Last updated: 2020-03-14

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Rmd 909764a jhsiao999 2020-03-14 add anova results post batch correction
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Rmd 060d627 jhsiao999 2020-01-12 correct for C1 batch effect in fluorescence intensities


Introduction/summary

We fit the following model to estimate individual effect \(\gamma_i\) and C1 plate effect \(\beta_j\) in fluorescence intensities. In notation,

\[ y_{ijk} = \mu + \tau_i + \beta_j + \epsilon_{ijk} \] where \(i = 1,2,..., I\) and \(j = 1,2,..., J\). The parameters are estimated under sum-to-zero constraints \(\sum \tau_i = 0\) and \(\sum \beta_j = 0\).

Note that in this model 1) not all \(y_{ij.}\) exists due to the incompleteness of the design, 2) the effects of individual and block are nonorthogonal, 3) the effects are additive due to the block design.

We found significant C1 plate effect in fluorescence intensities and corrected for this effect in GFP, RFP and DAPI channels. The corrected estimates are computed as

\[ \hat{y}_{ijk} = y_{ijk} - \hat{\beta}_j \] for all channels.

Data and packages

library(data.table)
library(dplyr)
library(ggplot2)
library(cowplot)
library(RColorBrewer)
library(scales)
library(car)
library(lsmeans)
library(SingleCellExperiment)

Read in filtered data.

sce <- readRDS(file="data/sce-final.rds")
cdata <- data.frame(colData(sce))
rdata <- data.frame(rowData(sce))

Estimate source of variation

Statistical tests show that for GFP, there’s significant plate effect (corresponds to experiment variable, P-value < 2E-16) but not significant individual effect (corresponds to chip_id varialbe).

lm.rfp <- lm(rfp.median.log10sum~factor(chip_id)+factor(experiment),
             data = cdata)
lm.gfp <- lm(gfp.median.log10sum~factor(chip_id)+factor(experiment),
             data = cdata)
lm.dapi <- lm(dapi.median.log10sum~factor(chip_id)+factor(experiment),
             data = cdata)

aov.lm.rfp <- Anova(lm.rfp, type = "III")
aov.lm.gfp <- Anova(lm.gfp, type = "III")
aov.lm.dapi <- Anova(lm.dapi, type = "III")
aov.lm.rfp
Anova Table (Type III tests)

Response: rfp.median.log10sum
                    Sum Sq  Df  F value    Pr(>F)    
(Intercept)        134.171   1 572.0156 < 2.2e-16 ***
factor(chip_id)      2.446   5   2.0860 0.0650143 .  
factor(experiment)   9.396  15   2.6706 0.0005482 ***
Residuals          203.362 867                       
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
aov.lm.gfp
Anova Table (Type III tests)

Response: gfp.median.log10sum
                    Sum Sq  Df   F value  Pr(>F)    
(Intercept)        209.745   1 2011.7679 < 2e-16 ***
factor(chip_id)      1.285   5    2.4657 0.03136 *  
factor(experiment)  12.352  15    7.8984 < 2e-16 ***
Residuals           90.393 867                      
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
aov.lm.dapi
Anova Table (Type III tests)

Response: dapi.median.log10sum
                    Sum Sq  Df   F value  Pr(>F)    
(Intercept)        219.276   1 6110.5970 < 2e-16 ***
factor(chip_id)      0.424   5    2.3621 0.03836 *  
factor(experiment)  11.582  15   21.5164 < 2e-16 ***
Residuals           31.112 867                      
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Visualize indivdual and plate variation

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Estimate plate

Contrast test to estimate the effect of C1 plate.

# make contrast matrix for plates
# each plate is compared to the average
n_plates <- uniqueN(cdata$experiment)
contrast_plates <- matrix(-1, nrow=n_plates, ncol=n_plates)
diag(contrast_plates) <- n_plates-1


gfp.plates <- summary(lsmeans(lm.gfp, specs="experiment", contrast=contrast_plates))
rfp.plates <- summary(lsmeans(lm.rfp, specs="experiment", contrast=contrast_plates))
dapi.plates <- summary(lsmeans(lm.dapi, specs="experiment", contrast=contrast_plates))

Substract plate effect from the raw estimates.

