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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?

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    $\begingroup$ 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. $\endgroup$ – StasK Jan 28 '12 at 23:00
  • $\begingroup$ 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? $\endgroup$ – KuJ Jan 30 '12 at 4:00
  • $\begingroup$ 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). $\endgroup$ – StasK Jan 30 '12 at 16:54
  • $\begingroup$ 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. $\endgroup$ – KuJ Feb 1 '12 at 7:31
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If you can build a regression model for something, it means to me that this is a measurable quantity. While a linear regression model is a special case of the general SEM, the greater strength of SEM is, arguably, being able to accommodate latent variables and measurement error in predictors. If you want to build a structural equation model for the latent variable BLAH (renal function), you need to have a study where several different ways to measure it have been undertaken (serum creatinine levels, inulin clearance). If, in turn, these variables are obtained from "clinical formulae" (another regression model, as far as I understand), that messes up the model quite a bit, and you need to figure out exactly which of the variables affect the measurement process, and which one affects the underlying latent variable (without knowing anything about the biochemisty of whatever it is that you are interested in, I would dare suggesting that age and gender affect the latent variable, rather than the measurement process). Ideally, you would want your equations linking the latent variables with the measured variables to be linear in parameters, so you would need to apply the typical transformations, such as logs. The standard language of structural equation models are path diagrams; mainstream statisticians tend to stare at them with little understanding of what's going on, but social scientists have found them to be very handy in explaining the relations between variables. I think this paper explains it quite well, although I don't know how closely it follows the biomedical language (it is written by psychometricians): http://www.citeulike.org/user/ctacmo/article/2663951.

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  • $\begingroup$ Gender, age, race, body weight, body height, diseases and drugs are formative indicators whereas serum creatinine level is a reflective indicator for GFR. Should partial least squares (PLS) be used instead of SEM in this hybrid case of both formative and reflective indicators? $\endgroup$ – KuJ Feb 2 '12 at 2:25
  • $\begingroup$ Don't ever mention PLS in my presence if you want me to respond again :). What you have then is a MIMIC (multiple indicators, multiple causes) model, and that's what you should look up. You should be able to set up your this SEM model in any decent SEM software. To identify your latent variable, you need to have at least two "reflective" indicators of it (e.g., measured GFR and creatinine level). While psychology uses "formative" and "reflective" indicators terminology which I find awkward, sociologists use "causal" and "effect" indicators terminology, so you might want to look these up, too. $\endgroup$ – StasK Feb 2 '12 at 19:45
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Yes SEM can do that. You enter the measured and latent variables into the model, specify their relationships, and then you will get quite a lot of output. This output will include a structural equation (looks like a regression equation, with coefficients, standard errors, etc) and an R^2 result. SEM also allows you to specify other relationships such as allowing covariance between serum creatinine and inulin.

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