nbinomWaldTest {DESeq2} | R Documentation

## Wald test for the GLM coefficients

### Description

This function tests for significance of coefficients in a Negative Binomial GLM, using previously calculated `sizeFactors` (or `normalizationFactors`) and dispersion estimates. See `DESeq` for the GLM formula.

### Usage

    nbinomWaldTest(
      object,
      betaPrior = FALSE,
      betaPriorVar,
      modelMatrix = NULL,
      modelMatrixType,
      betaTol = 1e-08,
      maxit = 100,
      useOptim = TRUE,
      quiet = FALSE,
      useT = FALSE,
      df,
      useQR = TRUE,
      minmu = 0.5
    )

### Arguments

`object` | a DESeqDataSet
`betaPrior` | whether or not to put a zero-mean normal prior on the non-intercept coefficients
`betaPriorVar` | a vector with length equal to the number of model terms including the intercept. betaPriorVar gives the variance of the prior on the sample betas on the log2 scale. if missing (default) this is estimated from the data
`modelMatrix` | an optional matrix, typically this is set to NULL and created within the function
`modelMatrixType` | either "standard" or "expanded", which describe how the model matrix, X of the formula in `DESeq`, is formed. "standard" is as created by `model.matrix` using the design formula. "expanded" includes an indicator variable for each level of factors in addition to an intercept. betaPrior must be set to TRUE in order for expanded model matrices to be fit.
`betaTol` | control parameter defining convergence
`maxit` | the maximum number of iterations to allow for convergence of the coefficient vector
`useOptim` | whether to use the native optim function on rows which do not converge within maxit
`quiet` | whether to print messages at each step
`useT` | whether to use a t-distribution as a null distribution, for significance testing of the Wald statistics. If FALSE, a standard normal null distribution is used. See next argument `df` for information about which t is used. If `useT=TRUE` then further calls to `results` will make use of `mcols(object)$tDegreesFreedom` that is stored by `nbinomWaldTest`.
`df` | the degrees of freedom for the t-distribution. This can be of length 1 or the number of rows of `object`. If this is not specified, the degrees of freedom will be set by the number of samples minus the number of columns of the design matrix used for dispersion estimation. If `"weights"` are included in the `assays(object)`, then the sum of the weights is used in lieu of the number of samples.
`useQR` | whether to use the QR decomposition on the design matrix X while fitting the GLM
`minmu` | lower bound on the estimated count while fitting the GLM

### Details

The fitting proceeds as follows: standard maximum likelihood estimates for GLM coefficients (synonymous with "beta", "log2 fold change", "effect size") are calculated. Then, optionally, a zero-centered Normal prior distribution (`betaPrior`) is assumed for the coefficients other than the intercept.

Note that this posterior log2 fold change estimation is now not the default setting for `nbinomWaldTest`, as the standard workflow for coefficient shrinkage has moved to an additional function `link{lfcShrink}`.

For calculating Wald test p-values, the coefficients are scaled by their standard errors and then compared to a standard Normal distribution. The `results` function without any arguments will automatically perform a contrast of the last level of the last variable in the design formula over the first level. The `contrast` argument of the `results` function can be used to generate other comparisons.

The Wald test can be replaced with the `nbinomLRT` for an alternative test of significance.

Notes on the log2 fold change prior:

The variance of the prior distribution for each non-intercept coefficient is calculated using the observed distribution of the maximum likelihood coefficients. The final coefficients are then maximum a posteriori estimates using this prior (Tikhonov/ridge regularization). See below for details on the prior variance and the Methods section of the DESeq2 manuscript for more detail. The use of a prior has little effect on genes with high counts and helps to moderate the large spread in coefficients for genes with low counts.

The prior variance is calculated by matching the 0.05 upper quantile of the observed MLE coefficients to a zero-centered Normal distribution. In a change of methods since the 2014 paper, the weighted upper quantile is calculated using the `wtd.quantile` function from the Hmisc package (function has been copied into DESeq2 to avoid extra dependencies). The weights are the inverse of the expected variance of log counts, so the inverse of 1/mu-bar + alpha_tr using the mean of normalized counts and the trended dispersion fit. The weighting ensures that noisy estimates of log fold changes from small count genes do not overly influence the calculation of the prior variance. See `estimateBetaPriorVar`. The final prior variance for a factor level is the average of the estimated prior variance over all contrasts of all levels of the factor.

When a log2 fold change prior is used (betaPrior=TRUE), then `nbinomWaldTest` will by default use expanded model matrices, as described in the `modelMatrixType` argument, unless this argument is used to override the default behavior. This ensures that log2 fold changes will be independent of the choice of reference level. In this case, the beta prior variance for each factor is calculated as the average of the mean squared maximum likelihood estimates for each level and every possible contrast.

### Value

a DESeqDataSet with results columns accessible with the `results` function. The coefficients and standard errors are reported on a log2 scale.

### See Also

`DESeq`, `nbinomLRT`

### Examples

    dds <- makeExampleDESeqDataSet()
    dds <- estimateSizeFactors(dds)
    dds <- estimateDispersions(dds)
    dds <- nbinomWaldTest(dds)
    res <- results(dds)

[Package DESeq2 version 1.32.0 Index]