---
title: "cellmig: quantifying cell migration speed with 
hierarchical Bayesian models"
author: "Simo Kitanovski (simo.kitanovski@uni-due.de)"
output:
  BiocStyle::html_document
vignette: >
  %\VignetteEncoding{UTF-8}
  %\VignetteIndexEntry{User Manual: cellmig}
  %\VignetteEngine{knitr::rmarkdown}
editor_options: 
  markdown: 
    wrap: 72
---

```{r setup, include = FALSE, warning = FALSE}
knitr::opts_chunk$set(comment = FALSE, 
                      warning = FALSE, 
                      message = FALSE)
```

```{r}
library(cellmig)
library(ggplot2)
library(ggforce)
ggplot2::theme_set(new = theme_bw(base_size = 10))
```

# Background

High-throughput tracking of cells with time-lapse microscopy enables the
analysis of cell migration across many wells treated under different
conditions. Such experiments generate substantial technical and biological
variability, making technical and biological replicates necessary. This
leads to hierarchically structured datasets: cells are nested within
technical replicates, which in turn are nested within biological replicates.

Most current statistical analyses ignore the hierarchical structure and
do not explicitly quantify uncertainty from technical or biological
variability. The Bioconductor package `r Biocpkg("cellmig")` addresses this
gap by implementing Bayesian hierarchical models for cell migration
analysis. It quantifies condition-specific changes in migration speed
(e.g., drug effects) while modeling nested data structures, producing
uncertainty-aware estimates through credible intervals.

Currently, there are no other Bioconductor packages specialized 
for hierarchical high-throughput cell migration data analysis. 
`r Biocpkg("cellmig")` addresses this gap and integrates naturally into 
the Bioconductor ecosystem.


# Installation
To install this package, start R (version "4.5") and enter:

```{r, eval=FALSE}
if (!require("BiocManager", quietly = TRUE))
    install.packages("BiocManager")

BiocManager::install("cellmig")
```


# Data

This is how a typical cell migration data looks like $\rightarrow$ a
table.

Each row is a **cell** with the following features:

-   well = unique well ID (w1, w2, w3, etc.).
-   plate = unique plate ID (p1, p2, p3, etc.). Each plate is a
    biological replicate. A plate contains multiple wells, some of which
    are treated with the same compound and dose (technical replicates)
-   compound = compound name (c1, c2, c3, etc.)
-   dose = compound concentration (0, 1, 5, 10, low, mid, high, etc.)
-   v = Observed cell migration speed (numeric) in micrometers per minute
-   offset = binary (0 or 1). Indicates whether a treatment should be
    used for batch correction across plates. By default offset = 0 (no
    correction). Set to 1 for specific treatment groups (compound x
    dose) used as offsets. Ensure that this treatment group appears on
    each plate.

```{r}
data("d", package = "cellmig")
str(d)
```

In this vignette we will use simulated data from:

-   **plates** ($p$): 1, 2, ... , 3
-   **wells** ($w$): 1, 2, ... , 378
-   **cells** per well with their migration speed `v`
-   wells are treated with **compounds** 1, 2, ..., 6 at **dose** 1, 2,
    ..., 7.
-   combination of a compound and dose is a **treatment group** ($t$)
    $\rightarrow$ 1, 2, ..., 42.


# Visualizing raw cell speed

Each dot represents a cell; y-axis is velocity. Facets represent compounds,
x-axis represents dose. Plate is indicated by color. Technical replicates
(wells) are stacked next to each other and have the same color.

```{r, fig.width=7, fig.height=6}
ggplot(data = d)+
  facet_wrap(facets = ~paste0("compound=", compound), 
             scales = "free_y", ncol = 2)+
  geom_sina(aes(x = as.factor(dose), col = plate, y = v, group = well), 
            size = 0.5)+
  theme_bw()+
  theme(legend.position = "top",
        strip.text.x = element_text(margin = margin(0.03,0,0.03,0, "cm")))+
  ylab(label = "migration speed")+
  xlab(label = '')+
  scale_color_grey()+
  guides(color = guide_legend(override.aes = list(size = 3)))+
  guides(shape = guide_legend(override.aes = list(size = 3)))+
  scale_y_log10()+
  annotation_logticks(base = 10, sides = "l")
```

