The primary objective of this study is to determine whether a dose-adjusted prophylaxis fondaparinux regimen of 2.5 milligrams (mg) subcutaneously administered every (q) 48 hours (hr) in patients with renal failure achieves peak and trough levels similar to patients with normal renal function, and protects patients from developing venous thromboembolism (VTE). Our hypothesis is that a dose-adjusted fondaparinux regimen, which extends the dosing interval from q24 to q48 hr, in patients with estimated creatinine clearance of < 30 ml/min, will be safe and effective.