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2_BioPAN_species_case.Rmd
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2_BioPAN_species_case.Rmd
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---
output: html_document
editor_options:
chunk_output_type: console
---
## Active Case
Let us consider the pathway of `PS(42:8)` to `PE(42:8)` to `PC(42:8)`.
The dataset are as follows:
```{r label=Active_Species_Data, fig.height=figheight, fig.width=figwidth, message=FALSE, warning=FALSE, dpi=150}
samples <- c("24h CON", "24h CON", "24h CON",
"24h AA", "24h AA", "24h AA")
group <- c("CON", "CON", "CON",
"AA", "AA", "AA")
PS42_8 <- c(0.039096671, 0.048629063, 0.033723608,
0.047177176, 0.041427748, 0.043042335)
PE42_8 <- c(0.005358486, 0.00509418, 0.00489321,
0.160215808, 0.151076058, 0.166159881)
PC42_8 <- c(0.01543998, 0.015312104, 0.015252706,
1.286319709, 1.083053662, 1.261169034)
active_data <- tibble::tibble(
Sample = samples,
Group = group,
`PS(42:8)` = PS42_8,
`PE(42:8)` = PE42_8,
`PC(42:8)` = PC42_8
)
active_data
```
### `PS(42:8)` to `PE(42:8)`
**Compute the weight for product `PE(42:8)` over reactant `PS(42:8)` for each sample.**
```{r label=weight_vector_PE42_8_over_PS42_8, message=FALSE, warning=FALSE}
weights <- (active_data$`PE(42:8)`/active_data$`PS(42:8)`)
active_data <- active_data %>%
dplyr::mutate(`PE(42:8) over PS(42:8)` = weights)
active_data %>%
dplyr::select(-c(.data$`PC(42:8)`))
```
**Compute a one-sided Welch $t$-test between the samples of interest (Group AA) and the control samples (Group CON).**
```{r label=t.test_PE42_8_over_PS42_8, message=FALSE, warning=FALSE, results='asis'}
aa_samples <- active_data %>%
dplyr::filter(.data$Group == "AA") %>%
dplyr::pull(.data$`PE(42:8) over PS(42:8)`)
control_samples <- active_data %>%
dplyr::filter(.data$Group == "CON") %>%
dplyr::pull(.data$`PE(42:8) over PS(42:8)`)
t1 <- t.test(aa_samples, control_samples, alternative = "greater")
report::report(t1)
cat(paste("$p$ value is", format(t1$p.value, scientific = TRUE, nsmall = 3)))
```
**Convert the $p$ value into a $Z$ Score.**
This is also the pathway score for `PS(42:8)` to `PE(42:8)`.
```{r label=Zscore_PE42_8_over_PS42_8, message=FALSE, warning=FALSE, results='asis'}
z_score1 <- qnorm(1 - t1$p.value)
cat(paste("$Z$ score for `PS(42:8)` to `PE(42:8)` is", format(z_score1, nsmall = 3)))
```
### `PE(42:8)` to `PC(42:8)`
**Compute the weight for product `PC(42:8)` over reactant `PE(42:8)` for each sample.**
```{r label=weight_vector_PC42_8_over_PE42_8, message=FALSE, warning=FALSE}
weights <- (active_data$`PC(42:8)`/active_data$`PE(42:8)`)
active_data <- active_data %>%
dplyr::mutate(`PC(42:8) over PE(42:8)` = weights)
active_data %>%
dplyr::select(-c(.data$`PS(42:8)`,.data$`PE(42:8) over PS(42:8)`))
```
**Compute a one-sided Welch $t$-test between the samples of interest (Group AA) and the control samples (Group CON).**
```{r label=t.test_PC42_8_over_PE42_8, message=FALSE, warning=FALSE, results='asis'}
aa_samples <- active_data %>%
dplyr::filter(.data$Group == "AA") %>%
dplyr::pull(.data$`PC(42:8) over PE(42:8)`)
control_samples <- active_data %>%
dplyr::filter(.data$Group == "CON") %>%
dplyr::pull(.data$`PC(42:8) over PE(42:8)`)
t2 <- t.test(aa_samples, control_samples, alternative = "greater")
report::report(t2)
cat(paste("$p$ value is", format(t2$p.value, scientific = TRUE, nsmall = 3)))
```
**Convert the $p$ value into a $Z$ score.**
This is also the pathway score for `PE(42:8)` to `PC(42:8)`.
```{r label=Zscore_PC42_8_over_PE42_8, message=FALSE, warning=FALSE, results='asis'}
z_score2 <- qnorm(1 - t2$p.value)
cat(paste("$Z$ score for `PE(42:8)` to `PC(42:8)` is", format(z_score2, nsmall = 3)))
```
**Compute $Z_{A}$ for pathway `PS(42:8)` to `PE(42:8)` to `PC(42:8)`.**
Recall the formula is defined as:
where $k$ is 2 and $Z_{i}$ are the pathway scores `PS(42:8)` to `PE(42:8)` and `PE(42:8)` to `PC(42:8)` computed earlier.
```{r label=Zscore_active_pathway, message=FALSE, warning=FALSE, results='asis'}
z_a <- (1/sqrt(2)) * (z_score1 + z_score2)
cat(paste("$Z_{A}$ is", format(z_a, nsmall = 3)))
```
With this settings,
Since $Z_{A} > 1.645$, the pathway is classified as active.
## Suppressed Case
Let us consider the pathway of `PS(32:0)` to `PE(32:0)` to `PC(32:0)`.
