# Composite Scores

While adopt also allows implementation of custom scores via
subclassing, for most applications a simple point-wise arithmetic on
scores is sufficient. For instance, consider the case of a utility
maximizing approach to planning where not a hard constraint on power but
rather a trade-off between power and expected sample size is required.
The simplest utility function would just be a weighted sum of both power
(negative weight since we minimize costs!) and expected sample size.

Consider the following situation

```
H_0 <- PointMassPrior(.0, 1)
H_1 <- PointMassPrior(.2, 1)
datadist <- Binomial(.1, two_armed = FALSE)
ess <- ExpectedSampleSize(datadist, H_1)
power <- Power(datadist, H_1)
toer <- Power(datadist, H_0)
```

Adoptr supports such `CompositeScores`

via the
`composite`

function:

`objective <- composite({ess - 50*power})`

The new unconditional score can be evaluated as usual, e.g.

```
design <- TwoStageDesign(
n1 = 100,
c1f = .0,
c1e = 2.0,
n2_pivots = rep(150, 5),
c2_pivots = sapply(1 + adoptr:::GaussLegendreRule(5)$nodes, function(x) -x + 2)
)
evaluate(objective, design)
#> [1] 50.16813
```

Note that conditional and unconditional scores cannot be mixed in an
expression passed to `composite`

. Composite conditional
score, however, are possible as well.

```
cp <- ConditionalPower(datadist, H_1)
css <- ConditionalSampleSize()
cs <- composite({css - 50*cp})
```

```
evaluate(cs, design, c(0, .5, 1))
#> [1] 200.0014 200.0003 200.0001
```

Of course, composite conditional scores can also be integrated

```
evaluate(expected(cs, datadist, H_1), design)
#> [1] 50.16813
```

and (due to linearity) the result is exactly the same as before.

## Functional Composition

Composite scores are not restricted to linear operations but support
any valid numerical expression:

```
cs <- composite({log(css) - 50*sin(cp)})
evaluate(cs, design, c(0, .5, 1))
#> [1] -36.55135 -36.55192 -36.55205
```

Even control flow is supported:

```
cs <- composite({
res <- 0
for (i in 1:3) {
res <- res + css
}
res
})
evaluate(cs, design, c(0, .5, 1))
#> [1] 750 750 750
```

The only real constraint is that the expression must be
vectorized.