Converts standard deviation score (SDS) into measurements using an age- and sex-conditional external reference.

z2y(
  z = c(-2, 0, 2),
  x = 1,
  sex = "M",
  sub = "N",
  ref = get("nl4.hgt"),
  dist = "LMS",
  dec = 3,
  sex.fallback = NA,
  sub.fallback = NA
)

Arguments

z

A numerical vector containing standard deviation scores that are to be converted. The length length(z) determines the size of the output vector.

x

A vector containing the values of the numerical covariate (typically decimal age or height) at which conversion is desired. Values are replicated to match length(y).

sex

A character vector indicating whether the male ("M") of female ("F")reference should be used. Values are replicated to match length(y).

sub

A character vector indicating the level of the sub field of the reference standard defined in ref

ref

A data frame containing a factor sex, a numerical variable age containing the tabulated decimal point ages, and two or more numerical variables with reference values. See details.

dist

A string identifying the type of distribution. Values values are: "NO", "BCCG", "LMS", "BCPE" and "BCT". The default is "LMS".

dec

A scalar value indicating the number of decimals used to round the value.

sex.fallback

The level of the sex field used when no match is found. The default sex.fallback=NA specifies that unmatched entries should receive a NA value.

sub.fallback

The level of the sub field used when no match is found. The default sub.fallback=NA specifies that unmatched entries should receive a NA value.

Value

For y2z(): A vector with length(y) elements containing the standard deviation score. For z2y(): A vector with length(z) elements containing quantiles.

Details

Functions z2y() and y2z() are the inverse of each other.

The argument dist determines the statistical distribution. The possibilities are as follows:

list("\"NO\"")

ref should contain columns mean and sd, containing the mean and the standard deviation in the external reference population.

list("\"LMS\"")

ref should contain columns L, S and M containing the LMS parameters.

list("\"BCCG\"")

ref should contain columns mu, sigma and nu containing the Box-Cox Cole-Green parameters.

list("\"BCPE\"")

ref should contain columns mu, sigma, nu and tau containing the Box-Cox Power Exponential parameters.

list("\"BCT\"")

ref should contain columns mu, sigma, nu and tau containing the Box-Cox T distribution parameters.

See also

Author

Stef van Buuren, 2010

Examples



boys <- boys7482

# quantile at SD=0 of age 2 years, 
# height Dutch boys
z2y(z=0, x=2)
#> [1] 88.85

# same for Dutch girls
z2y(z=0, x=2, sex="F")
#> [1] 87.49

# quantile at SD=c(-1,0,1) of age 2 years, BMI Dutch boys
z2y(z=c(-1,0,+1), x=2, ref=nl4.bmi)
#> [1] 15.173 16.420 17.770

# 0SD line (P50) in kg of weight for age in 5-10 year, Dutch boys
z2y(z=rep(0,6), x=5:10, ref=nl4.wgt)
#> [1] 19.82 22.37 25.03 27.86 30.76 33.79

# 95th percentile (P95), age 10 years, wfa, Dutch boys
z2y(z=qnorm(0.95), x=10, ref=nl4.wgt)
#> [1] 45.278

# table of P3, P10, P50, P90, P97 of weight for 5-10 year old dutch boys
# age per year
age <- 5:10
p <- c(0.03,0.1,0.5,0.9,0.97)
z <- rep(qnorm(p), length(age))
x <- rep(age, each=length(p))
w <- matrix(z2y(z, x=x, sex="M", ref=nl4.wgt), ncol=length(p),
 byrow=TRUE)
dimnames(w) <- list(age, p)
round(w,1)
#>    0.03  0.1  0.5  0.9 0.97
#> 5  15.8 16.9 19.8 23.4 25.4
#> 6  17.6 19.0 22.4 26.8 29.3
#> 7  19.5 21.1 25.0 30.3 33.4
#> 8  21.6 23.3 27.9 34.1 37.8
#> 9  23.6 25.5 30.8 38.1 42.5
#> 10 25.6 27.8 33.8 42.2 47.5

