Estimate Present-State Bias and Anchor-Based MIC Using Longitudinal Confirmatory Factor Analysis

mic_lcfa() estimates present-state bias and anchor-based minimal important change (MIC) using a longitudinal confirmatory factor analysis (LCFA) model.

Usage

mic_lcfa(
  mydat,
  trt = NULL,
  model = NULL,
  trt_cut = 1,
  auto_equalize = TRUE,
  pair_by = c("position", "suffix"),
  t1_suffix = NULL,
  t2_suffix = NULL,
  min_resp = 5L,
  B = 0L,
  report_every = 100L,
  N_ets = 5000L,
  score_method = c("irt", "cfa", "both"),
  return_prepared = FALSE,
  print_model = TRUE,
  verbose = TRUE
)

Arguments

mydat: Data frame containing paired Time 1 and Time 2 PROM items and one transition rating variable.
trt: Character. Name of the transition rating variable. If NULL, the final column of mydat is used.
model: Optional lavaan model syntax. If NULL, the model is generated automatically using lcfa_model().
trt_cut: Numeric. Cutpoint used to dichotomize the transition rating variable when it has more than two observed values. Values greater than or equal to trt_cut are coded as 1, and lower values are coded as 0. If the transition rating is already binary, the larger value is coded as 1 and trt_cut is ignored.
auto_equalize: Logical. If TRUE, item levels are equalized using equalize_levels().
pair_by: Character. Pairing method passed to equalize_levels() and lcfa_model(). "position" assumes Time 1 items followed by Time 2 items. "suffix" detects pairs using t1_suffix and t2_suffix.
t1_suffix: Regex suffix identifying Time 1 items when pair_by = "suffix".
t2_suffix: Regex suffix identifying Time 2 items when pair_by = "suffix".
min_resp: Integer. Minimum number of responses required in each response category before collapsing.
B: Integer. Number of bootstrap samples. Bootstrap confidence intervals are computed only if B >= 100.
report_every: Integer. Progress message interval during bootstrapping.
N_ets: Integer. Number of simulated theta values used for the IRT expected test score calculation. This argument is not used by the closed-form CFA method.
score_method: Character. Method used to map the latent MIC to the observed PROM score metric. Options are "irt", "cfa", and "both". "irt" uses mirt::expected.test(), "cfa" uses the closed-form CFA/probit expected-score method, and "both" returns both mappings.
return_prepared: Logical. If TRUE, returns prepared data, generated model, fitted LCFA object, and bootstrap details.
print_model: Logical. If TRUE, prints the generated lavaan model.
verbose: Logical. If TRUE, prints progress messages.

Value

A mic_lcfa object with elements including:

psb: estimated present-state bias;
MIC.theta: MIC on the latent-change scale;
MIC.ets: MIC on the observed PROM summed-score metric;
MIC.ets.irt: IRT-based expected-score MIC, if requested;
MIC.ets.cfa: CFA-based expected-score MIC, if requested;
MIC_CI: bootstrap confidence interval, if requested;
nboot: number of successful bootstrap estimates.

If return_prepared = TRUE, the returned object also contains the prepared data, generated lavaan model, fitted LCFA object, and bootstrap values.

Details

The input data should contain paired Time 1 and Time 2 PROM items plus one transition rating variable. Item pairs may be identified by column position or by suffixes. By default, paired item levels are first equalized using equalize_levels(), and lavaan syntax is generated using lcfa_model().

The LCFA model estimates the MIC on the latent-change scale. This latent MIC is then mapped onto the observed PROM summed-score metric using an expected score function.

The LCFA model uses both Time 1 and Time 2 item responses, together with the transition rating, to estimate the latent MIC and present-state bias. The latent MIC is then mapped onto the observed PROM summed-score metric.

at the baseline latent trait distribution, theta ~ N(0, 1);
at the shifted latent trait distribution, theta ~ N(MIC.theta, 1).

Two expected-score mappings are available through score_method:

"irt" uses an IRT-based expected test score method via mirt::expected.test(). This follows the published implementation of Terluin et al. (2024).
"cfa" uses a closed-form CFA probit expected-score method based on lavaan-estimated item loadings and thresholds. For each item, the method computes marginal category probabilities under theta ~ N(mu, 1), first with mu = 0 and then with mu = MIC.theta. These probabilities are used to obtain expected item scores, which are summed across items to obtain the expected PROM score.
"both" computes expected scores using both irt and cfa methods

Under the CFA probit method, the closed-form marginal cumulative probability for item threshold tau_k is based on the latent response model Y* = lambda * theta + error. If theta ~ N(mu, 1) and error ~ N(0, 1), then Y* ~ N(lambda * mu, lambda^2 + 1). Therefore, marginal category probabilities can be computed without simulating theta values or fitting an additional IRT model.

References

Terluin B, Trigg A, Fromy P, Schuller W, Terwee CB, Bjorner JB. Estimating anchor-based minimal important change using longitudinal confirmatory factor analysis. Qual Life Res. 2024;33:963-973. doi:10.1007/s11136-023-03577-w

Terluin B, Fromy P, Trigg A, Terwee CB, Bjorner JB. Effect of present state bias on minimal important change estimates: a simulation study. Quality of Life Research. 2024. doi:10.1007/s11136-024-03763-4

Terluin B, Griffiths P, Trigg A, Terwee CB, Bjorner JB. Present state bias in transition ratings was accurately estimated in simulated and real data. J Clin Epidemiol. 2022;143:128-136. doi:10.1016/j.jclinepi.2021.12.024

Examples

# \donttest{
set.seed(123)
sim <- simdat(N = 500, add_change = TRUE)
dat <- sim$datw

mydat <- dat[, c(
  sim$item_names$t1_items,
  sim$item_names$t2_items,
  "trat"
)]


out_both <- mic_lcfa(
  mydat = mydat,
  trt = "trat",
  trt_cut = 1,
  auto_equalize = TRUE,
  pair_by = "suffix",
  t1_suffix = "",
  t2_suffix = "\\.1",
  min_resp = 5,
  score_method = "both",
  B = 0,
  print_model = FALSE,
  verbose = FALSE
)

out_both$MIC.ets
#>      irt      cfa 
#> 2.610131 2.605668 
# }