## Significant digits (IMHO) [General Statistics]

Dear DLabes!

Oh, that's an interesting question!

A rather old (1988) reference from IUPAC (the International Union of Pure an Applied Chemistry) recommends giving location parameters (means, median) to two significant figures, and the relative standard deviation (RSD, CV) to three significant figures. You may download the reference here.

I would suggest rising the significant figures by one digit.

Problems arise if electronic data in full precision are transferred to the statistical database. Generally (paper-)reports contain only modified results (rounded to decimal places or significant figures, or - even worse - truncated values). If PK-parameters have to be recalculated from the paper-version or a PDF-file (

Most likely affected parameters are C

Two reasons call for rounding of analytical data before using them in PK:

a pragmatic one – avoid discrepancies between paper and electronic data which may raise unnecessary questions, and

a scientific one – use of full precision data implies a degree of accuracy/precision which is not correct.

Example:

Since the accuracy/precision of an analytical method is dependent on the concentration, it would be

However, I would always opt for significant digits – not decimal places. Imagine the situation, where the analytical method covers two orders of magnitude:

What we (silently) imply in the second column (rounding to

In the third column (rounding to

For many analytical methods even rounding to

Most analysts have swallowed Arlington Conferences I-III and are familiar with 15% accuracy/precison (20% at LLOQ); but routinely come up with

If I tell them, next time they should come up with

I do rounding of analytical data to three significant figures (I failed convincing sponsors that concentration-based rounding is a reasonable procedure).

C

No…

❝ […] precision of the pharmacokinetic metrics used in bioequivalence studies.

Oh, that's an interesting question!

A rather old (1988) reference from IUPAC (the International Union of Pure an Applied Chemistry) recommends giving location parameters (means, median) to two significant figures, and the relative standard deviation (RSD, CV) to three significant figures. You may download the reference here.

I would suggest rising the significant figures by one digit.

Problems arise if electronic data in full precision are transferred to the statistical database. Generally (paper-)reports contain only modified results (rounded to decimal places or significant figures, or - even worse - truncated values). If PK-parameters have to be recalculated from the paper-version or a PDF-file (

*i.e.*, during an inspection), results may differ from the ones reported…Most likely affected parameters are C

_{max}and t_{1/2}, whereas AUC as an integrated parameter is pretty robust.Two reasons call for rounding of analytical data before using them in PK:

a pragmatic one – avoid discrepancies between paper and electronic data which may raise unnecessary questions, and

a scientific one – use of full precision data implies a degree of accuracy/precision which is not correct.

Example:

`3.141592653589793 `

(result from data system)`3.1416 `

(four decimal places)`3.142 `

(four significant figures)Since the accuracy/precision of an analytical method is dependent on the concentration, it would be

*desirable*to take this into account and perfom rounding based on results form the validation. If the method comes up with ±2.3% at 30, with ±5.8% at 3.0 and with ±15% at 0.3 a rounding function may be set up.However, I would always opt for significant digits – not decimal places. Imagine the situation, where the analytical method covers two orders of magnitude:

`+-------------------+--------+--------+`

| raw data | 3 dec. | 3 sig. |

+-------------------+--------+--------+

| 31.41592653589793 | 31.416 | 31.4 |

| 3.14159265358979 | 3.142 | 3.14 |

| 0.31415926535898 | 0.314 | 0.314 |

+-------------------+--------+--------+

What we (silently) imply in the second column (rounding to

*three decimal places*) is suggesting our ability to distinguish between 31.4154 and 31.4165 – a difference of 0.0035% from the reported value! Of course it gets better going to lower concentrations: 0.32% at 0.314.In the third column (rounding to

*three significant figures*) we obtain 0.32% regardless the concentration – which is too low anyway…For many analytical methods even rounding to

*two*significant digits would be sufficient – but I would guess everybody would start screaming then: analysts, sponsors, regulators.Most analysts have swallowed Arlington Conferences I-III and are familiar with 15% accuracy/precison (20% at LLOQ); but routinely come up with

`3.141592653589793`

. Subconsciously they *belief*, that such a result is*more correct*than`3.14`

.If I tell them, next time they should come up with

`3.14159265358979323846264338327950288`

, they tell me, that I am a funny person. ❝ How do you act in this respect?

I do rounding of analytical data to three significant figures (I failed convincing sponsors that concentration-based rounding is a reasonable procedure).

❝ Do you have any standard regarding the significant digits or decimal places in reporting AUC, Cmax and so on?

C

_{max}taken from rounded data, therefore three significant figures; AUC as an integrated parameter to four significant figures (this makes sense according to propagation of uncertainty). Location parameters to the same number of digits; SD one more.❝ Does anybody know a regulative guideline?

No…

—

Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮

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*Dif-tor heh smusma*🖖🏼 Довге життя Україна!_{}Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮

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### Complete thread:

- Significant digits or decimal places d_labes 2008-03-26 13:15
- Significant digits (IMHO)Helmut 2008-03-26 16:12
- Significant digits or not significant digits ... d_labes 2008-03-27 10:10
- Significant digits or not significant digits ... Helmut 2008-03-27 20:43
- Significant digits or not significant digits ... d_labes 2008-03-28 11:00

- Significant digits or not significant digits ... Helmut 2008-03-27 20:43

- Significant digits or not significant digits ... d_labes 2008-03-27 10:10

- Significant digits (IMHO)Helmut 2008-03-26 16:12