are reasonably robust. Copyright © 2010 John Wiley & Sons, Ltd.