---
title: "LTFGRS Workflow: Prepare Genetic Liability for Multi-Trait Prediction"
author: "Emil Pedersen"
date: "`r Sys.Date()`"
output: html_document
vignette: >
  %\VignetteIndexEntry{LTFGRS Workflow: Prepare Genetic Liability for Multi-trait prediction}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```

**This vignette is heavily inspired by and re-uses code from the "LTFGRS Workflow: Prepare Genetic Liability for Prediction" vignette.**
***All data is simulated and is purely for demonstration purposes - This includes the CIP.***


This vignette is intended to give users of the package an overview of how to use the different functions of the package and how they are intended to work together to calculate a multi-trait genetic liability. The liability-based predictors can be used for prediction and as the outcome in a GWAS. If you want a refined outcome to be used in GWAS, please see the vignette titled "LTFGRS Workflow: Prepare Genetic Liability for multi-trait GWAS". This vignette focuses on preparing for prediction. This purpose requires the user to consider additional steps, such as censoring of future events and masking the outcome of the target individual. The vignette will cover the following steps:

- Simulate mock trio, phenotype, and CIP data
- Convert mock trio and phenotype data into a format suitable for estimate_liability()
  - Automatic identification of n-degree relatives
  - Censoring of future events on a family basis
  - Assign thresholds on censored families
  - Assign thresholds to family graphs
- Estimate the liability-based predictors using estimate_liability()
  - Both Gibbs and PA based estimators will be covered
  
  
First, we load the required packages.
```{r, results = 'hide',warning = FALSE, message = FALSE}
library(LTFGRS)
library(dplyr)
library(lubridate)
library(rmarkdown)
library(stringr)
```



## Simulate mock trio, phenotype, and CIP data
We will set some population parameters for the simulation. The parameters are as follows:
```{r}
set.seed(555)
Ntrait = 3 # number of traits to consider
h2_vec = rep(0.5, Ntrait) # heritability
corMat = matrix(0.3, nrow = Ntrait, ncol = Ntrait) # genetic correlation matrix
diag(corMat) = 1
K = .3 # population prevalence
all_outcomes = paste0("disorder_", c("1", "2", "3")) # disorder names
```



### Cumulative incidence proportions (CIP)
One of the key required input variables of LTFGRS is the population representative stratified cumulative incidence proportions (CIP) data. LTFGRS is able to utilise the population representative stratified CIPs to personalise thresholds for the liability-based predictors. The CIPs are typically obtained from large population registers or other sources that allow for population representative estimates. Here, we simulate a format similar to how stratified CIPs may be stored. We assume the CIPs have been stratified by sex and birth year. The population representative stratified CIPs has the interpretation of being the proportion of individuals born in a given year and sex that has been diagnosed with the outcome of interest by age $x$.

```{r}
# assuming we have been provided a CIP object of the following style:
CIP = expand.grid(list(age = 1:100,
                       birth_year = 1900:2024,
                       sex = 0:1)) %>%
  group_by(sex, birth_year) %>%
  mutate(cip = (1:n() - 1)/n() * K) %>%
  ungroup() %>% 
  print(n = 10)
```

Since we are simulating multiple phenotypes, we need a CIP for each phenotype. We can create a list of CIPs for each phenotype as follows:

```{r}
# creating dummy CIP list for multiple traits
CIP_list = lapply(1:Ntrait, function(i) {
  CIP
})
```
When applying to real data, the order of the CIPs should match the order of the phenotypes in the phenotype data. This is important for the function `prepare_thresholds_multi()` to correctly match the CIPs to the phenotypes.

