12  Regressions for many lipids

12.1 Libraries

library(here)
library(tidyverse)
library(broom)
library(ggpmisc)

12.2 Overview lm and ‘broom’ package

d_test <- tibble(InjVol = c(0,0.2, 0.4, 0.6, 0.8,1),
                  Response  = c(12, 23, 34,44, 89, 101)) 
                 
d_test

#> # A tibble: 6 × 2
#>   InjVol Response
#>    <dbl>    <dbl>
#> 1    0         12
#> 2    0.2       23
#> 3    0.4       34
#> 4    0.6       44
#> 5    0.8       89
#> 6    1        101

# Linear model
model <- lm(formula = Response ~ InjVol, data = d_test)

# Get result summary
summary(model)

#> 
#> Call:
#> lm(formula = Response ~ InjVol, data = d_test)
#> 
#> Residuals:
#>        1        2        3        4        5        6 
#>   8.1429   0.4857  -7.1714 -15.8286  10.5143   3.8571 
#> 
#> Coefficients:
#>             Estimate Std. Error t value Pr(>|t|)   
#> (Intercept)    3.857      8.043   0.480  0.65656   
#> InjVol        93.286     13.282   7.024  0.00216 **
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Residual standard error: 11.11 on 4 degrees of freedom
#> Multiple R-squared:  0.925,  Adjusted R-squared:  0.9062 
#> F-statistic: 49.33 on 1 and 4 DF,  p-value: 0.002165

# Get r^2 only
summary(model)$r.squared

#> [1] 0.9249954

# Using broom functions to summarize model results into a table
broom::glance(model) 

#> # A tibble: 1 × 12
#>   r.squared adj.r.squared sigma statistic p.value    df logLik   AIC   BIC
#>       <dbl>         <dbl> <dbl>     <dbl>   <dbl> <dbl>  <dbl> <dbl> <dbl>
#> 1     0.925         0.906  11.1      49.3 0.00216     1  -21.7  49.5  48.9
#> # … with 3 more variables: deviance <dbl>, df.residual <int>, nobs <int>

broom::tidy(model) 

#> # A tibble: 2 × 5
#>   term        estimate std.error statistic p.value
#>   <chr>          <dbl>     <dbl>     <dbl>   <dbl>
#> 1 (Intercept)     3.86      8.04     0.480 0.657  
#> 2 InjVol         93.3      13.3      7.02  0.00216

12.3 Import Datasets

d_orig <- read_csv(here("data/Testdata_Lipidomics_flat_wide_annotated_V1.csv"))

12.4 Prepare Data

# Convert to long format

# Convert to long format
d_long <- d_orig |> 
  pivot_longer(cols = -DataFileName:-InjVol, 
               names_to = "Lipid" , 
               values_to = "Area")

# Get a table with RQCs only and sort by Lipid
d_rqc <- d_long |> 
  filter(QCtype == "RQC") |> 
  arrange(Lipid)

12.5 Run regression for each lipid

In this example a logistic regression is used. The output of glm() is converted to a tidy table using the broom::tidy() function.

model <- as.formula("Area ~ InjVol")

d_res <- d_rqc %>%
  group_by(Lipid) %>%
  nest() %>%
  mutate(
    models = map(data, function(x) lm(model, data = x)), 
    #mandel = map(data, \(x) DCVtestkit::calculate_mandel(x, "InjVol", "Area")),
    #ppa = map(data, \(x) DCVtestkit::calculate_pra_linear(x, "InjVol", "Area")),
    tidy = map(models, function(x) broom::glance(x))) |> 
  unnest(c(tidy)) |> 
  dplyr::select(-data, -models)

# Fix DCVtestkit::calculate_pra_linear currently returning a list instead vector
# d_res$ppa <- unlist(d_res$ppa)

The results contain the combined estimates, errors, and P values for each term for each lipid species.

Lipid	r.squared	adj.r.squared	sigma	statistic	p.value	df	logLik	AIC	BIC	deviance	df.residual	nobs
CE 16:0	0.626274	0.602917	44054.0359	26.81215	0.000092	1	-216.9579	439.9159	442.5870	3.105213e+10	16	18
CE 16:1	0.834197	0.823834	8622.1216	80.50006	0.000000	1	-187.5984	381.1968	383.8679	1.189456e+09	16	18
CE 16:2	0.609873	0.585490	585.7358	25.01226	0.000131	1	-139.1925	284.3850	287.0561	5.489383e+06	16	18
CE 17:0	0.900585	0.894371	1178.0217	144.94082	0.000000	1	-151.7695	309.5390	312.2101	2.220376e+07	16	18
CE 17:1	0.945373	0.941959	1914.1239	276.89543	0.000000	1	-160.5071	327.0142	329.6854	5.862192e+07	16	18
CE 18:0	0.952998	0.950061	8748.1092	324.41314	0.000000	1	-187.8595	381.7190	384.3902	1.224471e+09	16	18
CE 18:1	0.944273	0.940791	522750.3432	271.11631	0.000000	1	-261.4843	528.9686	531.6397	4.372287e+12	16	18
CE 18:1 d7 (ISTD)	0.922337	0.917483	60313.2929	190.01887	0.000000	1	-222.6124	451.2248	453.8959	5.820309e+10	16	18
CE 18:2	0.950589	0.947501	2583852.0035	307.81495	0.000000	1	-290.2471	586.4942	589.1653	1.068207e+14	16	18
CE 18:3	0.767452	0.752918	88635.9222	52.80302	0.000002	1	-229.5421	465.0842	467.7553	1.257012e+11	16	18