Ideally you want to have a lower rate of trigs to HDL and for that ratio to be lower than 4.... ~~And above 1.6 for a male is ideal so if your HDL was 1.0 and you swapped cauli rice for the real thiing and saw your trigs rise to 4 that would be an issue for example.
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From Ben Bikman's book (Why We Get Sick) on insulin resistance (the root cause of metabolic disorder including type 2 diabetes), a high trig level is an indicator of too much glucose (from carbs) having to be converted into these lipids by the liver. Your HDL then becomes problematic when your natural HDL gets depleted by having to sweep up the excess trigs. This is why a poor ratio is much more strongly linked to cardiac events than having a high LDL cholesterol.
However there are no drugs to treat either a low HDL or a high trig so there is no commerical incentive to focus on this medically.
Yet you can both reduce your trigs (yours are low right now) and increase HDL by eating low carb and high fat as you've been trying to especially as the trigs are susceptible to the amount of carbs you are having. You may find that eating this way increases LDL but don't rush to take a statin if this happens but do keep looking at that ratio.