Two antidepressants that are commonly given to Alzheimer’s disease patients appear not only to be ineffective but may give side effects such as nausea and drowsiness, a study in Britain has found. In a paper published in the medical journal The Lancet on Tuesday, researchers urged doctors to think twice before prescribing these drugs to Alzheimer’s patients with depression. The two drugs used in the study were sertraline, marketed by Pfizer under the brand name Zoloft, and mirtazapine, known as Remeron in the United States.