## RFP
cdata$rfp.median.log10sum.adjust <- cdata$rfp.median.log10sum
rfp.plates$experiment <- as.character(rfp.plates$experiment)
cdata$experiment <- as.character(cdata$experiment)

exps <- unique(cdata$experiment)
for (i in 1:uniqueN(exps)) {
  exp <- exps[i]
  ii_exp <- which(cdata$experiment == exp)
  est_exp <- rfp.plates$lsmean[which(rfp.plates$experiment==exp)]
  cdata$rfp.median.log10sum.adjust[ii_exp] <- (cdata$rfp.median.log10sum[ii_exp] - est_exp)
}


## GFP
cdata$gfp.median.log10sum.adjust <- cdata$gfp.median.log10sum
gfp.plates$experiment <- as.character(gfp.plates$experiment)
cdata$experiment <- as.character(cdata$experiment)

exps <- unique(cdata$experiment)
for (i in 1:uniqueN(exps)) {
  exp <- exps[i]
  ii_exp <- which(cdata$experiment == exp)
  est_exp <- gfp.plates$lsmean[which(gfp.plates$experiment==exp)]
  cdata$gfp.median.log10sum.adjust[ii_exp] <- (cdata$gfp.median.log10sum[ii_exp] - est_exp)
}


## DAPI
cdata$dapi.median.log10sum.adjust <- cdata$dapi.median.log10sum
dapi.plates$experiment <- as.character(dapi.plates$experiment)
cdata$experiment <- as.character(cdata$experiment)

exps <- unique(cdata$experiment)
for (i in 1:uniqueN(exps)) {
  exp <- exps[i]
  ii_exp <- which(cdata$experiment == exp)
  est_exp <- dapi.plates$lsmean[which(dapi.plates$experiment==exp)]
  cdata$dapi.median.log10sum.adjust[ii_exp] <- (cdata$dapi.median.log10sum[ii_exp] - est_exp)
}

Visualize intensities after adjusting for C1 plate effect.

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Analysis of variation on data after correcting for plate effect shows that plate effect is no longer a significant contributor of variation in fluorescence intensity.

lm.rfp.adjust <- lm(rfp.median.log10sum.adjust~factor(chip_id)+factor(experiment),
             data = cdata)
lm.gfp.adjust <- lm(gfp.median.log10sum.adjust~factor(chip_id)+factor(experiment),
             data = cdata)
lm.dapi.adjust <- lm(dapi.median.log10sum.adjust~factor(chip_id)+factor(experiment),
             data = cdata)

aov.lm.rfp <- Anova(lm.rfp, type = "III")
aov.lm.gfp <- Anova(lm.gfp, type = "III")
aov.lm.dapi <- Anova(lm.dapi, type = "III")
aov.lm.rfp
Anova Table (Type III tests)

Response: rfp.median.log10sum
                    Sum Sq  Df  F value    Pr(>F)    
(Intercept)        134.171   1 572.0156 < 2.2e-16 ***
factor(chip_id)      2.446   5   2.0860 0.0650143 .  
factor(experiment)   9.396  15   2.6706 0.0005482 ***
Residuals          203.362 867                       
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
aov.lm.gfp
Anova Table (Type III tests)

Response: gfp.median.log10sum
                    Sum Sq  Df   F value  Pr(>F)    
(Intercept)        209.745   1 2011.7679 < 2e-16 ***
factor(chip_id)      1.285   5    2.4657 0.03136 *  
factor(experiment)  12.352  15    7.8984 < 2e-16 ***
Residuals           90.393 867                      
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
aov.lm.dapi
Anova Table (Type III tests)

Response: dapi.median.log10sum
                    Sum Sq  Df   F value  Pr(>F)    
(Intercept)        219.276   1 6110.5970 < 2e-16 ***
factor(chip_id)      0.424   5    2.3621 0.03836 *  
factor(experiment)  11.582  15   21.5164 < 2e-16 ***
Residuals           31.112 867                      
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
R version 3.5.1 (2018-07-02)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Scientific Linux 7.4 (Nitrogen)

Matrix products: default
BLAS/LAPACK: /software/openblas-0.2.19-el7-x86_64/lib/libopenblas_haswellp-r0.2.19.so

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

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

other attached packages:
 [1] SingleCellExperiment_1.4.1  SummarizedExperiment_1.12.0
 [3] DelayedArray_0.8.0          BiocParallel_1.16.0        
 [5] matrixStats_0.55.0          Biobase_2.42.0             
 [7] GenomicRanges_1.34.0        GenomeInfoDb_1.18.1        
 [9] IRanges_2.16.0              S4Vectors_0.20.1           
[11] BiocGenerics_0.28.0         lsmeans_2.30-0             
[13] emmeans_1.3.0               car_3.0-2                  
[15] carData_3.0-2               scales_1.0.0               
[17] RColorBrewer_1.1-2          cowplot_0.9.4              
[19] ggplot2_3.2.1               dplyr_0.8.0.1              
[21] data.table_1.12.0          

