Private sector workers in the Greater Boston area saw their wages and salaries increase 3.9 percent over the last year, the highest increase among the nation’s 15 largest metropolitan area and the largest for that period since the federal government began indexing compensation costs in 2007.

The high rate of wage and salary growth is an indicator of a strengthening economy, but it also is a warning signal that efforts to contain health care and other costs may face difficulty if the economy keeps humming along. For example, the state has set a target of 3.6 percent for the annual growth in overall health care spending. In 2013, health care spending grew at a 2.3 percent rate, but that figure is likely to rise as wages and salaries increase.

The US Bureau of Labor Statistics on Tuesday released its employment cost index, which attempts to measure total compensation growth in the country’s 15 largest metropolitan areas. Total compensation consists of wage and salary growth plus any increase in employee benefits such as health care and paid leave.

Total compensation in the Boston metropolitan area grew at a 3.6 percent pace from March 2014 through March 2015, while wage and salary growth over that period was 3.9 percent. Boston was one of three metropolitan areas where both total compensation and wage and salary growth were greater than national averages. The national average for both total compensation and wage and salary growth was 2.8 percent.

Seattle had total compensation growth of 4.4 percent and wage and salary growth of 2.9 percent over the March 2014 to March 2015 period. Atlanta had 3.9 percent growth in total compensation and 1.8 percent for wages and salaries. By contrast, Detroit reported a slight decline in total compensation over the year-long period and a negligible increase in wages and salaries. Philadelphia and New York City fell slightly below the national averages on both measures.

A BLS spokeswoman said the difference in total compensation for Boston, Seattle, and Atlanta is attributable to sharp differences in the employee benefits portion of the calculation, which may reflect differences in the mix of occupations, employers, and unionized workers in those cities. Unionized workers, for example, tend to receive more employee benefits than nonunion workers.

The Boston metropolitan area stretches from Boston west to Worcester and north up to Manchester, N.H.