  
### Trio information
The trio information presented here is a manually constructed to resemble a typical way the trio data may be stored. The names are chosen such that they resemble the relationship to the proband. This means there are simple names such as "dad", "mom", or "sib". There are also more complex names such as "pgf" for paternal grand father, "muncle" for maternal uncle, "hsmcousin" for half-sibling maternal cousin, etc. The suffixes "H" and "W" mean husband and wife, respectively.

```{r}
# hand curated trio information, taken from LTFHPlus vignette:
# https://emilmip.github.io/LTFHPlus/articles/FromTrioToFamilies.html
family = tribble(
  ~id, ~momcol, ~dadcol,
  "pid", "mom", "dad",
  "sib", "mom", "dad",
  "mhs", "mom", "dad2",
  "phs", "mom2", "dad",
  "mom", "mgm", "mgf",
  "dad", "pgm", "pgf",
  "dad2", "pgm2", "pgf2",
  "paunt", "pgm", "pgf",
  "pacousin", "paunt", "pauntH",
  "hspaunt", "pgm", "newpgf",
  "hspacousin", "hspaunt", "hspauntH",
  "puncle", "pgm", "pgf",
  "pucousin", "puncleW", "puncle",
  "maunt", "mgm", "mgf",
  "macousin", "maunt", "mauntH",
  "hsmuncle", "newmgm", "mgf",
  "hsmucousin", "hsmuncleW", "hsmuncle"
)
```


### Phenotype data
We will simulate a liability based on the family structure defined above to assign a case-control outcome to each individual. Then other covariates such as sex and age are randomly assigned. To get the case-control status, we first generate a (population) graph, calculate a kinship matrix based on the heritability, genetic correlation, and kinship coefficient, and finally, draw liabilities from a multivariate normal with the calculated kinship matrix as covariance matrix. However, since it is a multi-trait application, the covariance matrix derived from the trio information is $N_{trait}$ times larger in all directions compared to a single-trait application.

```{r}

# creating a graph for the family
graph = prepare_graph(.tbl = family, icol = "id", mcol = "momcol", fcol = "dadcol")
# calculating the kinship matrix based on the graph
cov_mat_obj = graph_based_covariance_construction_multi(
  fid = "fam",
  pid = "pid",
  cur_proband_id = "pid",
  cur_family_graph = graph,
  h2_vec = h2_vec,
  genetic_corrmat = corMat,
  useMixture = FALSE,
  phen_names = c("1", "2", "3"),
  add_ind = TRUE)

# creating a phenotype for the family
liabs = MASS::mvrnorm(n = 1, mu = rep(0, nrow(cov_mat_obj$cov)), Sigma = cov_mat_obj$cov)
```


```{r}
pheno = tibble(
  id = names(liabs),
  status = liabs > qnorm(K, lower.tail = F),
  # no consideration for generation etc in sex, fdato or birth_year:
  sex = rep(sample(0:1, size = length(liabs)/Ntrait, replace = TRUE), Ntrait),
  fdato = rep(dmy(paste0(sample(1:28, length(liabs)/Ntrait, replace = T), "/", sample(1:12, length(liabs)/Ntrait, replace = T), "/", sample(1940:2000, length(liabs)/Ntrait, replace = T))), Ntrait),
  birth_year = year(fdato),
  # age of onset only after fdato
  disorder = purrr::map2_chr(.x = status, .y = birth_year,
                         ~ if(.x) paste0(sample(1:28, 1), "/", sample(1:12, 1), "/", sample((.y + 1):2010, 1)) else NA),
  # end of follow up assigned here
  indiv_eof = dmy("31/12/2010")) %>% # blanket time stop, meant to simulate end of registers
  mutate(
    # converting to date format
    disorder = dmy(disorder),
    # eof either blanket time stop or event date
    indiv_eof = pmin(indiv_eof, disorder, na.rm = T)) %>% 
  filter(str_detect(id, "pid_g", negate = T)) %>%   # remove the genetic liability of the proband
  # status is not required here. Only used it to generate the age of diagnosis.
  select(-contains("status"))
paged_table(pheno)
```

An isolated look at one individual shows the additional information we have on an individual compared to single-trait:

```{r}
pheno %>% filter(str_detect(id, "pid"))
```

Next, we format the phenotype data into a format that can be derived from most biobanks or electronic health records. The format is such that each row is an individual and columns specify information on that individual. Phenotype specific information follow the naming convention of `<base_string>_<disorder_name>`. For example, `age_eof_disorder_1` is the age at end of follow up for disorder 1.

```{r}
# helper function - from: https://stackoverflow.com/questions/7963898/extracting-the-last-n-characters-from-a-string-in-r
substrRight <- function(x, n){
  substr(x, nchar(x)-n+1, nchar(x))
}
pheno = pheno %>%
  mutate(trait = substrRight(id, 1),
         id = substr(id, 1, nchar(id) - 2)) %>%
  tidyr::pivot_wider(names_from = trait,
                     values_from = c(disorder, indiv_eof),
                     names_glue = "{.value}_{trait}")
# sorting out names, such that they follow the required pattern with suffix ending in one of the disorder names:
colnames(pheno)[-(1:7)] = str_replace_all(colnames(pheno)[-(1:7)], 
                                          c("_1" = "_disorder_1", 
                                            "_2" = "_disorder_2", 
                                            "_3" = "_disorder_3"))
```
The formatted phenotype data can be inspected below:
```{r}
paged_table(pheno)
```

