# Overview of Pediatric Blood Pressure Distributions

    library(pedbp)

# 1 Introduction

Part of the work of Martin et al. (2022) required transforming blood pressure measurement into percentiles based on published norms. This work was complicated by the fact that data for pediatric blood pressure percentiles is sparse and generally only applicable to children at least one year of age and requires height, a commonly unavailable data point in electronic health records for a variety of reasons.

A solution to building pediatric blood pressure percentiles was developed and is presented here for others to use. Inputs for the developed method are:

1. Patient sex (male/female) required
2. Systolic blood pressure (mmHg) required
3. Diastolic blood pressure (mmHg) required
4. Patient height (cm) if known.

Given the inputs, the following logic is used to determine which data sets will be used to inform the blood pressure percentiles. Under one year of age, the data from Gemelli et al. (1990) will be used; a height input is not required for this patient subset. For those at least one year of age with a known height, data from Expert Panel on Integrated Guidelines for Cardiovascular Health and Risk Reduction in Children and Adolescents (2011) (hereafter referred to as ‘NHLBI/CDC’ as the report incorporates recommendations and inputs from the National Heart, Lung, and Blood Institute [NHLBI] and the Centers for Disease Control and Prevention [CDC]). If height is unknown and age is at least three years, then data from Lo et al. (2013) is used. Lastly, for children between one and three years of age with unknown height, blood pressure percentiles are estimated by the NHLBI/CDC data using as a default the median height for each patient’s sex and age.

With version 2.0.0 and later, the option to select the specific reference source data was introduced along with the additional Flynn et al. (2017) reference.

The sources are:

1. Gemelli et al. (1990) for kids under one year of age.
2. Lo et al. (2013) for kids over three years of age and when height is unknown.
3. Expert Panel on Integrated Guidelines for Cardiovascular Health and Risk Reduction in Children and Adolescents (2011) for kids 1 through 18 years of age with known stature.
4. Flynn et al. (2017) for kids 1 through 18 years of age with known stature.

The data from Flynn et al. (2017) and Expert Panel on Integrated Guidelines for Cardiovascular Health and Risk Reduction in Children and Adolescents (2011) are similar but for one major difference. Flynn et al. (2017) excluded overweight and obese ( BMI above the 85th percentile) children and Expert Panel on Integrated Guidelines for Cardiovascular Health and Risk Reduction in Children and Adolescents (2011) included overweight and obese children.

# 2 Estimating Pediatric Blood Pressure Distributions

There are two functions provided for working with blood pressure distributions. These methods use Gaussian distributions for both systolic and diastolic blood pressures with means and standard deviations either explicitly provided in an aforementioned source or derived by optimizing the parameters such that the sum of squared errors between the provided quantiles from an aforementioned source and the distribution quantiles is minimized. The provided functions, a distribution function and a quantile function, follow a similar naming convention to the distribution functions found in the stats library in R.

Arguments named `p_sbp` and `p_dbp` are probabilities on the 0 to 1 scale. Arguments named `height_percentile` and displayed percentiles in text or plots use percentile points on the 0 to 100 scale.

## 2.1 Percentiles

What percentile for systolic and diastolic blood pressure is 100/60 for a 44 month old male with unknown height?

    p_bp(q_sbp = 100, q_dbp = 60, age = 44, male = 1)
    ## $sbp_p
    ## [1] 0.7700861
    ##
    ## $dbp_p
    ## [1] 0.72739

Using the default source of `martin2022` the data source for the above is Lo et al. (2013) since height was not specified. The same result could be found by explicitly using the `lo2013` source.

    p_bp(q_sbp = 100, q_dbp = 60, age = 44, male = 1, source = "lo2013")
    ## $sbp_p
    ## [1] 0.7700861
    ##
    ## $dbp_p
    ## [1] 0.72739

