Democratic candidates for the Senate in Arizona, Nevada, Pennsylvania and Wisconsin lead their Republican rivals and are running well ahead of President Biden in key states where he continues to struggle, according to polls by The New York Times, The Philadelphia Inquirer and Siena College.

The battleground surveys of registered voters indicate that the president’s difficulties against former President Donald J. Trump may not be enough to sink other Democrats, especially Senate incumbents who are facing less-well-known Republicans.

Ticket-splitters are not abundant — about 10 percent of Trump voters back the Democratic candidate for Senate in the four states, while about 5 percent of Biden supporters back the Republican.

But those voters are enough to give Democrats a chance at holding the Senate, where they currently hold a one-seat majority. To maintain control, the Democrats would have to sweep every competitive Senate seat and win the White House.

[You can find the full results of the polls, including the exact questions that were asked, here. You can see answers to common questions about our polling process here.]