Carlyle Group LP agreed to buy the Ortho Clinical unit of Johnson & Johnson for $4.15 billion, a deal that would shed the health-care products company’s only diagnostics division.

The agreement is expected to close in the middle of the year, Washington-based Carlyle said today in a statement. Revenue has been slipping at the unit for blood and cholesterol tests, and it isn’t one of the market leaders, Chief Executive Officer Alex Gorsky said when New Brunswick, New Jersey-based J&J put the business up for sale last year.

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