## **Mean migration speed** per well

VIsualizing mean speed within wells highlights plate-specific batch effects.

```{r, fig.width=7, fig.height=6}
dm <- aggregate(v~well+plate+compound+dose, data = d, FUN = mean)
ggplot(data = dm)+
  facet_wrap(facets = ~paste0("compound=", compound), 
             scales = "free_y", ncol = 2)+
  geom_sina(aes(x = as.factor(dose), col = plate, y = v, group = well), 
            size = 1.5, alpha = 0.7)+
  theme_bw()+
  theme(legend.position = "top",
        strip.text.x = element_text(margin = margin(0.03,0,0.03,0, "cm")))+
  ylab(label = "migration speed")+
  xlab(label = '')+
  scale_color_grey()+
  guides(color = guide_legend(override.aes = list(size = 3)))+
  guides(shape = guide_legend(override.aes = list(size = 3)))+
  scale_y_log10()+
  annotation_logticks(base = 10, sides = "l")
```

# `cellmig` analysis

We will use this data to infer the **overall treatment effects**
(parameter $\delta_t$), relative to a control treatment (the offset) to
correct for plate-specific batch effects. At the same time,
`r Biocpkg("cellmig")` will quantify many different features of the data
using its model parameters (e.g., variability between technical or
biological replicates; or plate-specific treatment effects
($\gamma_{pt}$)).

## Model fitting

We fit the Stan model employed by `r Biocpkg("cellmig")` with the
control parameters defined in the list `control`. There are many other
input parameters in `control`, check the `cellmig` function documentation.

```{r, fig.width=7, fig.height=3.5}
o <- cellmig(x = d,
             control = list(mcmc_warmup = 300, # nr. of MCMC warmup step?
                            mcmc_steps = 1000, # nr. of MCMC iteration steps?
                            mcmc_chains = 2,   # nr. of MCMC chains
                            mcmc_cores = 2))   # nr. of MCMC cores
```

## What are the **overall treatment effects** ($\delta_t$) on speed?

To extract the means, medians, and 95% Highest Density Intervals (HDIs,
quantifying parameter value uncertainty) of $\delta_t$, we have to
access the data.frame `delta_t` in the output object `posteriors`:

```{r}
str(o$posteriors$delta_t)
```


## Visualizing $\delta_t$

It is better to visualize the mean $\delta_t$s and their 95% HDIs

-   Dot: Posterior mean of $\delta_t$
-   Error bar: 95% highest density interval (HDI) of $\delta$
-   $\exp(\delta)$: Fold change in cell speed relative to control

As compound t=1 was selected as control (by setting offset=1), the
treatment effects of this compounds are not shown.

```{r, fig.width=6, fig.height=3.3}
ggplot(data = o$posteriors$delta_t)+
  geom_line(aes(x = dose, y = mean, col = compound, group = compound))+
  geom_point(aes(x = dose, y = mean, col = compound))+
  geom_errorbar(aes(x = dose, y = mean, ymin = X2.5., ymax = X97.5., 
                    col = compound), width = 0.1)+
  ylab(label = expression("Overall treatment effect ("*delta*")"))+
  theme(legend.position = "top")
```

## Dose-response `profiles`

For "rectangular datasets", i.e. datasets with multiple compounds and
overlapping doses, we can study the treatment dose-response profiles by
hierarchical clustering based on the complete posteriors of $\delta_t$,
account for uncertainty in this parameter.

