My doctor has been ordering home oxygen for positive/presumed positive patients as soon as oxygen saturation levels start to drop to keep them from developing extensive lung damage. Often keeps them from needing hospitalization if started early.
I think one of the reasons we're seeing less deaths per infection rates now than early on is that doctors learned about the very odd feature of Covid-19 which is 'silent hypoxia' that damages lungs
before the onset of shortness of breath. Low oxygen saturation levels indicate hypoxia. The message at the beginning of the pandemic was to wait until experiencing shortness of breath before seeking treatment. That's when we were hearing of people dying in ambulances, crashing and needing emergency ventilator support as soon as they got to the hospital because their lungs were damaged from low oxygen levels before they ever became short of breath--very out of the ordinary.
Tests can show false negatives, especially early on. If you're running a fever or are otherwise symptomatic (the biggest thing I keep hearing is loss of smell), checking O2 sats at home is a good idea.
If levels start dropping, call your provider. Pulse oximeters are inexpensive. It's worth having one to not only to help your provider determine need for treatment if you're infected, but also for peace of mind these days.
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Bolded the above not because I'm an expert, but because this is a long post!

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Good article from late April in lay language:
'Silent hypoxia' may be killing COVID-19 patients. But there's hope.
Professional publication from August:
Why COVID-19 Silent Hypoxemia Is Baffling to Physicians
Hypoxemia--the term in the title is a little more involved than hypoxia in that it also has to do with oxygen pressure, but hypoxia (low oxygen saturation measure by a pulse oximeter) is a good early indicator that things are going wrong. A main take away from the scientific publication below is this sentence:
A disproportionate number of patients with COVID-19 are elderly and have diabetes. Both factors blunt the response of the respiratory control system to hypoxia.
This is such a weird characteristic of Covid-19 that the authors of this scientific article actually use news reports as part of the introductory material. That's so NOT the norm for a medical article but shows the novelty of this part of the Covid disease process.
Excerpt:
The Wall Street Journal considers it a medical mystery as to why “large numbers of Covid-19 patients arrive at hospitals with blood-oxygen levels so low they should be unconscious or on the verge of organ failure. Instead they are awake, talking—not struggling to breathe” (
1).
Science judges the lack of patient discomfort at extraordinarily low blood-oxygen concentrations as defying basic biology (
2). Writing in
The New York Times, Dr. Levitan, with 30 years of emergency medicine experience, notes “A vast majority of Covid pneumonia patients I met had remarkably low oxygen saturations at triage—seemingly incompatible with life—but they were using their cellphones . . . they had relatively minimal apparent distress, despite dangerously low oxygen levels” (
3). Despite this extensive coverage in the news media, the topic has not been addressed in medical journals.