Those percentiles would be modified if height was 103 cm:

    p_bp(q_sbp = 100, q_dbp = 60, age = 44, male = 1, height = 103)
    ## $sbp_p
    ## [1] 0.7434636
    ##
    ## $dbp_p
    ## [1] 0.8678361
    p_bp(q_sbp = 100, q_dbp = 60, age = 44, male = 1, height = 103, source = "nhlbi")
    ## $sbp_p
    ## [1] 0.7434636
    ##
    ## $dbp_p
    ## [1] 0.8678361

If you don’t have the height, but you do have the height percentiles you can use that instead:

    p_height_for_age(103, male = 1, age = 44)
    ## [1] 0.795653
    x <- p_bp(q_sbp = 100, q_dbp = 60, age = 44, male = 1, height_percentile = 80, source = "nhlbi")
    x
    ## $sbp_p
    ## [1] 0.7434636
    ##
    ## $dbp_p
    ## [1] 0.8678361

A plotting method to show where the observed blood pressures are on the distribution function is also provided.

    bp_cdf(sbp = 100, dbp = 60, age = 44, male = 1, height_percentile = 80, source = "nhlbi")

Vectors of blood pressures can be used as well. `NA` values will return `NA`.

    bps <-
      p_bp(
             q_sbp  = c(100, NA, 90)
           , q_dbp  = c(60, 82, 48)
           , age    = 44
           , male   = 1
          )
    bps
    ## $sbp_p
    ## [1] 0.7700861        NA 0.3639854
    ##
    ## $dbp_p
    ## [1] 0.7273900 0.9995515 0.1903674

If you want to know which data source was used in computing each of the percentile estimates you can look at the `bp_params` attribute:

    attr(bps, "bp_params")
    ##   source male age sbp_mean sbp_sd dbp_mean dbp_sd height_percentile
    ## 1 lo2013    1  36     93.2    9.2     55.1    8.1                NA
    ## 2 lo2013    1  36     93.2    9.2     55.1    8.1                NA
    ## 3 lo2013    1  36     93.2    9.2     55.1    8.1                NA
    str(bps)
    ## List of 2
    ##  $ sbp_p: num [1:3] 0.77 NA 0.364
    ##  $ dbp_p: num [1:3] 0.727 1 0.19
    ##  - attr(*, "bp_params")='data.frame':    3 obs. of  8 variables:
    ##   ..$ source           : chr [1:3] "lo2013" "lo2013" "lo2013"
    ##   ..$ male             : int [1:3] 1 1 1
    ##   ..$ age              : num [1:3] 36 36 36
    ##   ..$ sbp_mean         : num [1:3] 93.2 93.2 93.2
    ##   ..$ sbp_sd           : num [1:3] 9.2 9.2 9.2
    ##   ..$ dbp_mean         : num [1:3] 55.1 55.1 55.1
    ##   ..$ dbp_sd           : num [1:3] 8.1 8.1 8.1
    ##   ..$ height_percentile: num [1:3] NA NA NA
    ##  - attr(*, "class")= chr [1:2] "pedbp_bp" "pedbp_p_bp"

## 2.2 Quantiles

If you have a percentile value and want to know the associated systolic and diastolic blood pressures:

    q_bp(
           p_sbp = c(0.701, NA, 0.36)
         , p_dbp = c(0.85, 0.99, 0.50)
         , age = 44
         , male = 1
        )
    ## $sbp
    ## [1] 98.05096       NA 89.90218
    ##
    ## $dbp
    ## [1] 63.49511 73.94342 55.10000

## 2.3 Working With More Than One Patient

The `p_bp` and `q_bp` methods are designed accept vectors for each of the arguments. These methods expected each argument to be length 1 or all the same length.