Panel A: dendrogram constructed by hierarchical clustering with average
linkage, based on euclidean distances between vectors of $\delta_t$
(shown in panel B) of each compound (leaf) across doses. Branch support
values show branch robustness (label = 1000 implies this branch was
encountered in each of the 1000 dendrograms constructed from the
posterior of $\delta_t$). Plate-specific treatment dose-responses based
on parameters $\gamma_pt$.

-   Dot in panel B/C: Posterior mean of $\delta_t$ and $\gamma_pt$
-   Error bar: 95% highest density interval (HDI)

```{r, fig.width=9.5, fig.height=5}
get_dose_response_profile(x = o, exponentiate = TRUE)+
  patchwork::plot_layout(widths = c(.7, 1, 4))
```

## Pairwise comparisons of treatment effects

Pairwise dot-plot comparison $\rightarrow$ x minus y axis

(Left panel) Differences in overall treatment effects. Log fold change
(LFC; described by parameter $\rho_{ij}$) between overall treatments
effects ($\delta_t$) of row ($i$) vs. column ($j$) treatment groups.
Tile colors and labels represent $\rho_{ij}$. (Right panel) Probability
of differential treatment effect described by parameter $\pi_{ij}$. Tile
colors and labels represent $\pi_{ij}$.

-   x/y-axis treatment groups (combinations of compounds and doses)
-   $\rho$: Difference between treatment groups at y-x axis.
-   $\pi$: probability of observing either a completely positive or
    negative $\rho$

```{r, fig.width=14, fig.height=6}
u <- get_pairs(x = o, exponentiate = FALSE)
u$plot
```

## Violin plots of pairwise differences

-   from_groups: vector of treatment groups to consider (combinations of
    compounds and doses)
-   to_group: target treatment group
-   violins show the posterior distributions of the differences ($\rho$:
    each element from `from_groups` vs. `to_group`).
-   label: probability, $\pi$, of observing completely positive or
    negative $\rho$

```{r, fig.width=7, fig.height=2.5}
str(get_groups(x = o))
```


```{r, fig.width=7, fig.height=2.5}
u <- get_violins(x = o, 
                 from_groups = get_groups(x = o)$group,
                 to_group = "C2|D1",
                 exponentiate = FALSE)
u$plot
```

## Posterior predictive checks (PPCs)

### Compare simulated data to observed data at the **cell level**
To assess model validity, we performed posterior predictive checks,
which showed that the simulated data (pink violin) were consistent with
the observed data (black violins). Each dot is a cell.

```{r, fig.width=6, fig.height=6}
g <- get_ppc_violins(x = o, wrap = TRUE, ncol = 3)
g+scale_y_log10()
```

### Compare mean velocity per well
Using posterior predictive checks we compared the mean simulated
speed per well (y-axis) with the observed mean per well (x-axis).
Each dot is a well.

```{r, fig.width=4, fig.height=4}
g <- get_ppc_means(x = o)
g
```

## Other model parameters

```{r, fig.height=2, fig.width=6}
g_alpha_p <- ggplot(data = o$posteriors$alpha_p)+
  geom_errorbarh(aes(y = plate_id, x = mean, xmin = X2.5., xmax = X97.5.),
                 height = 0.1)+
  geom_point(aes(y = plate_id, x = mean))

g_sigma <- ggplot()+
  geom_errorbarh(data = o$posteriors$sigma_bio,
                 aes(y = "sigma_bio",
                     x = mean, xmin = X2.5., xmax = X97.5.),
                 height = 0.1)+
  geom_errorbarh(data = o$posteriors$sigma_tech,
                 aes(y = "sigma_tech",
                     x = mean, xmin = X2.5., xmax = X97.5.),
                 height = 0.1)+
  geom_point(data = o$posteriors$sigma_bio,
             aes(y = "sigma_bio", x = mean))+
  geom_point(data = o$posteriors$sigma_tech,
             aes(y = "sigma_tech", x = mean))+
  ylab(label = '')

g_alpha_p|g_sigma
```

# Session Info

```{r}
sessionInfo()
```
