I obtained negative svalues from the lfcShrink function of DESeq2 using the ashr shrinkage estimator.
The values are very small and close to 0: the smallest is -1.110223e-16, the largest negative is -1.199592e-19. Should I set them to zero?

Apart from the analysis that I performed (see code below), should svalue >= 0 in any case or is it expected that in some conditions it is < 0 ?

I used glmGamPoi to fit dispersion and then calculated surrogate variables that I added to the model.
Then, re-estimated the dispersion and performed Wald test and shrinkage with ashr.

dds <- DESeqDataSetFromMatrix(countData = mat, colData = coldata, design = ~ Donor + condition)
dds <- DESeq(dds, betaPrior = F, parallel = T, fitType = "glmGamPoi", sfType = "poscount", minmu = 1e-6)

## compute surrogate variables
rle <- rlog(dds, blind = T)
library(sva)
mod <- model.matrix( ~ Donor + condition, data = coldata)
mod0 <- model.matrix( ~ Donor, data = coldata)
svobj <- sva(dat = assay(rle), mod = mod, mod0 = mod0)
covariates <- svobj$sv
for (n.sv in 1:dim(svobj$sv)[2]) {
    colData(dds)[[paste0("SV", n.sv)]] <- svobj$sv[, n.sv]
}
base.design.factors <- "Donor + condition"
design.formula <- paste0("~ ",
                         paste0(paste0("SV", 1:dim(svobj$sv)[2]),
                                collapse = " + "),
                         " + ",
                         base.design.factors)

## update design formula
design(dds) <- as.formula(design.formula)

## re-estimate disperion
dds <- estimateDispersions(dds, fitType = "glmGamPoi")

## perform test
dds <- nbinomWaldTest(dds, useT = T, minmu = 1e-6, betaPrior = F)

## shrink FC and get svalues
lfc.res <- lfcShrink(dds, contrast = c("condition", "a", "b"), type = "ashr", svalue = T)

dim(lfc.res)
# [1] 6071    4
dim(lfc.res[lfc.res$svalue < 0, ])
# [1] 1957    4

sessionInfo()

R version 4.0.3 (2020-10-10)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Ubuntu 20.04.1 LTS

Matrix products: default
BLAS:   /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.9.0
LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.9.0

locale:
 [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C               LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8     LC_MONETARY=en_US.UTF-8   
 [6] LC_MESSAGES=en_US.UTF-8    LC_PAPER=en_US.UTF-8       LC_NAME=C                  LC_ADDRESS=C               LC_TELEPHONE=C            
[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       

attached base packages:
 [1] grid      parallel  stats4    stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
 [1] corrplot_0.84               DEGreport_1.26.0            dplyr_1.0.2                 tximport_1.18.0             seriation_1.2-9            
 [6] ggpubr_0.4.0                ComplexHeatmap_2.6.2        sva_3.38.0                  genefilter_1.72.0           mgcv_1.8-33                
[11] nlme_3.1-151                BiocParallel_1.24.1         limma_3.46.0                DESeq2_1.30.0               SummarizedExperiment_1.20.0
[16] Biobase_2.50.0              MatrixGenerics_1.2.0        matrixStats_0.57.0          GenomicRanges_1.42.0        GenomeInfoDb_1.26.2        
[21] IRanges_2.24.1              S4Vectors_0.28.1            BiocGenerics_0.36.0         scales_1.1.1                ggsci_2.9                  
[26] ggthemes_4.2.0              RColorBrewer_1.1-2          pheatmap_1.0.12             viridis_0.5.1               viridisLite_0.3.0          
[31] ggrepel_0.9.0               ggplot2_3.3.3               DT_0.17                     data.table_1.13.6           flexdashboard_0.5.2        

loaded via a namespace (and not attached):
  [1] readxl_1.3.1                backports_1.2.1             circlize_0.4.12             plyr_1.8.6                  ConsensusClusterPlus_1.54.0
  [6] splines_4.0.3               digest_0.6.27               foreach_1.5.1               htmltools_0.5.0             magrittr_2.0.1             
 [11] memoise_1.1.0               cluster_2.1.0               openxlsx_4.2.3              annotate_1.68.0             Nozzle.R1_1.1-1            
 [16] colorspace_2.0-0            blob_1.2.1                  haven_2.3.1                 xfun_0.20                   crayon_1.3.4               
 [21] RCurl_1.98-1.2              jsonlite_1.7.2              survival_3.2-7              iterators_1.0.13            glue_1.4.2                 
 [26] registry_0.5-1              gtable_0.3.0                zlibbioc_1.36.0             XVector_0.30.0              GetoptLong_1.0.5           
 [31] DelayedArray_0.16.0         car_3.0-10                  shape_1.4.5                 abind_1.4-5                 DBI_1.1.0                  
 [36] edgeR_3.32.0                rstatix_0.6.0               Rcpp_1.0.5                  xtable_1.8-4                lasso2_1.2-21.1            
 [41] tmvnsim_1.0-2               clue_0.3-58                 foreign_0.8-81              bit_4.0.4                   htmlwidgets_1.5.3          
 [46] httr_1.4.2                  ellipsis_0.3.1              farver_2.0.3                pkgconfig_2.0.3             reshape_0.8.8              
 [51] XML_3.99-0.5                locfit_1.5-9.4              labeling_0.4.2              tidyselect_1.1.0            rlang_0.4.10               
 [56] AnnotationDbi_1.52.0        munsell_0.5.0               cellranger_1.1.0            tools_4.0.3                 generics_0.1.0             
 [61] RSQLite_2.2.2               broom_0.7.3                 evaluate_0.14               stringr_1.4.0               ggdendro_0.1.22            
 [66] yaml_2.2.1                  knitr_1.30                  bit64_4.0.5                 zip_2.1.1                   purrr_0.3.4                
 [71] compiler_4.0.3              rstudioapi_0.13             curl_4.3                    png_0.1-7                   ggsignif_0.6.0             
 [76] tibble_3.0.4                geneplotter_1.68.0          stringi_1.5.3               forcats_0.5.0               lattice_0.20-41            
 [81] Matrix_1.3-2                psych_2.0.12                vctrs_0.3.6                 pillar_1.4.7                lifecycle_0.2.0            
 [86] GlobalOptions_0.1.2         cowplot_1.1.1               bitops_1.0-6                R6_2.5.0                    TSP_1.1-10                 
 [91] gridExtra_2.3               rio_0.5.16                  codetools_0.2-18            MASS_7.3-53                 rjson_0.2.20               
 [96] withr_2.3.0                 mnormt_2.0.2                GenomeInfoDbData_1.2.4      hms_0.5.3                   tidyr_1.1.2                
[101] rmarkdown_2.6               carData_3.0-4               Cairo_1.5-12.2              logging_0.10-108

If I use "local" dispersion fit after adding the surrogate variable, then I obtain no more the negative values, so I am switching to this setting now.

See here for some relevant threads:

https://github.com/stephens999/ashr/issues/117

https://github.com/stephens999/ashr/issues/123

I think he has pushed a fix.