# Can structural equation models be used to derive clinical formulae?

Structural equation models (sem) are used to model latent variables. Renal function is a latent variable measured by serum creatinine levels (with measurement errors) expressed by many different clinical formulae derived from linear regression models. Inulin clearance is a gold standard for renal function. However, hundreds of articles had studied the relative "accuracies" of these formulae as compared to surrogate "gold standards". Can sem be used to derive a clinical formula from serum creatinine and inulin clearance for the estimation of renal function?

• I consider myself to be reasonably good in structural equation modeling, but I cannot really see how to answer this question. What is a clinical formula? There are things absolutely trivial to you as a clinician or a biostatistician, but this is essentially a different language, and you need to provide a better translation. – StasK Jan 28 '12 at 23:00
• For example, glomerular filtration rate (GFR) is a measurement of renal function. A clinical formula for GFR is: GFR (mL/min/1.73 m$^2$) = 175 x (serum creatinine level)$^{-1.154}$ x (age)$^{-0.203}$ x (0.742 if female). This formula was derived from the anti-log of a linear regression of log-transformed X and Y variables. Because both inulin clearance (the gold standard of renal function) and serum creatinine levels are measurements with errors and inulin clearance is not usually measured clinically. Can SEM (which accounts for measurement errors) be used to derive a clinical formula for GFR? – KuJ Jan 30 '12 at 4:00
• OK, that clarifies things a bit: my understanding is that in the above formula, everything has been measured somehow with an equipment that provides a numeric reading (GFR, serum creatinine), or is an observable patient characteristic (age, gender). For the model that you are contemplating, please describe what are the variables that you have, how you obtain them, and what you think the causal relations between the variables are (which function causes which rate to go up or down). – StasK Jan 30 '12 at 16:54
• Inulin clearance is theoretically a "gold standard" for GFR if it is not measured with error, although it is measured with error in practice and is usually not measured clinically. Therefore, true GFR is not known and is a "latent variable". GFR is higher in men, blacks, youth, obesity or tall person. GFR is lower in diseases (e.g. diabetes mellitus and hypertension) and drugs (e.g analgesics), etc. Lower GFR non-linearly increases serum creatinine level. All clinical formulae for GFR uses gender, age and creatinine, although these variables account only for 60-80% of variance. – KuJ Feb 1 '12 at 7:31