    eg_data <- read.csv(system.file("example_data", "for_batch.csv", package = "pedbp"))
    eg_data
    ##           pid age_months male height..cm. sbp..mmHg. dbp..mmHg.
    ## 1   patient_A         96    1          NA        102         58
    ## 2   patient_B        144    0         153        113         NA
    ## 3   patient_C          4    0          62         82         43
    ## 4 patient_D_1         41    1          NA         96         62
    ## 5 patient_D_2         41    1         101         96         62

    bp_percentiles <-
      p_bp(
             q_sbp  = eg_data$sbp..mmHg.
           , q_dbp  = eg_data$dbp..mmHg.
           , age    = eg_data$age
           , male   = eg_data$male
           , height = eg_data$height
           )
    bp_percentiles
    ## $sbp_p
    ## [1] 0.5533069 0.7680539 0.2622697 0.6195685 0.6101919
    ##
    ## $dbp_p
    ## [1] 0.4120704        NA 0.1356661 0.8028518 0.9011250

    str(bp_percentiles)
    ## List of 2
    ##  $ sbp_p: num [1:5] 0.553 0.768 0.262 0.62 0.61
    ##  $ dbp_p: num [1:5] 0.412 NA 0.136 0.803 0.901
    ##  - attr(*, "bp_params")='data.frame':    5 obs. of  8 variables:
    ##   ..$ source           : chr [1:5] "lo2013" "nhlbi" "gemelli1990" "lo2013" ...
    ##   ..$ male             : int [1:5] 1 0 0 1 1
    ##   ..$ age              : num [1:5] 96 144 3 36 36
    ##   ..$ sbp_mean         : num [1:5] 100.7 105 89 93.2 93
    ##   ..$ sbp_sd           : num [1:5] 9.7 10.9 11 9.2 10.7
    ##   ..$ dbp_mean         : num [1:5] 59.8 62 54 55.1 47
    ##   ..$ dbp_sd           : num [1:5] 8.1 10.9 10 8.1 11.6
    ##   ..$ height_percentile: num [1:5] NA 50 NA NA 75
    ##  - attr(*, "class")= chr [1:2] "pedbp_bp" "pedbp_p_bp"

Going from percentiles back to quantiles:

    q_bp(
           p_sbp  = bp_percentiles$sbp_p
         , p_dbp  = bp_percentiles$dbp_p
         , age    = eg_data$age
         , male   = eg_data$male
         , height = eg_data$height
         )
    ## $sbp
    ## [1] 102 113  82  96  96
    ##
    ## $dbp
    ## [1] 58 NA 43 62 62

# 3 Blood Pressure Charts

Percentiles over age:

    bp_chart()

The percentiles curves for a males in the 75th height percentile based on the Flynn et al. (2017) data:

    bp_chart(male = 1, height_percentile = 75, source = "flynn2017")

# 4 References

Expert Panel on Integrated Guidelines for Cardiovascular Health and Risk Reduction in Children and Adolescents. 2011. “Expert Panel on Integrated Guidelines for Cardiovascular Health and Risk Reduction in Children and Adolescents: Summary Report.” Pediatrics 128 (Supplement_5): S213–56. https://doi.org/10.1542/peds.2009-2107C.
Flynn, Joseph T, David C Kaelber, Carissa M Baker-Smith, et al. 2017. “Clinical Practice Guideline for Screening and Management of High Blood Pressure in Children and Adolescents.” Pediatrics 140 (3).
Gemelli, M, R Manganaro, C Mamí, and F De Luca. 1990. “Longitudinal Study of Blood Pressure During the 1st Year of Life.” European Journal of Pediatrics 149 (5): 318–20. https://doi.org/10.1007/BF02171556.
Lo, Joan C, Alan Sinaiko, Malini Chandra, et al. 2013. “Prehypertension and Hypertension in Community-Based Pediatric Practice.” Pediatrics 131 (2): e415–24. https://doi.org/10.1542/peds.2012-1292.
Martin, Blake, Peter E DeWitt, Halden F Scott, Sarah Parker, and Tellen D Bennett. 2022. “Machine Learning Approach to Predicting Absence of Serious Bacterial Infection at PICU Admission.” Hospital Pediatrics 12 (6): 590–603. https://doi.org/https://doi.org/10.1542/hpeds.2021-005998.