# Calculating anthropometric z-scores using zscorer

#### Mark Myatt

#### 2019-10-19

# Calculating anthropometric z-scores using `zscorer`

The main function in the `zscorer` package is `addWGSR()`.

To demonstrate its usage, we will use the accompanying dataset in `zscorer` called `anthro3`. We inspect the dataset as follows:

    anthro3

which returns:

    #>   psu age sex weight height muac oedema
    #> 1   1  10   1    5.7   64.2  125      2
    #> 2   1  10   2    5.8   64.4  121      2
    #> 3   1   9   2    6.5   62.2  139      2
    #> 4   1  11   9    6.5   64.9  129      2
    #> 5   1  24   2    6.5   72.9  120      2
    #> 6   1  12   2    6.6   69.4  126      2

`anthro3` contains anthropometric data from a Rapid Assessment Method (RAM) survey from Burundi.

Anthropometric indices (e.g. weight-for-height z-scores) have not been calculated and added to the data.

We will use the `addWGSR()` function to add weight-for-height (wfh) z-scores to the example data:

    svy <- addWGSR(data = anthro3, sex = "sex", firstPart = "weight",
                   secondPart = "height", index = "wfh")
    #> ===========================================================================

A new column named wfhz has been added to the dataset:

    #>   psu age sex weight height muac oedema  wfhz
    #> 1   1  10   1    5.7   64.2  125      2 -2.73
    #> 2   1  10   2    5.8   64.4  121      2 -2.04
    #> 3   1   9   2    6.5   62.2  139      2  0.13
    #> 4   1  11   9    6.5   64.9  129      2    NA
    #> 5   1  24   2    6.5   72.9  120      2 -3.44
    #> 6   1  12   2    6.6   69.4  126      2 -2.26

The `wfhz` column contains the weight-for-height (wfh) z-scores calculated from the `sex`, `weight`, and `height` columns in the `anthro3` dataset. The calculated z-scores are rounded to two decimals places unless the `digits` option is used to specify a different precision (run `?addWGSR` to see description of various parameters that can be specified in the `addWGSR()` function).

The `addWGSR()` function takes up to nine parameters to calculate each index separately, depending on the index required. These are described in the Help files of the `zscorer` package which can be accessed as follows:

    ?addWGSR

The standing parameter specifies how “stature” (i.e. length or height) was measured. If this is not specified, and in some special circumstances, height and age rules will be applied when calculating z-scores. These rules are described in the table below.

index | standing | age | height | Action
--- | --- | --- | --- | ---
hfa or lfa | standing | < 731 days |  | index = lfa height = height + 0.7 cm
hfa or lfa | supine | < 731 days |  | index = lfa
hfa or lfa | unknown | < 731 days |  | index = lfa
hfa or lfa | standing | ≥ 731 days |  | index = hfa
hfa or lfa | supine | ≥ 731 days |  | index = hfa height = height - 0.7 cm
hfa or lfa | unknown | ≥ 731 days |  | index = hfa
wfh or wfl | standing |  | < 65 cm | index = wfl height = height + 0.7 cm
wfh or wfl | standing |  | ≥ 65 cm | index = wfh
wfh or wfl | supine |  | ≤ 110 cm | index = wfl
wfh or wfl | supine |  | more than 110 cm | index = wfh height = height - 0.7 cm
wfh or wfl | unknown |  | < 87 cm | index = wfl
wfh or wfl | unknown |  | ≥ 87 cm | index = wfh
bfa | standing | < 731 days |  | height = height + 0.7 cm
bfa | standing | ≥ 731 days |  | height = height - 0.7 cm

The `addWGSR()` function will not produce error messages unless there is something very wrong with the data or the specified parameters. If an error is encountered in a record then the value NA is returned. Error conditions are listed in the table below.

Error condition | Action
--- | ---
Missing or nonsense value in `standing` parameter | Set `standing` to `3` (unknown) and apply appropriate height or age rules.
Unknown `index` specified | Return NA for z-score.
Missing `sex` | Return NA for z-score.
Missing `firstPart` | Return NA for z-score.
Missing `secondPart` | Return NA for z-score.
`sex` is not male (`1`) or female (`2`) | Return NA for z-score.
`firstPart` is not numeric | Return NA for z-score.
`secondPart` is not numeric | Return NA for z-score.
Missing `thirdPart` when `index = "bfa"` | Return NA for z-score.
`thirdPart` is not numeric when `index = "bfa"` | Return NA for z-score.
`secondPart` is out of range for specified index | Return NA for z-score.

We can see this error behaviour using the example data:

    table(is.na(svy$wfhz))
    #>
    #> FALSE  TRUE
    #>   220     1

We can display the problem record:

    svy[is.na(svy$wfhz), ]
    #>   psu age sex weight height muac oedema wfhz
    #> 4   1  11   9    6.5   64.9  129      2   NA

The problem is due to the value 9 in the `sex` column, which should be coded 1 (for male) and 2 (for female). Z-scores are only calculated for records with sex specified as either 1 (male) or 2 (female). All other values, including NA, will return NA.

The `addWGSR()` function requires that data are recorded using the required units or required codes (see `?addWGSR` to check units required by the different function parameters).

