Estimate the empirical conditional cumulative distribution function

Usage

ccdf(
  Y,
  X,
  Z = NULL,
  method = c("OLS", "logistic"),
  fast = TRUE,
  space_y = FALSE,
  number_y = 10
)

Arguments

Y: a numeric vector of size n containing the preprocessed expressions from n samples (or cells).
X: a data frame containing numeric or factor vector(s) of size n containing the variable(s) to be tested (the condition(s) to be tested).
Z: a data frame containing numeric or factor vector(s) of size n containing the covariate(s).
method: a character string indicating which method to use to compute the CCDF, either 'OLS' or 'logistic'. Default is 'OLS' for greater computational speed.
fast: a logical flag indicating whether the fast implementation of logistic regression should be used. Only if method == 'logistic'. Default is TRUE.
space_y: a logical flag indicating whether the y thresholds are spaced. When space_y is TRUE, a regular sequence between the minimum and the maximum of the observations is used. Default is FALSE.
number_y: an integer value indicating the number of y thresholds (and therefore the number of regressions) to perform the test. Only used if space_y is TRUE. Default is 10.

Value

A list with the following elements:

cdf: a vector of the cumulative distribution function of a given gene.
ccdf: a vector of the conditional cumulative distribution function of a given gene, computed given X. Only if Z is NULL.
ccdf_nox: a vector of the conditional cumulative distribution function of a given gene, computed given Z only (i.e. X is ignored.). Only if Z is not NULL.
ccdf_x: a vector of the conditional cumulative distribution function of a given gene, computed given X and Z. Only if Z is not NULL.
y_sort: a vector of the sorted expression points at which the CDF and the CCDFs are calculated.
x_sort: a vector of the variables associated with y_sort.
z_sort: a vector of the covariates associated with y_sort. Only if Z is not NULL.

Details

The space_y / number_y grid controls both the resolution of the statistic and its computational cost. See cit_multi for details on this trade-off.

References

Gauthier M, Agniel D, Thiébaut R & Hejblum BP (2021). Distribution-free complex hypothesis testing for single-cell RNA-seq differential expression analysis, bioRxiv 445165. doi:10.1101/2021.05.21.445165 .

Examples


set.seed(123)
n <- 500
X <- as.factor(rbinom(n = n, size = 1, prob = 0.5))
Y <- ((X == 1) * rnorm(n = n, 0, 1)) + ((X == 0) * rnorm(n = n, 0.5, 1))
res <- ccdf(Y, data.frame(X = X), method = "OLS")