## Preparing for `estimate_liability()`

In a real world scenario, we will not have access to all of the information used above. We will assume that the objects `CIP_list`, `family`, and `pheno` are the only information available to the user. These objects hold information that can often be extracted from population registers or bio banks.

- `CIP_list`: The `CIP_list` object carry information about the prevalence all considered outcomes of interest in the population and therefore also on how each participant fits into the population distribution. 
- `family`: The `family` object holds the trio information, i.e. information about the family structure and how each individual is related to each other. In a real world scenario this object may contains millions of unique individuals.
- `pheno`: The `pheno` object holds phenotypic information on each individual present in the trio information and on each outcome being considered.


### Population graph
With the `family` object, which holds the trio information, we can construct a population graph. The population graph holds all familial connects identified in the trio information and will form the basis of how families are identified. In real-world applications, the population graph may contain millions of individuals.
We generate the (population) graph 
```{r}
graph = prepare_graph(.tbl = family, 
                      icol = "id",
                      mcol = "momcol", 
                      fcol = "dadcol")
```


### Automatic identification of n-degree relatives

When we want to calculate a family genetic risk score, we need to create a pedigree based on the proband and relations should be relative to the proband. We are interested in identifying all family members up to some degree of relatedness, $n$, without having to manually find all of these family members. Manually identifying family members up to degree $4$ is both time consuming and error prone. We have implemented an automatic detection of family members that utilise a graph based on all individuals in the trio information (ideally population registers) and neighbourhood graphs. In short, we create a pedigree (directed graph) with every individual in the trio data and copy sections around a proband with all individuals that are $n$ steps away from the proband in the graph (This is a neighbourhood graphs of degree n, here called a family graph).

```{r}
# Identify family members of degree n
family_graphs = get_family_graphs(pop_graph = graph,
                                  ndegree = 1,
                                  proband_vec = pheno$id,
                                  fid = "fid",
                                  fam_graph_col = "fam_graph")
family_graphs %>% print(n = 4)
```


### Censoring of future events on a family basis

The purpose of the genetic liability estimated here is prediction. In epidemiology (and many other fields) there is an emphasis on ensuring future events are not used to base predictions on. Hence, we need to ensure that, within a family, no events that happen after the end of follow up of the proband is used to estimate the genetic liability of the proband. In real world analysis, the end of follow up can be due to the proband being diagnosed or any censoring event, such as end of register follow up, emigration, or death.
   The function `familywise_censoring_multi()` is a wrapper function around `familywise_censoring()`. It applied the the proband's end of follow up to all family members and all outcomes. As such, it offers a way to censor future events on a family basis, by censoring all events that happen after the end of follow up of the proband (`indiv_eof`) of the **target outcome**, specified with the `target outcome` argument.

```{r}
# calculate family specific thresholds

info = familywise_censoring_multi(
  family_graphs = family_graphs,
  tbl = pheno %>% rename(pid = id),
  start = "fdato",
  end_base = "indiv_eof",
  phen_names = all_outcomes,
  target_outcome = "disorder_1",
  status_col_base = "status",
  aod_col_base = "aod",
  age_eof_col_base = "age_eof",
  fam_graph_col = "fam_graph",
  fid = "fid",
  pid = "pid",
  simplify = TRUE # simplifies output by removing all columns not specific to an outcome.
)

paged_table(info)
```
The simplified return of function `familywise_censoring_multi()` will return a tibble with the following additional columns for **each outcome**, following the naming convention of `<base_string>_<disorder_name>`. The end of follow-up applied across a family (and all disorders) is the one specified by `target_outcome`. Hence, events that happen in the proband for a different outcome than the `target_outcome`, but before the end of follow-up for the `target_outcome`, will not be censored. The columns generated for a given outcome are as follows:

- `status`: Assigned case-control status based on the family-wise censoring time, i.e. if the event happened after the end of follow up of the family, the status is set to `FALSE` (0).
- `aod`: The age of diagnosis, NA for controls.
- `age`: The age at the end of the family-wise follow up.

