Standardize Raw Cognitive Scores using Regression Models

Get normative scores by standardizing using regression models adjusting for one or all of age, sex and education.

Usage

std_scores_using_regression(
  raw_scores,
  var_name,
  reg_coefs,
  age,
  education,
  sex,
  delay,
  sd
)

Arguments

raw_scores

Numeric vector of raw scores

var_name

String with name of the variable. Used to get correct means and standard deviations, or regression coefficients.

reg_coefs

named vector with coefficients to be used for calculating expected score. Can include the following named entries:

• intercept

• age

• education

• sex

• delay

age

Numeric vector with ages in years

education

Numeric vector with years of education. Used for subset of variables only.

sex

Character vector with sex of participants. Must be either "m" (for male) or "f" (for female). Used for subset of variables only

delay

Only for standardizing MEMUNITS ("Logical Memory, Delayed") in which case it is the time of delay in minutes

sd

estimated standard deviation

Normative Scores from Regression Model

In general, we standardize scores by subtracting an estimate of the (possibly conditional) expected value of the variable considered, and divide the difference by an estimate of the (possibly conditional) standard deviation.

When we aim to do this using a regression model that adjusts for age, sex, and years of education, we find the conditional expected value as

$$ \mu = \beta_0 + \beta_{age} \cdot \verb|age| + \beta_{education} \cdot \verb|education| + \beta_{sex} \cdot \verb|sex| $$

where \(\verb|sex|\) is \(1\) if the patient is female, and \(0\) otherwise. std_scores_using_regression takes the coefficients in a named vector \(\verb|c(intercept = |\beta_0\verb|, age = |\beta_{age}\verb|, education = |\beta_{education}\verb|, sex = |\beta_{sex}\verb|)|\).

The normative score is then given as \(\verb|(raw_scores - |\mu\verb|)/sd|\), where sd is the estimated standard deviation passed to the sd argument. This will typically be the root mean squared error (RMSE) from the linear regression model.

One final caveat: for consistency, we "flip the sign" for normative scores where higher raw score values correspond to worse performance. This is the case for the trail making scores (both written and oral) related to time and number of errors.