The dataset are as follows:
```{r label=Suppressed_Species_Data_1, fig.height=figheight, fig.width=figwidth, message=FALSE, warning=FALSE, dpi=150}
samples <- c("24h CON", "24h CON", "24h CON",
"24h AA", "24h AA", "24h AA")
group <- c("CON", "CON", "CON",
"AA", "AA", "AA")
PS32_0 <- c(0.11392858, 0.080762026, 0.128541348,
0.656895224, 0.800790573, 0.592724899)
PE32_0 <- c(0.046063214, 0.043759251, 0.047335343,
0.175927791, 0.183855506, 0.194325215)
PC32_0_1 <- c(1.074150848, 0.726798053, 0.412228743,
1.94494173, 1.520645133, 1.337827826)
PC32_0_2 <- c(0.928888882, 0.964353269, 0.789633482,
1.666428947, 1.375398801, 1.616097007)
suppressed_data <- tibble::tibble(
Sample = samples,
Group = group,
`PS(32:0)` = PS32_0,
`PE(32:0)` = PE32_0,
`PC(32:0) 1` = PC32_0_1,
`PC(32:0) 2` = PC32_0_2
)
suppressed_data
```
BioPAN will give a warning on the duplicated transition `PC(32:0)` and sum them up.
```{r label=Suppressed_Species_Data_2, fig.height=figheight, fig.width=figwidth, message=FALSE, warning=FALSE, dpi=150}
suppressed_data <- tibble::tibble(
Sample = samples,
Group = group,
`PS(32:0)` = PS32_0,
`PE(32:0)` = PE32_0,
`PC(32:0)` = PC32_0_1 + PC32_0_2
)
suppressed_data
```
### `PS(32:0)` to `PE(32:0)`
**Compute the weight for product `PE(32:0)` over reactant `PS(32:0)` for each sample.**
```{r label=weight_vector_PE32_0_over_PS32_0, message=FALSE, warning=FALSE}
weights <- (suppressed_data$`PE(32:0)`/suppressed_data$`PS(32:0)`)
suppressed_data <- suppressed_data %>%
dplyr::mutate(`PE(32:0) over PS(32:0)` = weights)
suppressed_data %>%
dplyr::select(-c(.data$`PC(32:0)`))
```
**Compute a one-sided Welch $t$-test between the samples of interest (Group AA) and the control samples (Group CON).**
```{r label=t.test_PE32_0_over_PS32_0, message=FALSE, warning=FALSE, results='asis'}
aa_samples <- suppressed_data %>%
dplyr::filter(.data$Group == "AA") %>%
dplyr::pull(.data$`PE(32:0) over PS(32:0)`)
control_samples <- suppressed_data %>%
dplyr::filter(.data$Group == "CON") %>%
dplyr::pull(.data$`PE(32:0) over PS(32:0)`)
t1 <- t.test(aa_samples, control_samples, alternative = "less")
report::report(t1)
cat(paste("$p$ value is", format(t1$p.value, scientific = TRUE, nsmall = 3)))
```
**Convert the $p$ value into a $Z$ score.**
This is also the pathway score for `PS(32:0)` to `PE(32:0)`.
```{r label=Zscore_PE32_0_over_PS32_0, message=FALSE, warning=FALSE, results='asis'}
z_score1 <- qnorm(1 - t1$p.value)
cat(paste("$Z$ score for`PS(32:0)` to `PE(32:0)` is", format(z_score1, nsmall = 3)))
```
### `PE(32:0)` to `PC(32:0)`
**Compute the weight for product `PC(32:0)` over reactant `PE(32:0)` for each sample.**
```{r label=weight_vector_PC32_0_over_PE32_0, message=FALSE, warning=FALSE}
weights <- (suppressed_data$`PC(32:0)`/suppressed_data$`PE(32:0)`)
suppressed_data <- suppressed_data %>%
dplyr::mutate(`PC(32:0) over PE(32:0)` = weights)
suppressed_data %>%
dplyr::select(-c(.data$`PS(32:0)`,.data$`PE(32:0) over PS(32:0)`))
```
**Compute a one-sided Welch $t$-test between the samples of interest (Group AA) and the control samples (Group CON).**
```{r label=t.test_PC32_0_over_PE32_0, message=FALSE, warning=FALSE, results='asis'}
aa_samples <- suppressed_data %>%
dplyr::filter(.data$Group == "AA") %>%
dplyr::pull(.data$`PC(32:0) over PE(32:0)`)
control_samples <- suppressed_data %>%
dplyr::filter(.data$Group == "CON") %>%
dplyr::pull(.data$`PC(32:0) over PE(32:0)`)
t2 <- t.test(aa_samples, control_samples, alternative = "less")
report::report(t2)
cat(paste("$p$ value is", format(t2$p.value, scientific = TRUE, nsmall = 3)))
```
**Convert the $p$ value into a $Z$ score.**
This is also the pathway score for `PE(32:0)` to `PC(32:0)`.
```{r label=Zscore_PC32_0_over_PE32_0, message=FALSE, warning=FALSE, results='asis'}
z_score2 <- qnorm(1 - t2$p.value)
cat(paste("$Z$ score for `PE(32:0)` to `PC(32:0)` is", format(z_score2, nsmall = 3)))
```
**Compute $Z_{A}$ for pathway `PS(32:0)` to `PE(32:0)` to `PC(32:0)`.**
Recall the formula is defined as:
where $k$ is 2 and $Z_{i}$ are the pathway scores `PS(32:0)` to `PE(32:0)` and `PE(32:0)` to `PC(32:0)` computed earlier.
```{r label=Zscore_suppressed_pathway, message=FALSE, warning=FALSE, results='asis'}
z_a <- (1/sqrt(2)) * (z_score1 + z_score2)
cat(paste("$Z_{A}$ is", format(z_a, nsmall = 3)))
```
With this settings,
Since $Z_{A} > 1.645$, the pathway is classified as suppressed.