The above information is used to calculate the personalised thresholds for each individual while also accounting for the fact that each family may have differing levels of information available to them. 

### Assign thresholds to censored families

Once the `status`, `aod`, and `age` are known for each outcome, we can assign thresholds to each family and their family members. Notably, this means that if an individual appears in multiple families, e.g. as a proband and as a relative to a different proband, that individual may have multiple (potentially different) thresholds assigned to them. The use of `fid` and `pid` helps ensure that each individual can still be uniquely identified.

   Due to data privacy, it is possible to encounter CIPs values that are only provided at set values, e.g. a CIP value for each whole year by birth year and sex, such as what is shown in with the `CIP` object. However, the observed ages (or age of diagnosis) are typically not integer values. This means we may need to approximate the CIP values between the provided values. We offer an XGboost based approach to interpolate the CIPs between the provided values.


```{r}
# thresholds: personalised, fixed upper and lower threshold
multi_thrs = prepare_thresholds_multi(
  .tbl = info,
  CIP_list = CIP_list, 
  phen_names = all_outcomes, 
  personal_thr = TRUE, 
  lower_equal_upper = TRUE
)

```

Note: Currently, it is possible to experience negative ages at the end of follow up. This is due to the family-wise end of follow up ending before an individual is born, e.g. proband is diagnosed in their youth, then has a child later in life. These individuals will get a non-informative threshold ($-\infty$ to max of `min_CIP_value` and the predicted CIP [`K_i`]). In other words, these individuals will have no impact on the estimate.

The function `prepare_thresholds_multi()` is a wrapper around `prepare_thresholds()` and as such handles the application of `prepare_thresholds()` and formatting of its result into one tibble. The columns generated for a given outcome follow the naming convention of `<base_string>_<disorder_name>`. `prepare_thresholds()` has several options that are worth pointing out. The first is `lower_equal_upper`, which is used to determine if the `upper` and `lower` thresholds should be the same for cases or not. This may be useful if the CIP values are considered very accurate, as it may lead to more accurate genetic liability estimates. The second is `personal_thr`, which specifies if thresholds should be based on `K_i` or `K_pop`. Basing the thresholds on `K_i` yields personalised thresholds that are based on the stratification of the CIPs. With the argument `Kpop`, it is possible to determine how the `K_pop` values are calculated. The current default option for `Kpop` is `"useMax`, which calculates `K_pop` as the maximum within each strata provided in the CIPs. Alternatively, a tibble can be provided with the `Kpop` argument, which shares columns with `.tbl`, e.g. sex, such that user-specific `K_pop` values can be specified.

The function `prepare_thresholds_multi()` will return a tibble with the following additional columns for **each outcome**, following the naming convention of `<base_string>_<disorder_name>`:

- `K_i`: The CIP value for the individual. `K_i` is predicted if interpolation is used.
- `K_pop`: The population prevalence. Currently calculated as the maximum CIP value within the CIP stratum an individual belongs to, e.g. for a male born in $2000$, `K_pop` is the maximum CIP value observed among males born in the year $2000$. Alternatively, acquired user-specified values through the `Kpop` argument.
- `thr`: The liability threshold used to determine case-control status. `thr` is used to determine the upper and lower thresholds of an individual.
- `lower`: lower threshold of an individual.
- `upper`: upper threshold of an individual.

If the mixture model is not used to calculate the genetic liability, only `lower` and `upper` are needed.

```{r}
paged_table(multi_thrs)
```


