Question

A 52-year-old man presents to the clinic reporting progressively worsening swelling in his lower extremities and profound daytime fatigue over the past four months. His wife, who accompanies him, notes that he frequently falls asleep during conversations and snores loudly at night. His medical history includes obesity, essential hypertension, and diet-controlled type 2 diabetes mellitus. He has no history of tobacco use.

Vital signs show a temperature of $36.8^\circ\text{C}$ ($98.2^\circ\text{F}$), heart rate of $88/\text{min}$, blood pressure of $135/85\text{ mmHg}$, respiratory rate of $14/\text{min}$, and oxygen saturation of $89\%$ on room air. BMI is $42\text{ kg/m}^2$.

Physical examination reveals prominent jugular venous distention with noticeable *a* waves. Cardiac auscultation demonstrates a right ventricular heave, a loud pulmonic component of the second heart sound ($P_2$), and a holosystolic murmur at the left lower sternal border that increases in intensity with inspiration. The lungs are clear to auscultation bilaterally. Bilateral $3+$ pitting edema is present up to the knees.

Laboratory studies show:
Hemoglobin: $16.8\text{ g/dL}$
Thyroid-stimulating hormone (TSH): $2.5\text{ \mu U/mL}$ (Normal: $0.4-4.0\text{ \mu U/mL}$)
Free T4: $1.2\text{ ng/dL}$ (Normal: $0.9-1.7\text{ ng/dL}$)

An arterial blood gas analysis obtained on room air reveals:
pH: $7.37$
$\text{PaCO}_2$: $56\text{ mmHg}$
$\text{PaO}_2$: $60\text{ mmHg}$
$\text{HCO}_3^-$: $31\text{ mEq/L}$

Which of the following is the most appropriate next step in the diagnostic evaluation or management of this patient?