Simulate from the non-longitudinal mixture model.

```
hb_sim_mixture(
n_study = 5,
n_group = 3,
n_patient = 100,
n_continuous = 0,
n_binary = 0,
s_delta = 1,
s_beta = 1,
s_sigma = 1,
m_omega = 0,
s_omega = 1,
p_omega = 1/n_study,
alpha = omega[pi],
delta = stats::rnorm(n = n_group - 1, mean = 0, sd = s_delta),
beta = stats::rnorm(n = n_continuous + n_binary, mean = 0, sd = s_delta),
sigma = stats::runif(n = 1, min = 0, max = s_sigma),
pi = sample.int(n = n_study, size = 1, prob = p_omega),
omega = stats::rnorm(n = n_study, mean = m_omega, sd = s_omega)
)
```

- n_study
Number of studies to simulate.

- n_group
Number of groups (e.g. study arms) to simulate per study.

- n_patient
Number of patients to simulate per study per group.

- n_continuous
Number of continuous covariates to simulate (all from independent standard normal distributions).

- n_binary
Number of binary covariates to simulate (all from independent Bernoulli distributions with p = 0.5).

- s_delta
Numeric of length 1, prior standard deviation of the study-by-group effect parameters

`delta`

.- s_beta
Numeric of length 1, prior standard deviation of the fixed effects

`beta`

.- s_sigma
Numeric of length 1, prior upper bound of the residual standard deviations.

- m_omega
Numeric of length 1 or

`n_study`

, prior control group mean of each study. If length`n_study`

, then the last element corresponds to the current study, and the others are for historical studies.- s_omega
Numeric of length 1 or

`n_study`

, prior control group standard deviation of each study. If length`n_study`

, the the last element corresponds to the current study, and the others are for historical studies.- p_omega
Numeric of length

`n_study`

, prior mixture proportion of each study. If length`n_study`

, then the last element corresponds to the current study, and the others are for historical studies.- alpha
Numeric vector of length 1 for the pooled and mixture models and length

`n_study`

for the independent and hierarchical models.`alpha`

is the vector of control group mean parameters.`alpha`

enters the model by multiplying with`$matrices$x_alpha`

(see the return value). The control group in the data is the one with the`group`

column equal to 1.- delta
Numeric vector of length

`n_group - 1`

of treatment effect parameters.`delta`

enters the model by multiplying with`$matrices$x_delta`

(see the return value). The control (non-treatment) group in the data is the one with the`group`

column equal to 1.- beta
Numeric vector of

`n_continuous + n_binary`

fixed effect parameters. The first`n_continuous`

betas are for the continuous covariates, and the rest are for the binary covariates.`betas`

enters the model by multiplying with`$matrices$x_alpha`

(see the return value).- sigma
Numeric vector of

`n_study`

study-specific residual standard deviations.- pi
Integer of length 1, index of the mixture component randomly chosen for

`alpha`

.- omega
Numeric of length

`n_study`

, Candidate placebo mean parameters drawn from each of the mixture components.

A list with the following elements:

`data`

: tidy long-form dataset with the patient-level data. one row per patient and indicator columns for the study, group (e.g. treatment arm), and patient ID. The`response`

columns is the patient response. The other columns are baseline covariates. The control group is the one with the`group`

column equal to 1, and the current study (non-historical) is the one with the maximum value of the`study`

column. Only the current study has any non-control-group patients, the historical studies have only the control group.`parameters`

: named list of model parameter values. See the model specification vignette for details.`matrices`

: A named list of model matrices. See the model specification vignette for details.

Other simulate:
`hb_sim_hierarchical()`

,
`hb_sim_independent()`

,
`hb_sim_pool()`

```
hb_sim_mixture()$data
#> # A tibble: 300 × 4
#> study group patient response
#> <int> <int> <int> <dbl>
#> 1 1 1 1 0.920
#> 2 1 1 2 0.678
#> 3 1 1 3 1.03
#> 4 1 1 4 1.08
#> 5 1 1 5 0.606
#> 6 1 1 6 0.859
#> 7 1 1 7 0.774
#> 8 1 1 8 0.844
#> 9 1 1 9 0.963
#> 10 1 1 10 0.641
#> # … with 290 more rows
```