# Composite Scores

    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

    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] 59.34104

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] 200.2961 200.0316 200.0021

Of course, composite conditional scores can also be integrated

    evaluate(expected(cs, datadist, H_1), design)
    #> [1] 59.34104

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] -36.39139 -36.53500 -36.55095

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.