Skip to contents

Sensitivity Analysis for Sample Size Planning From the AIPE Perspective for a Polynomial Change Parameter

Source: R/ss_aipe_pcm_sensitivity.R
ss_aipe_pcm_sensitivity.Rd

Quantifies how much misspecification of the population between-subject slope variance and within-subject error variance distorts an AIPE-based sample size plan for the group-by-time polynomial change parameter. On each replication the function simulates two independent groups of n subjects each, measured at \(M = f \times D + 1\) timepoints, where every subject has a true linear slope drawn from \(N(0, \mathrm{true\_variance\_trend})\) and within-subject observations have residual variance true_error_variance. Subject-level OLS slopes are computed in each group, the between-group difference in mean slopes (the change parameter \(\beta_{m1}\) that ss_aipe_pcm plans for) is estimated, and a two-group t-confidence interval on that difference (pooled standard error, \(2n - 2\) degrees of freedom) is recorded. The function only handles trend = "linear" in the simulator; for quadratic / cubic trends, the planner's closed-form solution is still available via ss_aipe_pcm.

Usage

ss_aipe_pcm_sensitivity(
  true_variance_trend = NULL,
  true_error_variance = NULL,
  estimated_variance_trend = NULL,
  estimated_error_variance = NULL,
  duration,
  frequency,
  width,
  n_per_group = NULL,
  conf_level = 0.95,
  assurance = NULL,
  G = 1000,
  print_iter = FALSE,
  filename = NULL
)

Arguments

true_variance_trend

Population between-subject variance of the polynomial change coefficient (the data generating \(\sigma^2_{\upsilon_m}\) of Kelley & Rausch, 2011).

true_error_variance

Population within-subject error variance (\(\sigma^2_\epsilon\)).

estimated_variance_trend

Planning value of variance_trend passed to ss_aipe_pcm; supply this and estimated_error_variance, or supply n_per_group.

estimated_error_variance

Planning value of error_variance passed to ss_aipe_pcm.

duration

Study duration (in time units).

frequency

Number of measurements per unit time. Total timepoints = \(f \times D + 1\).

width

Desired full width of the CI on the between-group difference in change parameters (\(\beta_{m1}\)).

n_per_group

Number of subjects to evaluate (incompatible with the estimated-variance arguments).

conf_level

Confidence level (default 0.95).

assurance

Optional assurance probability passed to the planner.

G

Number of Monte Carlo replications.

print_iter

Logical.

filename

Optional path to a CSV file; when supplied, the per-replication results (the slope difference, its interval limits and width, and the two tail misses) are written there, appended when the file already exists, and a throwaway run should point it at tempfile(fileext = ".csv"); the default NULL writes nothing.

Value

A data.frame with rows for mean / median / SD of the realized estimated slope difference and CI width, the proportion of intervals at or below width, tail-specific and overall non-coverage of the population slope difference (0 by construction in this simulator), and the input echoes, including assurance (present only when an assurance was supplied).

References

Kelley, K., & Rausch, J. R. (2011). Sample size planning for longitudinal models: Accuracy in parameter estimation for polynomial change parameters. Psychological Methods, 16(4), 391–405. doi:10.1037/a0023352

Maxwell, S. E., Delaney, H. D., & Kelley, K. (2027). Designing experiments and analyzing data: A model comparison perspective (4th ed.). Routledge. (See Chapters 11 and 15.)

See also

ss_aipe_pcm, ss_aipe_mixed_effects_sensitivity

design_consequences for what a chosen design delivers: power, the Type S (sign) and Type M (exaggeration) errors of the significance filter, and the expected confidence interval width.

Other AIPE sample size planning: ss_aipe_c_sensitivity(), ss_aipe_cliff_delta(), ss_aipe_cliff_delta_sensitivity(), ss_aipe_composite_sem(), ss_aipe_equivalence_r(), ss_aipe_equivalence_r_sensitivity(), ss_aipe_equivalence_smd(), ss_aipe_equivalence_smd_sensitivity(), ss_aipe_icc(), ss_aipe_icc_sensitivity(), ss_aipe_indirect_effect(), ss_aipe_indirect_effect_sensitivity(), ss_aipe_mixed_effects_sensitivity(), ss_aipe_omega_squared(), ss_aipe_omega_squared_sensitivity(), ss_aipe_partial_r(), ss_aipe_partial_r_sensitivity(), ss_aipe_r(), ss_aipe_r_sensitivity(), ss_aipe_reliability_sensitivity(), ss_aipe_semipartial_r(), ss_aipe_semipartial_r_sensitivity()

Author

Ken Kelley kkelley@nd.edu

Examples

# Every replication simulates two full groups of subjects, fits a slope
# for each subject, and forms a confidence interval on the difference in
# mean slopes. G = 20 keeps the example quick; a reported sensitivity
# study deserves the default G = 1000. With the planning values equal to
# the population values, the realized mean width should sit at or just
# under the target.
set.seed(113)
ss_aipe_pcm_sensitivity(
  true_variance_trend = 0.003, true_error_variance = 0.0262,
  estimated_variance_trend = 0.003, estimated_error_variance = 0.0262,
  duration = 4, frequency = 1, width = 0.05,
  G = 20, print_iter = FALSE
)
#>  term                     value  
#>  mean_slope_diff          0.00529
#>  median_slope_diff        0.00307
#>  sd_slope_diff            0.0104 
#>  mean_ci_width            0.0511 
#>  median_ci_width          0.051  
#>  sd_ci_width              0.00298
#>  pct_ci_less_w            0.45   
#>  pct_ci_miss_low          0.05   
#>  pct_ci_miss_high         0      
#>  total_type_I_error       0.05   
#>  n_per_group              71     
#>  n_timepoints             5      
#>  true_variance_trend      0.003  
#>  true_error_variance      0.0262 
#>  estimated_variance_trend 0.003  
#>  estimated_error_variance 0.0262 
#>  duration                 4      
#>  frequency                1      
#>  width                    0.05   
#>  conf_level               0.95   
#> 
#> Confidence level: 95%