Table 2

Overview of research designs to assess individual differences in the response to exercise training for a given trait*

Design	Assumptions	Measure of interindividual response variance†	Limitations
Uncontrolled designs (one group pre–post design)
1. Single premeasurement and postmeasurement	No change would occur in any subject without the intervention. No measurement error or day-to-day variability.	Variance of observed change scores.	Cannot establish if observed change or its variance is attributable to treatment.
2. Multiple premeasurements and postmeasurements	No change would occur in any subjects without the intervention. Multiple preassessments and postassessments adequately sample the measurement error and day-to-day variability.	Variance of the of the observed change score minus the sum of the average within subject prevariance and postvariance. Can be estimated using classic ANOVA or mixed model.	May be able to remove variance due to measurement error and day-to-day variability but still cannot establish if the estimated interindividual response variability would occur without the intervention. Multiple assessments required.
3. Longitudinal with repeated measurements spread over time	No change would occur in any subject without the intervention. All subject’s true change occurs according to a linear (or other specific) parametric model. Measurement error and day-to-day variability can be captured by the deviation of observed measures from linear (or other) model.	Estimated variance of random slopes as estimated from a linear mixed model.	If linear (or other) model is correct then measurement error and day-to-day variance can be removed but still cannot establish if average change or variance of change is caused by treatment. Multiple assessments required.
Control group designs (parallel RCT comparing intervention(s) to control)
4. Single premeasurement and postmeasurement	Total of all sources of variance other than interindividual response are identical in the intervention and control arm. Assumes individuals would have consistent training effect.	Variance of the observed change in the intervention arm minus variance of the observed change in the control arm.	Relies on strong untestable assumptions. Difference in variation between training and control groups is neither necessary nor sufficient for subject-by-training interaction to be present.
5. Multiple premeasurements and postmeasurements	Multiple preassessments and postassessments adequately sample the measurement error and day-to-day variability. Within-individual variation in training effects the same in intervention and control arm.	Variance of the of the observed change score minus the sum of the average within subject pre and post variances. Can be estimated using classic ANOVA or mixed model.	Relies on model assumptions. Multiple assessments required.
6. Longitudinal with repeated measurements spread over time	All subject’s true change occurs according to a linear (or other specific) parametric model. Measurement error and day to day variability can be captured by deviation of observed measures from linear (or other) model.	Estimated variance of random slopes as estimated from a linear mixed model.	Relies on model assumptions. Multiple assessments required.
Other designs
7. Crossover study with multiple intervention and control periods	Prior treatment does not alter change during future periods. Measurement error and day-to-day variability remains constant over time.	Mixed linear model. In theory, the mixed effects model can isolate the true interindividual response variability for this design.	Costly, may require extensive washout periods, difficult to retain participants over entire study, potential carry-over effects may invalidate results.
8. External reliability studies	Variance of error estimated from external sources are equal to the variance of error in the current trial.	Subtract error variance estimated externally from total variance of change observed in current study.	Error estimates from external study may not accurately reflect current study.
9. Internal reliability substudy	Individuals have consistent training effect. A components of variance model.	Subtract internal estimate of error variance from total variance of change.	Fairly complicated analysis required. Assumes a particular components of variance model.

*Expanded from table 3 in Hecksteden et al.23
†Take the square root of the individual response variance to obtain SD of individual response (SD_IR).
ANOVA, analysis of variance; RCT, randomised controlled trials.