Yes the c-peptide can change after you start taking insulin. It’s not a static measure, and it’s results are very often ambiguous— it is easy to read to much into. In my estimation, only a couple ironclad facts can be absolutely gleaned from it—
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if it’s high and your blood sugar is significantly elevated it means you’re insulin resistant
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if it’s low and your blood sugar is elevated you are not producing a normal amount of insulin
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if it’s zero you’re not producing any insulin
The levels vary throughout the day for a healthy metabolism as it regulates it’s own glucose—
It can be helpful at initial presentation to distinguish between resistance and insufficiency— beyond that my doctor always likes to say that its only remaining value is to determine whether it is zero, or not.