Question

A $66$-year-old man is brought to the emergency department by his daughter due to a $3$-day history of progressively worsening shortness of breath and a persistent cough. He notes his baseline morning cough has increased in frequency, and his sputum has changed from clear to thick and yellowish-green. His medical history is significant for severe chronic obstructive pulmonary disease (COPD), hypertension, and hypothyroidism (managed with levothyroxine). He has a $45$-pack-year smoking history. His temperature is $37.8^\circ\text{C}$ ($100.0^\circ\text{F}$), pulse is $114/\text{min}$, blood pressure is $145/88\text{ mm Hg}$, respiratory rate is $28/\text{min}$, and oxygen saturation is $86\%$ on room air.

Physical examination reveals a barrel-shaped chest with accessory muscle use. Pulmonary auscultation demonstrates a prolonged expiratory phase, diffuse expiratory wheezes, and scattered rhonchi, but no crackles are heard. The jugular venous pressure is elevated at $10\text{ cm H}_2\text{O}$. Abdominal examination shows a liver edge that is palpable $3\text{ cm}$ below the right costal margin and is mildly tender. Trace bilateral lower extremity pitting edema is present.

Laboratory studies show:
Leukocyte count: $11,500/\text{mm}^3$
Serum sodium: $139\text{ mEq/L}$
Serum potassium: $4.1\text{ mEq/L}$
Serum bicarbonate: $31\text{ mEq/L}$
Blood urea nitrogen: $18\text{ mg/dL}$
Serum creatinine: $0.9\text{ mg/dL}$
Thyroid-stimulating hormone (TSH): $0.2\text{ \mu U/mL}$ (Normal: $0.4-4.0\text{ \mu U/mL}$)
Free T4: $1.2\text{ ng/dL}$ (Normal: $0.9-1.7\text{ ng/dL}$)

Arterial blood gas analysis on room air shows a pH of $7.31$, $\text{PaCO}_2$ of $62\text{ mm Hg}$, and $\text{PaO}_2$ of $54\text{ mm Hg}$.

Chest radiography reveals hyperinflated lung fields, flattened diaphragms, and an enlarged right descending pulmonary artery. There are no pleural effusions or focal alveolar opacities.

Which of the following is the most appropriate next step in management for this patient?