In dewittpe/pedbp: Pediatric Blood Pressure

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knitr::opts_chunk$set(collapse = TRUE, fig.align = "center")
library(pedbp)

Additional Utilities

Estimating Gaussian Mean and Standard Deviation

The NHLBI data for blood pressures provided values in percentiles. To get a mean and standard deviation that would work well for estimating other percentiles and quantiles via a Gaussian distribution we optimized for values of the mean and standard deviation such that for the provided quantiles $q_i$ at the $p_i$ percentiles and $X \sim N\left(\mu, \sigma\right)$,

$$ \sum_{i} \left(\Pr(X \leq q_i) - p_i \right)^2, $$

was minimized. The NHLBI data is provided to the end user.

data(list = "nhlbi_bp_norms", package = "pedbp")
str(nhlbi_bp_norms)

For an example of how we fitted the parameters:

d <- nhlbi_bp_norms[nhlbi_bp_norms$age == 144 & nhlbi_bp_norms$height_percentile == 50, ]
d <- d[d$male == 0, ]
d

est_norm(q = d$sbp, p = d$bp_percentile / 100)
est_norm(q = d$dbp, p = d$bp_percentile / 100)

bp_parameters[bp_parameters$male == 0 & bp_parameters$age == 144 & bp_parameters$height_percentile == 50, ]

The est_norm method comes with a plotting method too. The provided quantiles are plotted as open dots and the fitted distribution function is plotted to show the fit.

plot( est_norm(q = d$dbp, p = d$bp_percentile / 100) )

If you want to emphasize a data point you can do that as well. Here is an example from a set of quantiles and percentiles which are not Gaussian.

qs <- c(-1.92, 0.05, 0.1, 1.89) * 1.8 + 3.14
ps <- c(0.025, 0.40, 0.50, 0.975)

# with equal weights
w0 <- est_norm(qs, ps)
# weight to ignore one of the middle value and make sure to hit the other
w1 <- est_norm(qs, ps, weights = c(1, 2, 0, 1))
# equal weight the middle, more than the tails
w2 <- est_norm(qs, ps, weights = c(1, 2, 2, 1))

gridExtra::grid.arrange(
  plot(w0) + ggplot2::ggtitle(label = "w0", subtitle = paste0("Mean: ", round(w0$par[1], 2), " SD: ", round(w0$par[2], 3)))
  , plot(w1) + ggplot2::ggtitle(label = "w1", subtitle = paste0("Mean: ", round(w1$par[1], 2), " SD: ", round(w1$par[2], 3)))
  , plot(w2) + ggplot2::ggtitle(label = "w2", subtitle = paste0("Mean: ", round(w2$par[1], 2), " SD: ", round(w2$par[2], 3)))
  , nrow = 1
)