# standard set of Z-scores of weight for all tabulated ages, boys & girls
# and three etnicities
sds <- c(-2.5, -2, -1, 0, 1, 2, 2.5)
age <- nl4.wgt$x
z <- rep(sds, times=length(age))
x <- rep(age, each=length(sds))
sex <- rep(c("M","F"), each=length(z)/2)
w <- z2y(z=z, x=x, sex=sex, ref=nl4.wgt)
w <- matrix(w, ncol=length(sds), byrow=TRUE)
dimnames(w) <- list(age, sds)
data.frame(sub=nl4.wgt$sub,sex=nl4.wgt$sex,round(w,2), row.names=NULL)
#>     sub sex X.2.5   X.2   X.1    X0    X1    X2   X2.5
#> 1     N   M  2.58  2.77  3.15  3.55  3.97  4.40   4.62
#> 2     N   M  2.73  2.93  3.33  3.75  4.19  4.65   4.89
#> 3     N   M  2.87  3.08  3.50  3.94  4.40  4.89   5.14
#> 4     N   M  3.01  3.22  3.67  4.13  4.62  5.12   5.39
#> 5     N   M  3.16  3.38  3.84  4.33  4.84  5.37   5.65
#> 6     N   M  3.31  3.54  4.02  4.53  5.06  5.62   5.91
#> 7     N   M  3.46  3.70  4.20  4.72  5.27  5.85   6.15
#> 8     N   M  3.61  3.86  4.37  4.92  5.50  6.10   6.41
#> 9     N   M  3.75  4.01  4.54  5.11  5.71  6.34   6.66
#> 10    N   M  3.89  4.16  4.71  5.30  5.92  6.57   6.91
#> 11    N   M  4.03  4.30  4.87  5.48  6.12  6.80   7.15
#> 12    N   M  4.30  4.59  5.19  5.84  6.53  7.25   7.63
#> 13    N   M  4.56  4.86  5.51  6.19  6.92  7.69   8.09
#> 14    N   M  4.81  5.13  5.80  6.51  7.27  8.07   8.49
#> 15    N   M  5.05  5.38  6.07  6.82  7.62  8.46   8.90
#> 16    N   M  5.27  5.61  6.33  7.11  7.94  8.83   9.29
#> 17    N   M  5.48  5.83  6.58  7.39  8.25  9.18   9.66
#> 18    N   M  5.68  6.04  6.82  7.65  8.54  9.50  10.01
#> 19    N   M  5.86  6.23  7.03  7.89  8.81  9.80  10.33
#> 20    N   M  6.03  6.42  7.24  8.12  9.07 10.10  10.63
#> 21    N   M  6.38  6.78  7.63  8.55  9.54 10.62  11.18
#> 22    N   M  6.68  7.10  7.99  8.95  9.99 11.12  11.72
#> 23    N   M  6.95  7.38  8.30  9.30 10.39 11.56  12.19
#> 24    N   M  7.21  7.65  8.60  9.63 10.76 11.98  12.63
#> 25    N   M  7.45  7.90  8.88  9.94 11.10 12.37  13.04
#> 26    N   M  7.67  8.14  9.13 10.23 11.43 12.74  13.44
#> 27    N   M  7.86  8.34  9.37 10.50 11.74 13.11  13.83
#> 28    N   M  8.05  8.54  9.59 10.75 12.02 13.42  14.17
#> 29    N   M  8.24  8.74  9.82 11.00 12.30 13.74  14.51
#> 30    N   M  8.85  9.38 10.52 11.78 13.18 14.73  15.57
#> 31    N   M  9.79 10.36 11.62 13.02 14.59 16.35  17.30
#> 32    N   M 10.59 11.21 12.58 14.12 15.86 17.83  18.91
#> 33    N   M 11.39 12.06 13.52 15.19 17.09 19.26  20.45
#> 34    N   M 12.18 12.89 14.47 16.28 18.36 20.76  22.10
#> 35    N   M 12.98 13.74 15.45 17.42 19.72 22.40  23.91
#> 36    N   M 13.83 14.64 16.47 18.60 21.10 24.07  25.75
#> 37    N   M 14.67 15.54 17.50 19.82 22.57 25.87  27.76
#> 38    N   M 15.54 16.47 18.57 21.08 24.09 27.76  29.89
#> 39    N   M 16.39 17.38 19.64 22.37 25.69 29.79  32.21
#> 40    N   M 17.28 18.33 20.74 23.68 27.30 31.82  34.52
#> 41    N   M 18.14 19.26 21.85 25.03 28.99 34.02  37.07
