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Table 1 Description of retest correction approaches

From: Correction for retest effects across repeated measures of cognitive functioning: a longitudinal cohort study of postoperative delirium

Model

Analysis Sample

Retest Correction Method**

Additional Specifications to Basic Model*

Strengths

Weaknesses

1: No correction

SAGES surgery sample (delirium-positive and delirium-negative) N = 560

No correction for retest effect

Main effect: delirium group

Interactions: time × delirium group

Outcome: raw GCP

-Does not make manipulations to observed data

-Does not require a control group

-Difficult to separate retest effects from effects due to delirium/surgery

2: Mean difference correction

SAGES surgery sample (delirium-positive and delirium-negative) N = 560

Step 1: Calculate mean retest effect in NSC group:

\( R{(NSC)}_t=\frac{1}{N}\sum \limits_i GCP{(NSC)}_{it}- GCP{(NSC)}_{i0}; \)

t ∈ (1, 2, 6), i ∈ 1, 2, …, N)

Step 2: Calculate retest-corrected scores in surgical group:

GCPRCit = GCPit − R(NSC)t; where R(NSC)6 = RSC(NSC)12 = RSC(NSC)18

Main effect: delirium group

Interactions: time × delirium group

Outcome: mean difference corrected GCP

-Straightforward, constant (within occasion) transformation for all people

-Correction is uncorrelated with any other variable at each time point

-Potential variability due to the fact that precision of retest correction estimation is not accounted for

3: Predicted difference correction

SAGES surgery sample (delirium-positive and delirium-negative), N = 560

Step 1: Estimate linear regression equations in NSC group expressing the dependence of GCP score at follow-up on baseline GCP, centered at the overall mean of the GCP at baseline in the NSC group; The regression is estimated separately for each observation time point (follow-up month) t ∈ (1,2,6):

\( \kern0.75em GCP{(NSC)}_{it}={b}_{0t}+{b}_{1t}\left( GCP{(NSC)}_{i0}-{\overline{GCP(NSC)}}_0\right)+{e}_t \)

Step 2: Compute expected GCP performance given the NSC group regression equations:

\( E{(GCP)}_{it}={b}_{0t}+{b}_{1t}\left({GCP}_{i0}-{\overline{GCP(NSC)}}_0\right) \)

Step 3: Calculate retest effect in surgical (SRG) group:

R(SRG)it = GCPit − E(GCP)it; t ∈ (1, 2, 6)

Step 4: Calculate retest-corrected scores in surgical group:

GCPRCit = GCPit − R(SRG)t; t ∈ (1, 2, 6,12,18)

Main effect: delirium group

Interactions: time × delirium group

Outcome: predicted difference corrected GCP

-Retest effects will be more appropriately modeled if a baseline variable is known to predict retest effects

-The degree of correction could differ by group if predictors of the retest effect differ by group

-Inconsistent literature on variables predicting retest effect

-Variability due to precision of retest correction estimation is not accounted for in the model

4: Model-based correction

SAGES surgery sample (delirium-positive and delirium-negative), N = 560 & non-surgical comparison (NSC) sample, N = 118

Raw GCP is utilized for both the NSC and surgical groups, but this method differs from Model 1 (no correction) in that NSC data is modeled as the comparison group for both the delirium+ and delirium- groups. Relative differences between the delirium+ and delirium- groups are then calculated with post hoc tests.

Main effect: NSC, delirium group

Interactions: time × group

Outcome: raw GCP

-Standard errors are appropriately conservative

-Can model differences compared to another surgical group and a NSC sample

-Model estimates are reported in reference to the NSC group

-Potential analyses are restricted to variables observable in the NSC group

-Maintaining a NSC group is expensive and may introduce additional bias over time due to drop out or latent differences between the NSC and surgical groups.

  1. SAGES=Successful AGing after Elective Surgery; NSC = non-surgical controls; GCP = general cognitive performance
  2. *Basic model: Linear mixed effects model with random intercept and time piece from 2 to 18 months; fixed time indicator variables for months 1 and 2 and time piece from 2 to 18 months; fixed covariates: baseline age, sex, non-white race
  3. **The Approach 2 Step 1 equation defines the normative retest or practice effect [R(NSC)] as the mean difference in general cognitive performance (GCP) score from baseline among the non-surgical comparison (NSC) group. This effect is computed assuming no true change occurs within a six month time frame, or is vanishingly small relative to the practice or retest effect. The retest effect is simply the mean within-person difference between the time t follow-up and baseline observed cognitive test score (GCP). These are computed for months 1, 2 and 6 (per-protocol observation time points). Step 2 defines the retest corrected cognitive performance score (GCPRC) for a person (i) at time t as their observed score at time t minus the mean retest effect in the NSC group at time t. We set the 12 and 18 month follow-up equal to the six-month retest effect to reflect our assumption that practice or retest effects are constant following the six month follow-up