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Tipping-point analysis for missing posttests

Source: R/solomon_mi.R
tipping_point_solomon.Rd

[Experimental] Repeats fit_solomon_mi() over a range of offsets added to the imputed posttests of chosen Solomon groups, and reports the smallest offset in each direction at which the conclusion about a contrast changes. White et al. (2011, "Perform Sensitivity Analyses" section, para. 1) suggest reporting "how large an amount should be added to or subtracted from imputed outcomes" without changing the interpretation, and Little et al. (2012, p. 1358) call a finding robust if it holds over the plausible offsets.

Usage

tipping_point_solomon(
  y_post,
  treat,
  pretested,
  y_pre = NULL,
  contrast = "ATE (avg over pretest)",
  groups = "all",
  deltas = NULL,
  alpha = 0.05,
  m = 100,
  robust = c("HC3", "none"),
  seed = NULL,
  data = NULL
)

Arguments

y_post

Numeric posttest scores, with NA for missing posttests.

treat

Treatment indicator coded 0/1 (or logical). Designs with several treatments are not supported; see fit_solomon_glm().

pretested

Pretest indicator coded 0/1 (or logical).

y_pre

Optional numeric pretest scores, missing by design for unpretested participants.

contrast

The Solomon contrast to follow. Default is the average treatment effect.

groups

The groups whose imputed posttests are shifted: "all" (default), "treatment", "control", "pretested", "unpretested", or group numbers (1 pretested treatment, 2 pretested control, 3 unpretested treatment, 4 unpretested control).

deltas

Offsets to try, on the posttest scale. The default is 21 values from -1 to 1 pooled within-group standard deviations of the observed posttests. Zero is always included.

alpha

Significance level that defines the conclusion. Default 0.05.

m

Number of imputations for each offset. Default 100.

robust

Covariance for each completed-data analysis: "HC3" (default) or "none"; see fit_solomon_glm().

seed

Optional random-number seed. When NULL, one is drawn so that every offset uses the same imputations.

data

Optional data frame. When supplied, the other data arguments are looked up in it first, as bare column names (y_post = post) or as strings (y_post = "post").

Value

An object of class solomon_tipping with results (one row per offset: the offset in posttest units and in standard deviations, and the pooled estimate, interval, and p-value), tipping (the smallest negative and positive offsets at which the conclusion differs from the one under MAR, NA when it does not change within the range), and the settings used.

Details

Which groups. Offsets confined to some groups test different departures from missing at random. Offsets in the treatment groups (groups = "treatment") bear on the treatment effect. Offsets that differ between the pretested and unpretested groups, for example in the pretested treatment group alone (groups = 1), bear on the sensitization contrast.

Common random numbers. Every offset uses the same imputation draws, so the estimates change smoothly with the offset. The location of the tipping point still carries Monte Carlo error from the imputations: in the worked example on mai2020, the tipping point for sensitization ranged from 0.1 to 0.5 standard deviations across seeds with 100 imputations and was 0.3 with 2,000. Before reporting a tipping point, increase m or compare a few seeds.

Lifecycle

Experimental, with fit_solomon_mi(), whose validation study it shares.

References

Little, R. J., D'Agostino, R., Cohen, M. L., Dickersin, K., Emerson, S. S., Farrar, J. T., Frangakis, C., Hogan, J. W., Molenberghs, G., Murphy, S. A., Neaton, J. D., Rotnitzky, A., Scharfstein, D., Shih, W. J., Siegel, J. P., & Stern, H. (2012). The prevention and treatment of missing data in clinical trials. The New England Journal of Medicine, 367(14), 1355–1360. https://doi.org/10.1056/NEJMsr1203730

White, I. R., Horton, N. J., Carpenter, J., & Pocock, S. J. (2011). Strategy for intention to treat analysis in randomised trials with missing outcome data. BMJ, 342, Article d40. https://doi.org/10.1136/bmj.d40

See also

fit_solomon_mi(), plot_tipping_point()

Examples

d <- solomon_example
set.seed(82)
d$y_post[sample(nrow(d), 20)] <- NA
tipping_point_solomon(y_post, treat, pretested, y_pre, groups = "treatment",
                      deltas = seq(-10, 10, by = 2.5), m = 10, seed = 1, data = d)
#> Tipping-point analysis for missing posttests (m = 10 per offset)
#> Contrast: ATE (avg over pretest)
#> Offsets added to imputed posttests in: pretested treatment, unpretested treatment
#> Offset scale: pooled within-group SD of observed posttests = 9.3
#> 
#>  Offset Offset (SD) Estimate 95% CI          p    
#>  -10.0  -1.08       1.373    [-1.960, 4.706] 0.416
#>   -7.5  -0.81       1.706    [-1.581, 4.992] 0.306
#>   -5.0  -0.54       2.038    [-1.216, 5.293] 0.217
#>   -2.5  -0.27       2.371    [-0.866, 5.608] 0.149
#>    0.0   0.00       2.704    [-0.531, 5.938] 0.100
#>    2.5   0.27       3.036    [-0.211, 6.284] 0.067
#>    5.0   0.54       3.369    [ 0.094, 6.644] 0.044
#>    7.5   0.81       3.702    [ 0.385, 7.019] 0.029
#>   10.0   1.08       4.034    [ 0.661, 7.408] 0.020
#> 
#> Under MAR (offset 0): p = 0.100, not significant at alpha = 0.05.
#> No change in the conclusion over the negative offsets tried.
#> The conclusion changes at an offset of 5 (0.54 SD).