Pattern-mixture sensitivity analysis over a shift parameter delta

Missingness at random is not testable from the observed data: any value of E[Y | R = 0] is equally consistent with what was seen. A pattern-mixture sensitivity analysis parameterises the departure instead of assuming it away, E[Y | R = 0] = E[Y | R = 1] + delta, so the marginal mean traced over the grid is E[Y](delta) = E[Y|R=1] + (1 - P(R=1)) delta.

Usage

MissinM(Y, R, delta_grid, reference = 0)

Arguments

Y

Outcomes; entries where R is 0 are ignored and may be any placeholder, including NA.

R

Response indicator, 1 where Y is observed.

delta_grid

Shift values to trace.

reference

Value whose crossing defines the tipping point.

Value

List with estimate (mean at delta = 0), means, delta_grid, mar_mean, p_observed, tipping_delta, n_observed, n.

Details

delta = 0 is the MAR answer, recovered exactly. The mean is linear in delta with slope equal to the missingness rate: the analysis is fragile only in proportion to how much data is absent, and with nothing missing no delta can move it.

The TIPPING POINT is the delta at which the mean crosses reference, delta* = (reference - E[Y|R=1]) / P(R=0), so the conclusion can be stated as "the missing units would have to differ by delta* for this to reverse". With nothing missing there is no such delta and the field is NaN, not infinity: the conclusion cannot be tipped at all.

References

Daniels and Hogan (2008), Missing Data in Longitudinal Studies, Chapman and Hall/CRC. The mean and tipping point above are elementary consequences of the shift equation and are stated in full.

Examples

set.seed(4)
Y <- rnorm(100, 5); R <- rbinom(100, 1, 0.7); Y[R == 0] <- NA
m <- MissinM(Y, R, delta_grid = seq(-3, 3, by = 1), reference = 5)
m$means
#> [1] 4.20591 4.51591 4.82591 5.13591 5.44591 5.75591 6.06591