A day after a government panel said that healthy men should no longer get screened for prostate cancer, some doctors' groups and cancer patients' advocates began a campaign to convince the nation that the advice was misguided. Their hope is to copy the success of women's groups that successfully persuaded much of the country two years ago that it was a mistake for the same panel, the United States Preventive Services Task Force, to recommend against routine mammograms for women in their 40s. This time, the task force found that a P.S.A. blood test to screen for prostate cancer does not save lives, but results in needless medical procedures that have left tens of thousands of men impotent, incontinent or both. Both sides in the battle have marshaled distinct arguments, and both said their only goal was to protect patients. Caught in the middle are 44 million men in the United States over the age of 50 who must now decide whom to believe.