loaded via a namespace (and not attached):
 [1] splines_3.5.1          assertthat_0.2.1       GenomeInfoDbData_1.2.0
 [4] cellranger_1.1.0       yaml_2.2.0             pillar_1.3.1          
 [7] backports_1.1.2        lattice_0.20-38        glue_1.3.0            
[10] digest_0.6.20          promises_1.0.1         XVector_0.22.0        
[13] colorspace_1.3-2       sandwich_2.5-0         plyr_1.8.4            
[16] htmltools_0.3.6        httpuv_1.4.5           Matrix_1.2-17         
[19] pkgconfig_2.0.3        haven_1.1.2            zlibbioc_1.28.0       
[22] purrr_0.3.2            xtable_1.8-4           mvtnorm_1.0-11        
[25] whisker_0.3-2          openxlsx_4.1.0         later_0.7.5           
[28] rio_0.5.10             git2r_0.26.1           tibble_2.1.1          
[31] TH.data_1.0-9          withr_2.1.2            lazyeval_0.2.1        
[34] survival_2.43-1        magrittr_1.5           crayon_1.3.4          
[37] readxl_1.1.0           estimability_1.3       evaluate_0.12         
[40] fs_1.3.1               MASS_7.3-51.1          forcats_0.3.0         
[43] foreign_0.8-71         tools_3.5.1            hms_0.4.2             
[46] multcomp_1.4-8         stringr_1.3.1          munsell_0.5.0         
[49] zip_1.0.0              compiler_3.5.1         rlang_0.4.0           
[52] grid_3.5.1             RCurl_1.95-4.11        labeling_0.3          
[55] bitops_1.0-6           rmarkdown_1.10         gtable_0.2.0          
[58] codetools_0.2-15       abind_1.4-5            curl_3.2              
[61] R6_2.4.0               zoo_1.8-4              knitr_1.20            
[64] workflowr_1.6.0        rprojroot_1.3-2        stringi_1.2.4         
[67] Rcpp_1.0.3             tidyselect_0.2.5       coda_0.19-2           

sessionInfo()
R version 3.5.1 (2018-07-02)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Scientific Linux 7.4 (Nitrogen)

Matrix products: default
BLAS/LAPACK: /software/openblas-0.2.19-el7-x86_64/lib/libopenblas_haswellp-r0.2.19.so

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

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

other attached packages:
 [1] SingleCellExperiment_1.4.1  SummarizedExperiment_1.12.0
 [3] DelayedArray_0.8.0          BiocParallel_1.16.0        
 [5] matrixStats_0.55.0          Biobase_2.42.0             
 [7] GenomicRanges_1.34.0        GenomeInfoDb_1.18.1        
 [9] IRanges_2.16.0              S4Vectors_0.20.1           
[11] BiocGenerics_0.28.0         lsmeans_2.30-0             
[13] emmeans_1.3.0               car_3.0-2                  
[15] carData_3.0-2               scales_1.0.0               
[17] RColorBrewer_1.1-2          cowplot_0.9.4              
[19] ggplot2_3.2.1               dplyr_0.8.0.1              
[21] data.table_1.12.0          

loaded via a namespace (and not attached):
 [1] splines_3.5.1          assertthat_0.2.1       GenomeInfoDbData_1.2.0
 [4] cellranger_1.1.0       yaml_2.2.0             pillar_1.3.1          
 [7] backports_1.1.2        lattice_0.20-38        glue_1.3.0            
[10] digest_0.6.20          promises_1.0.1         XVector_0.22.0        
[13] colorspace_1.3-2       sandwich_2.5-0         plyr_1.8.4            
[16] htmltools_0.3.6        httpuv_1.4.5           Matrix_1.2-17         
[19] pkgconfig_2.0.3        haven_1.1.2            zlibbioc_1.28.0       
[22] purrr_0.3.2            xtable_1.8-4           mvtnorm_1.0-11        
[25] whisker_0.3-2          openxlsx_4.1.0         later_0.7.5           
[28] rio_0.5.10             git2r_0.26.1           tibble_2.1.1          
[31] TH.data_1.0-9          withr_2.1.2            lazyeval_0.2.1        
[34] survival_2.43-1        magrittr_1.5           crayon_1.3.4          
[37] readxl_1.1.0           estimability_1.3       evaluate_0.12         
[40] fs_1.3.1               MASS_7.3-51.1          forcats_0.3.0         
[43] foreign_0.8-71         tools_3.5.1            hms_0.4.2             
[46] multcomp_1.4-8         stringr_1.3.1          munsell_0.5.0         
[49] zip_1.0.0              compiler_3.5.1         rlang_0.4.0           
[52] grid_3.5.1             RCurl_1.95-4.11        labeling_0.3          
[55] bitops_1.0-6           rmarkdown_1.10         gtable_0.2.0          
[58] codetools_0.2-15       abind_1.4-5            curl_3.2              
[61] R6_2.4.0               zoo_1.8-4              knitr_1.20            
[64] workflowr_1.6.0        rprojroot_1.3-2        stringi_1.2.4         
[67] Rcpp_1.0.3             tidyselect_0.2.5       coda_0.19-2