122 lines
3.6 KiB
Elixir
122 lines
3.6 KiB
Elixir
defmodule Growth.Calc.ZScore do
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@moduledoc """
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Calculate z-score for a given measurement and the fitted values of Box-Cox by age/height:
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* **power** `t:l/0`
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* **median** `t:m/0`
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* **coefficientof variation** `t:s/0`
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This calculation is described in the [instructions provided by the World Health Organization](https://cdn.who.int/media/docs/default-source/child-growth/growth-reference-5-19-years/computation.pdf).
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## Examples:
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iex> measures =
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...> [
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...> [30, -1.7862, 16.9392, 0.1107],
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...> [14, -1.3592, 20.4951, 0.12579],
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...> [19, -1.6318, 16.049, 0.10038]
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...> ]
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iex> Enum.map(measures, &apply(Growth.Calc.ZScore, :compute, &1))
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[3.35390255606726, -3.7985108865993493, 1.4698319520484722]
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"""
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@typedoc """
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The **power** value in Box-Cox transformation.
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"""
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@type l :: number()
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@typedoc """
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The **median** value in Box-Cox transformation.
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"""
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@type m :: number()
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@typedoc """
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The **coefficient of variation** in Box-Cox transformation.
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"""
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@type s :: number()
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@spec compute(number(), l(), m(), s()) :: Growth.measure()
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@doc """
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Compute the adjusted z-score for a given measurement (`y`) and the Box-Cox values: power (`l`), median (`m`), and
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coefficient of variation (`s`).
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## Examples:
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iex> Growth.Calc.ZScore.compute(30, -1.7862, 16.9392, 0.1107)
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3.35390255606726
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iex> Growth.Calc.ZScore.compute(14, -1.3592, 20.4951, 0.12579)
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-3.7985108865993493
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iex> Growth.Calc.ZScore.compute(19, -1.6318, 16.049, 0.10038)
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1.4698319520484722
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"""
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def compute(nil, _, _, _) do
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nil
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end
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def compute(y, l, m, s) do
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y
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|> raw(l, m, s)
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|> adjust(y, l, m, s)
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end
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@spec raw(number(), l(), m(), s()) :: number()
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@doc """
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Compute the raw z-score for a given measurement (`y`) and the Box-Cox values, power (`l`), median (`m`), and
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coefficient of variation (`s`).
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## Examples
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iex> Growth.Calc.ZScore.raw(30, -1.7862, 16.9392, 0.1107)
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3.2353902101095855
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iex> Growth.Calc.ZScore.raw(14, -1.3592, 20.4951, 0.12579)
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-3.969714730727475
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iex> Growth.Calc.ZScore.compute(19, -1.6318, 16.049, 0.10038)
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1.4698319520484722
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"""
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def raw(y, l, m, s) do
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(:math.pow(y / m, l) - 1) / (s * l)
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end
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@spec adjust(number(), number(), l(), m(), s()) :: number()
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@doc """
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Adjust the raw z-score considering that extreme values, beyond -3 and 3 standard deviation, must be handled differently.
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"""
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def adjust(zscore, y, l, m, s) when zscore > 3 do
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[sd2, sd3, _, _] = cutoffs(l, m, s)
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sd_delta = sd3 - sd2
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3 + (y - sd3) / sd_delta
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end
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def adjust(zscore, y, l, m, s) when zscore < -3 do
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[_, _, sd2, sd3] = cutoffs(l, m, s)
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sd_delta = sd2 - sd3
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-3 + (y - sd3) / sd_delta
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end
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def adjust(zscore, _, _, _, _) do
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zscore
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end
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@spec cutoffs(number(), number(), number()) :: [number()]
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@doc """
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Calculate the standard deviations cutoffs (2, 3, -2, and -3) for a given set of fitted Box-Cox values: power (`l`),
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median (`m`), and coefficient of variation (`s`).
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These cutoffs are used to calculate the adjusted z-score.
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"""
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def cutoffs(l, m, s) do
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Enum.map([2, 3, -2, -3], &measure_at_standard_deviation(&1, l, m, s))
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end
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@spec measure_at_standard_deviation(integer(), number(), number(), number()) :: number()
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@doc """
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Calculate the measure value at a given standard deviation (`sd`), considering the fitted Box-Cox values: power (`l`),
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median (`m`), and coefficient of variation (`s`).
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"""
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def measure_at_standard_deviation(sd, l, m, s) do
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m * :math.pow(1 + l * s * sd, 1 / l)
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end
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end
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