What coagulation tests should be done at this point?

The patient presents with a high-probability clinical picture for venous thrombosis and pulmonary embolism (PE), given the swollen left calf, positive Homans sign (calf pain on simultaneous extension at the knee and flexion at the ankle), and several signs of PE including pleuritic pain, tachypnea, the friction rub, and a low oxygen saturation without fever or evidence of infection. As for the screening laboratory tests, there is no troponin leak indicative of myocardial ischemia, and the D-dimer is significantly elevated, which is compatible with ongoing thrombosis. At the same time, the D-dimer never establishes a diagnosis of venous thrombosis; its principle value is to rule out thrombosis in low-risk patients. Therefore, the patient must undergo an immediate radiologic workup for VTE including chest radiograph, compression ultrasound of the lower extremities, and ventilation/perfusion 01/Q) scanning. These study results are reported as follows: Chest radiograph shows a small left pleural effusion but no parenchymal abnormalities. Compression ultrasound reveals clot in the left popliteal and femoral veins with extension into the left iliac vein, as well as development of early collateral flow. The V/Q scan demonstrates 2 wedge-shaped areas of mismatch in the left lung and I mismatch in the right-read as high probability for PE. An electrocardiogram is also performed; there are no acute ST-T wave changes and no signs of right heart strain.