Should one account for absolute precision producing variable number of significant digits in a dependent variable measurement? If so how?

Question

Sometimes data for a variable are available in absolute precision, which can create different numbers of significant digits. For example, the CDC's estimates of state prevalences and incidence rates of HIV diagnoses report figures to a single decimal place of absolute precision, rather than, for example three significant digits (relative precision). For example, in 2017, the CDC reports that Alabama's prevalence^* was 15.9 HIV diagnoses per 100,000 persons age 13+, but reports Alaska's prevalence was 4.8 HIV diagnoses per 100,000 persons age 13+. Alabama's measurement is thus using 3 significant digits, and Alaska's is using 2 significant digits^** (contrast the value 4.8 with a value like 4.81, or 4.77).

Suppose I was modeling annual state prevalences of HIV diagnoses, say in a regression context:

1. Should I account for the resulting variability in significant digits? (What bias emerges in my estimates and inference if I do not?)

2. How? (I suppose I could truncate all figures to 2 significant digits, for example, rounding Alabama's 2017 prevalence to 16, but that necessarily discards information, decreasing precision. Are there alternatives I should consider?)

Bonus consideration: The distribution of values of the most significant digit of the CDC's figures skews strongly rightward, with most values being 0 or 1, some values being 2, and very few values being 3 or 5. Does this affect how I interpret any risk of bias in question (1) above?

NB: This is not a question about measurement error in a dependent variable in general—I am not asking about accounting for the reliability of the dependent variable figures generally.

^* Actually, what the CDC terms "prevalence" the epidemiology textbooks I am familiar with term "count of prevalent cases," and what the CDC terms "prevalence rate" the epidemiology textbooks I am familiar with term "prevalence". I side strongly with the latter nomenclature, as "rate" means change (usually over time), but prevalences are static measures by definition (although one may certainly measure change in prevalence over time, that is not what the reported measures are), thus "prevalence rate" lands as an oxymoron to me.

^** Assuming for the moment that Alaska's value in 3 significant digits is not actually 4.80.

References

CDC. (2018) Diagnoses of HIV Infection in the United States and Dependent Areas, 2017 (see Table 26).

Answer 1

Alabama's total 2010 population was about 4.8 million. Let's say 4 million age 13+. 15.9 diagnoses per 100,000 then comes to 636 diagnoses. If these are rare, Poisson-distributed events then the standard deviation in that number is about 25 diagnoses, about 4% of the total.* Corresponding error in the value of 15.9 is about $\pm 0.6$

Alaska's total 2010 population was about 700,000. Let's say 600,000 age 13+. At 4.8 diagnoses per 100,000 that's about 29 diagnoses total. Under the above assumptions, the standard deviation in that number is about 5 diagnoses, or 17% of the mean. Corresponding error in the value of 4.8 is about $\pm 0.8$.

Those inherent errors arising from counts of rare events would seem to overwhelm any issue you might fear in terms of the numbers of significant digits of the reported values. For those two examples, at least, the truncation to a single decimal digit seems to represent the inherent errors pretty well.

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*One could argue that almost all HIV cases are captured in the data, so it's not fair for this argument to assume that there is some broader population from which the cases are being sampled. This illustration would be for a hypothetical case where there is a large number of Alabamas with the same overall mean HIV prevalence; among such a set of Alabamas that would be the standard deviation among their prevalence values.