HCA Holdings Inc.'s earnings increased 31% in the fourth quarter thanks in part to an uptick in hospital admissions, the Nashville-based company reported. Earnings were $283 million on revenue of $7.7 billion. For 2010, earnings increased 14.5% to $1.2 billion compared to the same period a year ago. Revenue for the year was $30.7 billion, an increase of 2.1% over 2009. Same-facility admissions increased 1.4% in 2010, despite a nationwide decline in deliveries widely blamed on the weak economy.