### Assign thresholds to family graphs

The function `estimate_liability()` can use the family graphs to calculate all necessary values for the genetic liability, if the thresholds are stored as attributes in the family graphs. We can attach the thresholds from `multi_thrs` to `family_graphs` with the function `familywise_attach_attributes()`. The function merges on the `fid` column and attaches any columns in `fam_attr` that are specified in `cols_to_attach`. Since the purpose of the genetic liability we are estimating is prediction, we do not wish to use the information from the proband. We mask the proband's information by setting column with `upper` and `lower` in their name to $\infty$ and $-\infty$ (non-informative values) and all other values to be `NA`. The argument `proband_cols_to_censor` can then be used to censor a subset or all columns. If columns with `K_i` or `K_pop` in the name are in `proband_cols_to_censor`, they will be set to `NA`, which are uninformative in the PA algorithm and will not be problematic. 

```{r}
# attach family specific thresholds
ltfgrs_input = familywise_attach_attributes(
  family_graphs = family_graphs,
  fam_attr = multi_thrs,
  fam_graph_col = "fam_graph",
  attached_fam_graph_col = "masked_fam_graph",
  cols_to_attach = str_subset(colnames(multi_thrs), "lower|upper|K_i|K_pop"),
  proband_cols_to_censor = str_subset(colnames(multi_thrs), "lower|upper|K_i|K_pop"))
ltfgrs_input %>% print(n = 4)
```
The format is similar to the one used in `get_family_graphs()`. It is worth noting that the argument `proband_cols_to_censor` is only required if the purpose of the resulting genetic liability is prediction. 


```{r}
ltfgrs_input$masked_fam_graph[[1]]
```
The second row of the igraph (starting with "+attr:") shows the attributes that are available to each node in the graph.

**OBS:** There is one important decision to make. When calculating a genetic liability for prediction, we do not want to use future events to predict past events and we do not want to use the proband's information to predict the proband's genetic liability. Hence, we need to censor the proband's information and all information that happens after the end of follow up of the proband. This is done with the `proband_cols_to_censor` argument in `familywise_attach_attributes()`. 
However, with the introduction of multiple traits, it opens the opportunity to perform familywise_censoring with respect to a `target_outcome`, where events in the secondary outcomes (not the one chosen for `target_outcome`) has events in the proband. There are currently no clear guidelines on whether these events should be censored or not. If the events are not censored, it may lead to more accurate genetic liability estimates, but it may also lead to information leakage or information that is very closely tied to the target outcome. A cautious approach would be to censor all events in the proband, including all events in the secondary outcomes. It may lead to less accurate genetic liability estimates. The decision on whether to censor these events or not is left to the discretion of the user. In the example above, all information on the proband is censored.




## Estimating genetic liabilities with `estimate_liability()`

The function `estimate_liability()` is used to estimate the genetic liability. The function accepts two types of input, here we will only focus on the graph-based input generated above. The graph-based input offer the best flexibility and scalability. The function has two arguments that are worth pointing out. 

The first is `method`, which specifies the estimation method used to estimate the genetic liability. Currently, two methods are supported. The first is a Gibbs sampler that samples from a truncated multivariate normal distribution, `method = "Gibbs"`. The second is an iterative Pearson-Aitken approach, `method = "PA"`. Generally speaking, the Pearson-Aitken approach is faster.
   
The second argument is `useMixture`, which specifies whether to use the mixture model or not. The mixture model is currently only supported with `method = "PA"`. The mixture model considers the genetic liability of controls as a mixture of the truncated normal for cases and controls, rather than just the distribution of controls. This accounts for the possibility that some controls are undiagnosed cases and accounts for it in the genetic liability estimate.


### FGRS with personalised threshold and PA
```{r}
ltfgrs_pa = estimate_liability(family_graphs = ltfgrs_input,
                                h2 = h2_vec,
                               genetic_corrmat = corMat,
                               full_corrmat = diag(Ntrait),
                               phen_names = all_outcomes,
                               fid = "fid",
                               pid = "pid",
                               family_graphs_col = "masked_fam_graph",
                               method = "PA", # <- METHOD
                               target_phenotype = "disorder_1",
                               useMixture = F)
paged_table(ltfgrs_pa)
```
When using `method = "PA"`, an iterative conditioning is performed, which means the resulting estimate and uncertainty of the estimate is the expected mean value and variance of the last iteration, which is the proband's genetic liability. This is highlighted by the use of `var` in the output.

***OBS:*** The PA estimation approach currently only supports returning a genetic liability estimate for one of the provided outcomes at a time. The disorder that is returned in specified with the argument `target_phenotype`. The Gibbs sampling approach will return a genetic liability estimate for all provided outcomes at the same time. This means that if you want to get a genetic liability estimate for multiple outcomes, you will need to run the PA estimation approach multiple times, once for each outcome, while the Gibbs sampling approach can be run once to get estimates for all outcomes at the same time.



