Cut a robust spread above (or below) the dominant mode

The robust form of the conventional positivity rule, the negative population's centre plus k of its standard deviations. The centre is the dominant mode. Its spread is estimated twice, each estimate immune to a different contamination, and the smaller is used, since contamination only ever widens a spread:

Usage

tail_threshold(x, k = 3.5, side = c("upper", "lower"), adjust = 2)

Arguments

x

transformed values.

k

how many robust standard deviations from the mode. Default 3.5.

side

"upper" for a minority-positive marker, "lower" for a marker whose dominant mode is itself the positive population.

adjust

kernel bandwidth multiplier. Default 2.

Value

the cut.

Details

• the MAD of the half the positive tail cannot reach, mirrored about the mode, which a positive tail or shoulder on the cut side cannot inflate;

• the half-width at half maximum of the mode's flank on the cut side, converted to a standard deviation (HWHM / sqrt(2 ln 2)) after removing the kernel's own variance, which a second negative population on the far side cannot inflate. Peak width at half maximum is cytometry's established measure of a population's spread (the half-peak CV).

The second exists because the first fails where the negative cells are themselves two populations with different background, as monocytes and lymphocytes are on PBMC: the mirrored half takes in the second hump and the cut lands past a small positive shoulder, or past every cell. On one sepsis cohort the MAD alone put CD19 beyond every cell in 3 of 30 samples. For a single normal negative the two estimates agree.

NOT openCyto's gate_tail, which places the cut where the density's first derivative, past the reference peak's steepest descent, falls below a tolerance (cytoUtils .cytokine_cutpoint). On a normal negative mode the two land near each other. Under auto_tol the tolerance is 1% of the steepest slope, which a normal reaches 3.57 SD out. The default tol = 0.01 is an absolute slope, so where it cuts depends on the data's units and the population's share: 3.1 SD out of a unit-variance normal holding every event, 2.5 SD at SD 2, 3.6 SD at SD 0.5. The slope rule also depends on the kernel bandwidth; tried on the sepsis cohort it called 55% of one sample's cells Vd2+ at a bandwidth where it found the B cells, and was not adopted.