Final answer:
The patient's symptoms suggest obstruction of the superior vena cava from extrinsic compression, which is often seen in cases of lung cancer or lymphoma, particularly with a long history of smoking.
Step-by-step explanation:
The cause of the patient's facial edema is likely D) Obstruction of the superior vena cava from extrinsic compression. Considering the patient's extensive history of smoking, this could indicate a mass compressing the superior vena cava, leading to venous congestion and edema.
Facial edema can arise from various causes, which include angioedema associated with ACE inhibitors, impaired cardiac filling due to conditions such as cardiac tamponade, increased vascular permeability from C1 inhibitor deficiency as seen in hereditary angioedema, and physical obstruction of major veins. In the case presented, symptoms like a persistent cough, weight loss, and a history of smoking are classic pointers towards a potential malignancy causing extrinsic compression of the superior vena cava, rather than the other conditions listed.