### FGRS with personalised threshold and Gibbs
```{r}
ltfgrs_gibbs = estimate_liability(family_graphs = ltfgrs_input,
                                  h2 = h2_vec,
                                  genetic_corrmat = corMat,
                                  full_corrmat = diag(Ntrait),
                                  phen_names = all_outcomes,
                                  fid = "fid",
                                  pid = "pid",
                                  family_graphs_col = "masked_fam_graph",
                                  method = "Gibbs", # <- METHOD
                                  useMixture = F)
paged_table(ltfgrs_gibbs)
```
When using `method = Gibbs`, samples are drawn from a truncated multivariate normal distribution until the convergence criteria is met. The output is the mean of genetic liability and the uncertainty is the standard error of the mean. The standard error is denoted with the `se` in the column name. Notably, the uncertainties with the Gibbs and PA methods are different and should not be directly compared.


### FGRS with mixture model

The mixture model is currently only supported with the PA estimation method. The mixture model considers the genetic liability of controls as a mixture of the truncated normal for cases and controls, rather than just the distribution of controls. This accounts for the possibility that some controls are undiagnosed cases and accounts for it in the genetic liability estimate. Below is a full run of preparation for a mixture model application. In the data preparation steps, set `personal_thr = FALSE` and `lower_equal_upper = FALSE` when calculating thresholds. Make sure the `K_i` and `K_pop` are attached to the family graph too. Finally, set `useMixture = TRUE` in `estimate_liability()`.
```{r message=FALSE, warning=FALSE}
# creating a graph for the family with mixture model thresholds
graph_mixture = prepare_graph(.tbl = family, 
                              icol = "id",
                              mcol = "momcol",
                              fcol = "dadcol")

# Identify family members of degree n
family_graphs_mixture = get_family_graphs(pop_graph = graph_mixture,
                                          ndegree = 1,
                                          proband_vec = pheno$id,
                                          fid = "fid",
                                          fam_graph_col = "fam_graph")


info_mixture = familywise_censoring_multi(
  family_graphs = family_graphs_mixture,
  tbl = pheno %>% rename(pid = id),
  start = "fdato",
  end_base = "indiv_eof",
  phen_names = all_outcomes,
  target_outcome = "disorder_1",
  status_col_base = "status",
  aod_col_base = "aod",
  age_eof_col_base = "age_eof",
  fam_graph_col = "fam_graph",
  fid = "fid",
  pid = "pid",
  simplify = TRUE # simplifies output by removing all columns not specific to an outcome.
)


# thresholds: personalised, fixed upper and lower threshold
multi_thrs_mixture = prepare_thresholds_multi(
  .tbl = info_mixture, 
  CIP_list = CIP_list, 
  phen_names = all_outcomes, 
  personal_thr = FALSE, #<--
  lower_equal_upper = FALSE #<---
)


# attaching familywise censored thresholds to family graphs
ltfgrs_input = familywise_attach_attributes(
  family_graphs = family_graphs_mixture,
  fam_attr = multi_thrs_mixture,
  fam_graph_col = "fam_graph",
  attached_fam_graph_col = "masked_fam_graph_mixture",
  cols_to_attach = str_subset(colnames(multi_thrs), "lower|upper|K_i|K_pop"), #<-- includes K_i and K_pop
  proband_cols_to_censor = str_subset(colnames(multi_thrs), "lower|upper|K_i|K_pop")) #<--


PA_MT_mix = estimate_liability(family_graphs = ltfgrs_input,
                               family_graphs_col = "masked_fam_graph_mixture",
                               h2 = h2_vec,
                               genetic_corrmat = corMat,
                               phen_names = all_outcomes,
                               full_corrmat = diag(Ntrait),
                               target_phenotype = "disorder_1", 
                               useMixture = TRUE)#<-- using mixture model
paged_table(PA_MT_mix)
```


### Parallelisation 
The function `estimate_liability()` is able to use the `future` package to parallelise the estimation of the genetic liability. This is done by setting a suitable `plan` with the future backend. A plan suitable for most needs is `plan(multisession, workers = NCORES)`, which means that the function will run in parallel on the local PC utilising `NCORES`-cores. Other parallelisation options exist, but they are all handled by the future suit of packages.
