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I have a table of patient demographics like height, weight, and some lab values, as well as data on the doses of a drug that the patients received. Using the patient demographic data, I also used a few different dosing methods to re-calculate drug doses in silico.

I want to compare the new in silico doses to the actual doses of drug received, to see if the dosing methods I used are (in general) the same, more aggressive, or more conservative than the actual doses received.

One consideration is that while the dosing methods yield an exact dose (eg 1085 mg of drug), doses are always rounded to increments of 250 mg. So really, the only drug doses that can exist are 500 mg, 750 mg, 1000 mg, ..., all the way up to about 4000 mg. Since there is a discrete number of options, does that make the dosing a non-continuous variable, thus meaning I can't use a t-test?

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    $\begingroup$ There's a slight ambiguity. Are you saying that when a dosage of 1000mg is recorded, it really was 1000mg (so even though it was feasible that it could have been say 1005 and then recorded as 1005, that simply doesn't happen because only doses that are multiples of 250 are ever given), or are you saying that when recorded as 1000, the dose was actually somewhere between 875 mg and 1125mg because they're only recorded to the nearest 250? $\endgroup$
    – Glen_b
    Apr 8 '15 at 23:34
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    $\begingroup$ @Glen_b I mean that even if an exact dose is calculated to be 1005mg, the actual dose GIVEN will be 1000mg. Doses are pre-made in increments of 250mg, and as such we never give anything different than those (to adults anyways). $\endgroup$
    – Tony
    Apr 9 '15 at 2:04
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You should use rounded (administered) dose, since that is what the patient finally receives.

Also t-test can be used since the doses are a numeric value. Converting (500, 750, 1000) to (1, 2, 3) will actually alter the relation between 3 doses, since third dose is twice the first and not 3 times. Numerous medical articles mention the mean (SD) dose received by patients

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I was taught that parametric tests are robust to this kind of data violation IF there are enough options on your ordinal data that you can still have a roughly normal distribution of the dependents, and the data still has a meaningful ordinal scale. The rule of thumb we use is MINIMUM five levels, but more is much preferable. This is done in psychology all the time with likert type data. I don't have access to it right now, but the abstract of this looks promising http://onlinelibrary.wiley.com/doi/10.1002/sim.4780060110/abstract Robustness of the two independent samples t-test when applied to ordinal scaled data, by Timothy Heeren and Ralph D'Agostino, 2006.

I would probably run it parametrically and non-parametrically, and if the results agree i wouldn't worry about it. If they yield different results, I would think a bit about the data and decide which better answered your question. In your case, it sounds like you do have a continuous variable, but a poor way of measuring it. If that is the case I imagine (but don't know for sure) that your rounded ordinals shouldn't be too far off from the actual scale values if the error is not systematic.

edit* i found a paper that seems to address the issue of measurement error if you are interested. Harris and Smith (2008). Accounting for measurement error: A critical but often overlooked process.

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