---
title: "Composite Scores"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Composite Scores}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse   = TRUE,
  comment    = "#>",
  fig.width  = 7,
  fig.height = 5
)
```

```{r setup}
library(adoptr)
```



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 betweem 
power and expected sample size is required.
The simplest utility function would just be a weightes sum of both
power (negative weight since we minimize costs!) and expected
sample size.

Consider the following situation
```{r}
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:
```{r sum}
objective <- composite({ess - 50*power})
```

The new unconditional score can be evaluated as usual, e.g.
```{r}
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)
```

Note that conditional and unconditional scores cannot be mixed in an 
expression passed to `composite`. 
Composite conditional score, however, are possible as well.
```{r}
cp  <- ConditionalPower(datadist, H_1)
css <- ConditionalSampleSize()

cs  <- composite({css - 50*cp})
```

```{r}
evaluate(cs, design, c(0, .5, 1))
```

Of course, composite conditional scores can also be integrated
```{r}
evaluate(expected(cs, datadist, H_1), design)
```
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:
```{r}
cs <- composite({log(css) - 50*sin(cp)})
evaluate(cs, design, c(0, .5, 1))
```
Even control flow is supported:
```{r}
cs <- composite({
  res <- 0
  for (i in 1:3) {
    res <- res + css
  }
  res
})
evaluate(cs, design, c(0, .5, 1))
```
The only real constraint is that the expression must be vectorized.