The `addWGSR()` function will return incorrect values if the data are not recorded using the required units. For example, this attempt to add weight-for-age z-scores to the example data:

    svy <- addWGSR(data = svy, sex = "sex", firstPart = "weight",
                   secondPart = "age", index = "wfa")
    #> ===========================================================================

will give incorrect results:

    summary(svy$wfaz)
    #>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's
    #>   3.450   7.692   9.840   9.684  11.430  15.900       1

The odd range of values is due to age being recorded in months rather than days.

It is simple to convert all ages from months to days:

    svy$age <- svy$age * (365.25 / 12)
    head(svy)
    #>   psu      age sex weight height muac oedema  wfhz wfaz
    #> 1   1 304.3750   1    5.7   64.2  125      2 -2.73 3.45
    #> 2   1 304.3750   2    5.8   64.4  121      2 -2.04 3.95
    #> 3   1 273.9375   2    6.5   62.2  139      2  0.13 5.12
    #> 4   1 334.8125   9    6.5   64.9  129      2    NA   NA
    #> 5   1 730.5000   2    6.5   72.9  120      2 -3.44 3.82
    #> 6   1 365.2500   2    6.6   69.4  126      2 -2.26 5.01

before calculating and adding weight-for-age z-scores:

    svy <- addWGSR(data = svy, sex = "sex", firstPart = "weight",
                   secondPart = "age", index = "wfa")
    #> ===========================================================================
    head(svy)
    #>   psu      age sex weight height muac oedema  wfhz  wfaz
    #> 1   1 304.3750   1    5.7   64.2  125      2 -2.73 -4.13
    #> 2   1 304.3750   2    5.8   64.4  121      2 -2.04 -3.19
    #> 3   1 273.9375   2    6.5   62.2  139      2  0.13 -1.97
    #> 4   1 334.8125   9    6.5   64.9  129      2    NA    NA
    #> 5   1 730.5000   2    6.5   72.9  120      2 -3.44 -4.61
    #> 6   1 365.2500   2    6.6   69.4  126      2 -2.26 -2.56
    summary(svy$wfaz)
    #>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's
    #>  -4.610  -1.873  -1.085  -1.154  -0.480   2.600       1

The muac column in the example dataset is recorded in millimetres (mm). We need to convert this to centimetres (cm):

    svy$muac <- svy$muac / 10
    head(svy)
    #>   psu      age sex weight height muac oedema  wfhz  wfaz
    #> 1   1 304.3750   1    5.7   64.2 12.5      2 -2.73 -4.13
    #> 2   1 304.3750   2    5.8   64.4 12.1      2 -2.04 -3.19
    #> 3   1 273.9375   2    6.5   62.2 13.9      2  0.13 -1.97
    #> 4   1 334.8125   9    6.5   64.9 12.9      2    NA    NA
    #> 5   1 730.5000   2    6.5   72.9 12.0      2 -3.44 -4.61
    #> 6   1 365.2500   2    6.6   69.4 12.6      2 -2.26 -2.56

before using the `addWGSR()` function to calculate MUAC-for-age z-scores:

    svy <- addWGSR(svy, sex = "sex", firstPart = "muac",
                   secondPart = "age", index = "mfa")
    #> ===========================================================================
    head(svy)
    #>   psu      age sex weight height muac oedema  wfhz  wfaz  mfaz
    #> 1   1 304.3750   1    5.7   64.2 12.5      2 -2.73 -4.13 -1.97
    #> 2   1 304.3750   2    5.8   64.4 12.1      2 -2.04 -3.19 -1.88
    #> 3   1 273.9375   2    6.5   62.2 13.9      2  0.13 -1.97 -0.14
    #> 4   1 334.8125   9    6.5   64.9 12.9      2    NA    NA    NA
    #> 5   1 730.5000   2    6.5   72.9 12.0      2 -3.44 -4.61 -2.70
    #> 6   1 365.2500   2    6.6   69.4 12.6      2 -2.26 -2.56 -1.46

As a last example we will use the `addWGSR()` function to add body mass index-for-age (bfa) z-scores to the data to create a new variable called bmiAgeZ with a precision of 4 decimal places as:

    svy <- addWGSR(data = svy, sex = "sex", firstPart = "weight",
                   secondPart = "height", thirdPart = "age", index = "bfa",
                   output = "bmiAgeZ", digits = 4)
    #> ===========================================================================
    head(svy)
    #>   psu      age sex weight height muac oedema  wfhz  wfaz  mfaz bmiAgeZ
    #> 1   1 304.3750   1    5.7   64.2 12.5      2 -2.73 -4.13 -1.97 -2.6928
    #> 2   1 304.3750   2    5.8   64.4 12.1      2 -2.04 -3.19 -1.88 -2.0005
    #> 3   1 273.9375   2    6.5   62.2 13.9      2  0.13 -1.97 -0.14  0.0405
    #> 4   1 334.8125   9    6.5   64.9 12.9      2    NA    NA    NA      NA
    #> 5   1 730.5000   2    6.5   72.9 12.0      2 -3.44 -4.61 -2.70 -2.8958
    #> 6   1 365.2500   2    6.6   69.4 12.6      2 -2.26 -2.56 -1.46 -2.0796