01.Association09.Measuring change scores - sporedata/researchdesigneR GitHub Wiki

1. Use cases: in which situations should I use this method?

  • This design is used in situations where clinicians are interested in the change in outcome scores between baseline the end of the study. Note however that most research designs focus on a difference between groups (in order to create a control group or counterfactual) rather than between before and after treatment.

    • Because there are no control groups in pre-post treatment, the respective associations are skewed by factors such as changes in the surrounding environment. It is important to compare across groups rather than pre-post to take advantage of either causal modeling (which tries to mimic randomization) or randomization. The analysis is potentially biased when comparing pre-post status, and all confounding control is lost. Since this is of clinical interest, we suggest reporting pre-post without making any claims regarding effectiveness.

2. Input: what kind of data does the method require?

  • Outcome scores before and after a given intervention, along with covariates.

3. Algorithm: how does the method work?

Model mechanics

Change scores (e.g. ΔY=Y1−Y0), also known as ‘difference scores’, ‘gain scores’ and ‘change-from-baseline variables’, are composite variables that have been constructed from repeated measures of a single parent variable (Y) by subtracting a subsequent measure of the parent (Y1, ‘follow-up’) from a prior measure (Y0, ‘baseline’). The resulting composite variable retains information from both of its determining parents and hence will share a tautological association with either if analysed by regression or correlation [1]. This was first recognized by Oldham in 1962, who demonstrated that an association averaging r=±1/2–√ occurs between either of the parent variables (i.e. Y0 or Y1) and their difference (i.e. Y1−Y0) if both have similar variances but are otherwise unrelated [2]. This phenomenon explains the ‘law of initial value’ as a consequence of the sign disagreement between the baseline parent variable (Y0) and its transformation in the composite change score (−Y0), and is distinct from regression-to-the-mean [1] [3].

Relatively few analyses of change scores, however, involve straightforward tautological associations. More often, change scores are used as outcome variables in relation to a separate baseline treatment or exposure X0 (e.g. ‘How do beta-blockers affect change in blood pressure?’). One of the most widely recognized issues in this context is the discordance between change-score analyses (i.e. where the outcome-change score ΔY is regressed on the baseline exposure X0) and analyses of covariance (ANCOVA; i.e. where the follow-up outcome Y1 is regressed on the baseline exposure X0 and ‘adjusted for’ the baseline outcome Y0) [4] [5] [3].

‘Change scores’ provide a simple summary measure of the average change in a variable between two time points; they are commonly used when analysing ‘change’ in an outcome with respect to a baseline exposure [3].

Analyses of outcome-change scores do not estimate causal effects except under randomized experimental conditions; in some (non-randomized) situations, the implied ‘effect’ may be of the opposite sign to the total and/or direct causal effect[3].

Patients and clinicians are almost invariably interested in measuring change in health status, since that is what they perceive in their practice. In other words, are people getting better or worse over time, as a result of disease progression or a treatment? In response, data analysts will often calculate change scores, meaning the subtracting the last available health scores from the initial ones. For example, if a depression level is 6 now, but used to be 9, then the patient improved by 3 points. Unfortunately, this type of difference scores can have reliability issues -- see Issues in the use of change scores in randomized trials. Instead, some authors recommend that the analysis be carried out as an analysis of covariance (ANCOVA). In an ANCOVA model, the outcome (latest score) is the outcome (dependent variable), while the association with the intervention (treatment) is adjusted for the baseline score. So, the change score is not calculated, but one removes the bias of the initial score from the association between the intervention and the final score.

There is a huge body of literature on the topic, and one guideline seems to be that in randomized studies and studies with treatment assignment depending on the baseline, ANCOVA or models adjusting for the baseline score is the method of choice, whereas in nonrandomized studies, ANOVA of change or mixed/multilevel models seem less biased than ANCOVA. See ANCOVA versus change from baseline: more power in randomized studies, more bias in nonrandomized studies

Describing in words

Describing in images

Describing with code

Breaking down equations

Suggested companion methods

Learning materials

  1. Articles

4. Output: how do I interpret this method's results?

Typical tables and plots and corresponding text description

Metaphors

  1. Measuring change scores evaluate the difference within an individual, where the goal is to change or improve function, comparing the outcome in the same individuals.
  2. Also can identify and measure outcomes differences between individuals in a group.

Reporting guidelines

5. SporeData-specific

Templates

Data science functions

Data science packages

  • Usually handled through regression modeling, often mixed models

General description

Clinical areas of interest

Variable categories

Linkage to other datasets

Limitations

Related publications

SporeData data dictionaries

References

[1] Tu Y-K, Gilthorpe MS.Revisiting the relation between change and initial value: a review and evaluation.Stat Med. 2007;26:443–57.

[2] Oldham PD. A note on the analysis of repeated measurements of the same subjects.J Chronic Dis. 1962;15:969–77.

[3] Tennant PW, Arnold KF, Ellison G, & Gilthorpe MS. Analyses of ‘change scores’ do not estimate causal effects in observational data.International journal of epidemiology. 2021 June;1–12.

[4] Senn S. Change from baseline and analysis of covariance revisited.Stat Med. 2006 Dec 30;25(24):4334-44.

[5] Van Breukelen GJ. ANCOVA versus change from baseline had more power in randomized studies and more bias in nonrandomized studies.J Clin Epidemiol. 2006 Sep;59(9):920-5.

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