Impute response rates based on continuous outcome data

This function allows to impute response rates based on the post-test means, standard deviations and sample size using the normal-approximation method by Furukawa et al. (2005). Response rates can be imputed using the 50% symptom decrease threshold, user-defined cut-off values, or the reliable change index (Jacobson & Truax, 1991).

Usage

imputeResponse(m.trt.pre, m.trt.post, sd.trt.post, n.trt, 
               m.ctr.pre, m.ctr.post, sd.ctr.post, n.ctr,
               sd.trt.pre, sd.ctr.pre, 
               rho = 0.8, cutoff = NULL, lower.is.better = TRUE,
               method = c("cutpoint", "rci"))

Arguments

m.trt.pre: Pre-test mean in the (treatment) arm.
m.trt.post: Post-test mean in the (treatment) arm.
sd.trt.post: Post-test standard deviation in the (treatment) arm.
n.trt: Sample size in the (treatment) arm.
m.ctr.pre: Optional. Pre-test mean in the control arm.
m.ctr.post: Optional. Post-test mean in the control arm.
sd.ctr.post: Optional. Post-test standard deviation in the control arm.
n.ctr: Optional. Sample size in the control arm.
sd.trt.pre: Pre-test standard deviation in the (treatment) group. Required if method = "rci".
sd.ctr.pre: Optional. Pre-test standard deviation in the control group. Required if method = "rci".
rho: Reliability coefficient, used to calculate the reliable change when method = "rci". Set to 0.8 by default.
cutoff: User defined cut-off score for response. NULL by default, which means that 50% symptom decrease is used as the response criterion.
lower.is.better: Do lower values indicate better outcomes (e.g. less depression)? TRUE by default.
method: Method to define response. Either "cutpoint" (default; uses 50% symptom decrease as criterion, or a user-specified score in cutoff) or "rci", which means that the reliable change index (Jacobson & Truax, 1991) is used.

Value

If only values for the treatment arm are specified, imputeResponse

returns a data.frame with two columns:

trtResponder: Number of responders
nTrt: Total sample size of the treatment arm

If values are also specified for the control group, six additional columns are returned:

ctrResponder: Number of responders in the control group
nCtr: Total sample size of the treatment arm
logRR: Log-risk ratio of the difference in response rates in both arms
seLogRR: Standard error of the log-risk ratio
logOR: Log-odds ratio of the difference in response rates in both arms
seLogOR: Standard error of the log-odds ratio

Details

For more details see the Get Started vignette.

References

Furukawa, T. A., Cipriani, A., Barbui, C., Brambilla, P., & Watanabe, N. (2005). Imputing response rates from means and standard deviations in meta-analyses. International Clinical Psychopharmacology, 20(1), 49-52.

Jacobson, N. S., & Truax, P. (1991). Clinical significance: a statistical approach to defining meaningful change in psychotherapy research. Journal of Consulting and Clinical Psychology, 59(1), 12–19. https://doi.org/10.1037//0022-006x.59.1.12

Author

Mathias Harrer mathias.h.harrer@gmail.com

Examples

if (FALSE) {

# Calculate response using 50% method for one group.
imputeResponse(m.trt.pre = 20, m.trt.post = 11,
               sd.trt.post = 7, n.trt = 100)

# Calculate response for two groups and calculate effect sizes
imputeResponse(m.trt.pre = 20, m.trt.post = 11,
               sd.trt.post = 7, n.trt = 100,
               m.ctr.pre = 20, m.ctr.post = 18,
               sd.ctr.post = 6, n.ctr = 120)

# Calculate using user-defined response threshold
imputeResponse(m.trt.pre = 20, m.trt.post = 11,
               sd.trt.post = 7, n.trt = 100,
               m.ctr.pre = 20, m.ctr.post = 18,
               sd.ctr.post = 6, n.ctr = 120,
               cutoff = 15)

# Assuming higher outcomes are better...
imputeResponse(m.trt.pre = 20, m.trt.post = 11,
               sd.trt.post = 7, n.trt = 100,
               m.ctr.pre = 20, m.ctr.post = 18,
               sd.ctr.post = 6, n.ctr = 120,
               cutoff = 15, lower.is.better = FALSE)

# Using RCI, with an assumed reliability of 0.88
imputeResponse(m.trt.pre = 20, m.trt.post = 11,
               sd.trt.post = 7, n.trt = 100,
               m.ctr.pre = 20, m.ctr.post = 18,
               sd.ctr.post = 6, n.ctr = 120,
               method = "rci", rho = 0.88,
               sd.trt.pre = 8)

# Using a different pre-test SD in the control
imputeResponse(m.trt.pre = 20, m.trt.post = 11,
               sd.trt.post = 7, n.trt = 100,
               m.ctr.pre = 20, m.ctr.post = 18,
               sd.ctr.post = 6, n.ctr = 120,
               method = "rci", rho = 0.88,
               sd.trt.pre = 8, sd.ctr.pre = 9)

# Calculating many results at the same time
set.seed(123)
imputeResponse(m.trt.pre = runif(10, 10, 30), m.trt.post = runif(10, 8, 14),
               sd.trt.post = runif(10, 5, 8), n.trt = rpois(10, 150),
               m.ctr.pre = runif(10, 10, 30), m.ctr.post = runif(10, 13, 20),
               sd.ctr.post = runif(10, 5, 8), n.ctr = rpois(10, 150),
               method = "rci", rho = round(runif(10, 70, 90))/100,
               sd.trt.pre = runif(10, 7, 9))

set.seed(123)
imputeResponse(m.trt.pre = runif(10, 10, 30), m.trt.post = runif(10, 8, 14),
               sd.trt.post = runif(10, 5, 8), n.trt = rpois(10, 150),
               m.ctr.pre = runif(10, 10, 30), m.ctr.post = runif(10, 13, 20),
               sd.ctr.post = runif(10, 5, 8), n.ctr = rpois(10, 150))

set.seed(123)
imputeResponse(m.trt.pre = runif(10, 10, 30), m.trt.post = runif(10, 8, 14),
               sd.trt.post = runif(10, 5, 8), n.trt = rpois(10, 150),
               cutoff = 11:20)
}