Fairly trivial function to compute CSC, mainly useful if using group_by() piping to find CSCs for various groups/subsets in your data.

getCSC(formula1, data)

## Arguments

formula1 defines variables to use as score ~ grp where score has scores and grp has grouping is the data, typically cur_data() when called in tidyverse pipe

## Value

A single numeric value for the CSC

## Background

Like the CSC, the RCI comes out of the classic paper Jacobson, Follette & Revenstorf (1984). The thrust of the paper was about trying to bridge the gap between (quantitative) researchers who then, and still, tend to think in terms of aggregated data about change in therapy, and clinicians who tend to think about individual client's change.

The authors came up with two indices: the RCI, and the one here: the CSC or Clinically Significant Change (cut-off).

The authors defined three methods to set a criterion between "clinical" and "non-clinical" scores. Generally we prefer "help-seeking" and "non-help-seeking" to "clinical" and "non-clinical" to avoid automatically jumping into a disease/medical model.

For a measure cued so that higher scores indicate more problems the methods were as follows.

• Method a: the score 2 SD below the mean in the help-seeking group.

• Method b: the score 2 SD above the mean in the non-help-seeking group.

• Method c: the score between the means of the two groups defined so that, for Gaussian distributions of scores, the cutting point would misclassify the same proportions of each group. This is often spoken of as the point halfway between the two means but the definition is actually more subtle than that and will only be halfway between the means where the two groups have the same score SD. Where the groups have different SD the formula for method c is this.

$\frac{SD_{HS}*M_{notHS} + SD_{notHS}*M_{HS}}{SD_{HS}+SD_{notHS}}$

(with SD for Standard Deviation (doh!) and M for Mean)

## History/development log

Started before 5.iv.21

## References

• Jacobson, N. S., Follette, W. C., & Revenstorf, D. (1984). Psychotherapy outcome research: Methods for reporting variability and evaluating clinical significance. Behavior Therapy, 15, 336–352.

• Evans, C., Margison, F., & Barkham, M. (1998). The contribution of reliable and clinically significant change methods to evidence-based mental health. Evidence Based Mental Health, 1, 70–72. https://doi.org/0.1136/ebmh.1.3.70

getBootCICSC for CSC and bootstrap CI around it

Other RCSC functions: classifyScoresVectorByRCI(), getBootCICSC(), getRCIfromSDandAlpha()

Other RCSC functions: classifyScoresVectorByRCI(), getBootCICSC(), getRCIfromSDandAlpha()

Chris Evans

## Examples

if (FALSE) {
# example uses very crude simulated data but illustrates utility of being able to pipe grouped
# data into getCSC()
library(tidyverse)
set.seed(12345)
n <- 250 # total sample size
scores <- rnorm(n) # get some random numbers
# now random allocation to help-seeking or non-help-seeking samples
grp <- sample(c("HS", "notHS"), n, replace = TRUE)
# and random allocation by gender
gender <- sample(c("F", "M"), n, replace = TRUE)
list(scores = scores,
grp = grp,
gender = gender) %>%
as_tibble() %>%
mutate(scores = if_else(gender == "F", scores + .13, scores), # make women .13 higher scoring
### then make help-seeking group score 1.1 higher
scores = if_else(grp == "HS", scores + 1.1, scores)) -> tibDat
### now get CSC overall
tibDat %>%
summarise(CSC = getCSC(scores ~ grp, cur_data()))

### get CSC by gender
tibDat %>%
group_by(gender) %>%
summarise(CSC = getCSC(scores ~ grp, cur_data()))
}