---
title: "Tutorial: Mini-Meta Delta"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Tutorial: Mini-Meta Delta}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
```

When scientists perform replicates of the same experiment, the effect size of each replicate often varies, which complicates interpretation of the results. This vignette documents how `dabestr` is able to compute the meta-analyzed weighted effect size given multiple replicates of the same experiment. This can help resolve differences between replicates and simplify interpretation.

This function uses the generic _inverse-variance_ method to calculate the effect size, as follows:

$$\theta_{weighted} = \frac{\sum{\hat{\theta_i}}w_i}{\sum{w_i}}$$
where:

$$\hat{\theta_i}=\text{Mean difference for replicate } i$$
$$w_i=\text{Weight for replicate } i = \frac{1}{s_i^2}$$
$$s_i^2=\text{Pooled variance for replicate } i = \frac{(n_{test}-1)s_{test}^2 + (n_{control}-1)s_{control}^2} {n_{test}+n_{control}-2}$$
$$n = \text{sample size and } s^2 = \text{variance for control/test}$$
Note that this uses the _fixed-effects_ model of meta-analysis, as opposed to the random-effects model; that is to say, all variation between the results of each replicate is assumed to be due solely to sampling error. We thus recommend that this function only be used for replications of the same experiment, i.e. situations where it can be safely assumed that each replicate estimates the same population mean $\mu$.

DABEST can only compute weighted effect size for _mean difference only_, and not standardized measures such as Cohen’s d.

For more information on meta-analysis, please refer to Chapter 10 of the Cochrane handbook: https://training.cochrane.org/handbook/current/chapter-10

```{r setup, warning = FALSE, message = FALSE}
library(dabestr)
```

## Create dataset for demo
```{r}
set.seed(12345) # Fix the seed so the results are replicable.
# pop_size = 10000 # Size of each population.
N <- 20 # The number of samples taken from each population

# Create samples
c1 <- rnorm(N, mean = 3, sd = 0.4)
c2 <- rnorm(N, mean = 3.5, sd = 0.75)
c3 <- rnorm(N, mean = 3.25, sd = 0.4)

t1 <- rnorm(N, mean = 3.5, sd = 0.5)
t2 <- rnorm(N, mean = 2.5, sd = 0.6)
t3 <- rnorm(N, mean = 3, sd = 0.75)

# Add a `gender` column for coloring the data.
gender <- c(rep("Male", N / 2), rep("Female", N / 2))

# Add an `id` column for paired data plotting.
id <- 1:N

# Combine samples and gender into a DataFrame.
df <- tibble::tibble(
  `Control 1` = c1, `Control 2` = c2, `Control 3` = c3,
  `Test 1` = t1, `Test 2` = t2, `Test 3` = t3,
  Gender = gender, ID = id
)

df <- df %>%
  tidyr::gather(key = Group, value = Measurement, -ID, -Gender)
```

We now have 3 Control and 3 Test groups, simulating 3 replicates of the same experiment. Our dataset also has a non-numerical column indicating gender, and another column indicating the identity of each observation.

This is known as a ‘long’ dataset. See this [writeup](https://simonejdemyr.com/r-tutorials/basics/wide-and-long/) for more details.

```{r}
knitr::kable(head(df))
```

## Loading Data
Next, we load data as we would normally using `load()`. This time, however, we also specify the argument `minimeta = TRUE` As we are loading three experiments’ worth of data, `idx` is passed as a list of vectors, as follows:

```{r}
unpaired <- load(df,
  x = Group, y = Measurement,
  idx = list(
    c("Control 1", "Test 1"),
    c("Control 2", "Test 2"),
    c("Control 3", "Test 3")
  ),
  minimeta = TRUE
)
```

When this `dabest` object is printed, it should show that effect sizes will be calculated for each group, as well as the weighted delta. Note once again that weighted delta will only be calculated for mean difference.

```{r}
print(unpaired)
```

After applying the `mean_diff()` function to the `dabest` object, you can view the mean differences for each group as well as the weighted delta by printing the `dabest_effectsize_obj`.

```{r}
unpaired.mean_diff <- mean_diff(unpaired)

print(unpaired.mean_diff)
```

You can view the details of each experiment by accessing `dabest_effectsize_obj$boot_results`, as follows. This also contains details of the weighted delta.
```{r}
unpaired.mean_diff$boot_result
```

## Unpaired Data
Simply using the `dabest_plot()` function will produce a **Cumming estimation plot** showing the data for each experimental replicate as well as the calculated weighted delta.

```{r}
dabest_plot(unpaired.mean_diff)
```

You can also hide the weighted delta by passing the argument `show_mini_meta = FALSE`. In this case, the resulting graph would be identical to a multiple two-groups plot:

```{r}
dabest_plot(unpaired.mean_diff, show_mini_meta = FALSE)
```

## Paired Data
The tutorial up to this point has dealt with unpaired data. If your data is paired data, the process for loading, plotting and accessing the data is the same as for unpaired data, except the argument `paired = "sequential"` or `paired = "baseline"` and an appropriate `id_col` are passed during the `load()` step, as follows:

```{r}
paired.mean_diff <- load(df,
  x = Group, y = Measurement,
  idx = list(
    c("Control 1", "Test 1"),
    c("Control 2", "Test 2"),
    c("Control 3", "Test 3")
  ),
  paired = "baseline", id_col = ID,
  minimeta = TRUE
) %>%
  mean_diff()

dabest_plot(paired.mean_diff, raw_marker_size = 0.5, raw_marker_alpha = 0.3)
```