## Transformation of lab values [Study Per­for­mance]

Dear Ratnakar!

❝ My query is do we really need to mention the lab normal ranges in the protocol or only name of the tests are sufficient?

I haven’t seen reference ranges in any protocol yet.

❝ […] during one of the regulatory inspection it was suggested to mention reference ranges in the protocol.

Interesting. Which country’s inspector?

❝ […] slightly different normal ranges for some parameters

Yes, as you also have mentioned it is not uncommon that reference ranges change during the course of a study.

Consider transforming values* to a predefined range
$$R_t=S_L+\frac{R_u-I_L}{I_H-I_L}\left(S_H-S_L \right) \tag{12.5.1}$$where $$\small{R_u}$$ and $$\small{R_t}$$ denote the untransformed and transformed result, $$\small{(I_L,I_H)}$$ and $$\small{(S_L,S_H)}$$ are the investigators’ (lab) and standard (protocol) lower/upper limits of the reference range. In the protocol you may give the standard range and mention the planned transformation. However, if the lab's range don’t change as planned you don’t have to worry because $$\small{{R_t}=R_u}$$.
Example: Standard range 10–300 $$\small{(S_L,S_H)}$$, lab’s range changed to 8–240 $$\small{(I_L,I_H)}$$, measured 9 ($$\small{R_u}$$ within the lab's new range, but outside the old standard range), transformed value 11 ($$\small{R_t}$$ within the old standard range).

For details and an alternative method see Chow & Liu.*

• Chow S-C, Liu H-p. Design and Analysis of Clinical Trials. Concepts and Methodologies. New York: Wiley; 1998. p. 560–2.

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