# Non-binary Treatment Specification

#### 2024-10-29

Source:`vignettes/non-binary-treatment.Rmd`

`non-binary-treatment.Rmd`

## Binary Treatment

When creating a Design, handling binary treatment variables is
straightforward. If the treatment variable is either
`numeric`

with only values 0/1, or is `logical`

,
then `lmitt()`

will estimate a treatment effect of the
difference between the outcome in the treated group (`1`

or
`TRUE`

) versus the control group (`0`

or
`FALSE`

).

### Missing treatment status

In all cases (binary and non-binary), missing values are allowed and
any units of assignment with missing treatment values are excluded from
models fit via `lmitt()`

.

## Non-binary Treatment

However, the `_design()`

functions can take in any (reasonable) form of treatment assignment.

If the treatment variable is a `numeric`

with non-binary
values, it is treated as a continuous treatment effect and
`lmitt(y ~ 1, ...`

will estimate a single coefficient on
treatment.

If the treatment variable is a `character`

, it is treated
as a multi-level treatment variable and `lmitt(y ~ 1, ...`

will estimate treatment effects against a reference category. The
reference category is the first level defined according to R’s comparison of
characters.

`factor`

and `ordered`

objects are tricky to
deal with, so while a `Design`

can be created with
`factor`

or `ordered`

treatment variables,
`lmitt()`

will refuse to estimate a model unless it is also
provided a `dichotomy`

(see below).

### Dichotomzing a Non-binary Treatment

Studies may offer treatment to units at different times or provide
treatment to units in varying intensities. Researchers may be interested
in estimating treatment effects at different times or given a certain
threshold of provided treatment, however. `propertee`

accommodates these wishes by storing the time or intensity of treatment
for treated units in the `Design`

, then
offering a `dichotomy=`

argument to the weights calculation
functions `ett()`

/`ate()`

and the assginment
creation function `assigned()`

A `dichotomy`

is
presented as a formula, where the left-hand side is a logical statement
defining inclusion in the treatment group, and the right-hand side is a
logical statement defining inclusion in the control group. For example,
if `dose`

represents the intensity of a given treatment, we
could set a threshold of 200, say, mg:

`dose > 200 ~ dose <= 200`

All units of assignment with `dose`

above 200 are treated
units, and all units of assignment with `dose`

of 200 or
below are control units.

A `.`

can be used to define either group as the inverse of
the other. For example, the above dichotomy could be defined as either
of

```
dose > 200 ~ .
. ~ dose <= 200
```

Any units of assignment not assigned to either treatment or control
are assumed to have `NA`

for a treatment status and will be
ignored in the estimation of treatment effects.

`dose >= 300 ~ dose <= 100`

In this `dichotomy`

, units of assignment in the range
(100,300) are ignored.

### An Example

```
data(simdata)
table(simdata$dose)
#>
#> 50 100 200 250 300
#> 10 10 10 10 10
des1 <- rct_design(dose ~ uoa(uoa1, uoa2), data = simdata)
summary(des1)
#> Randomized Control Trial
#>
#> Structure Variables
#> --------- ---------
#> Treatment dose
#> Unit of Assignment uoa1, uoa2
#>
#> Number of units per Treatment group:
#> Txt Grp Num Units
#> 50 2
#> 100 2
#> 200 2
#> ...
#> 2 smaller treatment groups excluded.
#> Use `dtable` function to view full results.
```