#> 42    N   M 19.08 20.26 23.02 26.43 30.73 36.25  39.64
#> 43    N   M 19.97 21.24 24.18 27.86 32.54 38.65  42.44
#> 44    N   M 20.86 22.20 25.35 29.30 34.38 41.11  45.32
#> 45    N   M 21.78 23.20 26.54 30.76 36.22 43.51  48.12
#> 46    N   M 22.66 24.16 27.73 32.25 38.15 46.09  51.15
#> 47    N   M 23.59 25.18 28.97 33.79 40.10 48.62  54.07
#> 48    N   M 24.55 26.25 30.28 35.43 42.17 51.29  57.12
#> 49    N   M 25.53 27.36 31.69 37.23 44.48 54.28  60.53
#> 50    N   M 26.65 28.62 33.29 39.24 47.00 57.39  63.97
#> 51    N   M 27.85 29.99 35.06 41.48 49.79 60.77  67.64
#> 52    N   M 29.23 31.56 37.07 43.99 52.84 64.35  71.44
#> 53    N   M 30.74 33.29 39.29 46.77 56.22 68.31  75.64
#> 54    N   M 32.59 35.35 41.80 49.77 59.69 72.17  79.61
#> 55    N   M 34.62 37.58 44.46 52.87 63.22 76.06  83.62
#> 56    N   M 36.88 40.00 47.20 55.94 66.59 79.64  87.25
#> 57    N   M 39.20 42.43 49.87 58.82 69.65 82.80  90.42
#> 58    N   M 41.54 44.84 52.41 61.45 72.32 85.43  92.98
#> 59    N   M 43.65 47.01 54.66 63.77 74.67 87.77  95.30
#> 60    N   M 45.58 48.96 56.64 65.75 76.61 89.61  97.06
#> 61    N   M 47.22 50.62 58.32 67.43 78.26 91.18  98.58
#> 62    N   M 48.71 52.11 59.79 68.85 79.59 92.38  99.68
#> 63    N   M 49.95 53.35 61.02 70.06 80.75 93.45 100.70
#> 64    N   M 51.07 54.47 62.12 71.10 81.70 94.27 101.43
#> 65    N   M 52.01 55.41 63.06 72.04 82.62 95.15 102.28
#> 66    N   M 52.90 56.30 63.94 72.89 83.43 95.89 102.98
#> 67    N   M 53.88 57.26 64.84 73.70 84.10 96.37 103.33
#> 68    N   M 54.73 58.10 65.67 74.49 84.83 97.02 103.92
#> 69    N   M 55.58 58.95 66.50 75.28 85.56 97.65 104.50
#> 70    N   M 55.58 58.95 66.50 75.28 85.56 97.65 104.50
#> 71    N   F  2.58  2.77  3.15  3.55  3.97  4.40   4.62
#> 72    N   F  2.73  2.93  3.33  3.75  4.19  4.65   4.89
#> 73    N   F  2.87  3.08  3.50  3.94  4.40  4.89   5.14
#> 74    N   F  3.01  3.22  3.67  4.13  4.62  5.12   5.39
#> 75    N   F  3.16  3.38  3.84  4.33  4.84  5.37   5.65
#> 76    N   F  3.31  3.54  4.02  4.53  5.06  5.62   5.91
#> 77    N   F  3.46  3.70  4.20  4.72  5.27  5.85   6.15
#> 78    N   F  3.61  3.86  4.37  4.92  5.50  6.10   6.41
#> 79    N   F  3.75  4.01  4.54  5.11  5.71  6.34   6.66
#> 80    N   F  3.89  4.16  4.71  5.30  5.92  6.57   6.91
#> 81    N   F  4.03  4.30  4.87  5.48  6.12  6.80   7.15
#> 82    N   F  4.30  4.59  5.19  5.84  6.53  7.25   7.63
#> 83    N   F  4.56  4.86  5.51  6.19  6.92  7.69   8.09
#> 84    N   F  4.81  5.13  5.80  6.51  7.27  8.07   8.49
#> 85    N   F  5.05  5.38  6.07  6.82  7.62  8.46   8.90
#> 86    N   F  5.27  5.61  6.33  7.11  7.94  8.83   9.29
#> 87    N   F  5.48  5.83  6.58  7.39  8.25  9.18   9.66
#> 88    N   F  5.68  6.04  6.82  7.65  8.54  9.50  10.01
#> 89    N   F  5.86  6.23  7.03  7.89  8.81  9.80  10.33
#> 90    N   F  6.03  6.42  7.24  8.12  9.07 10.10  10.63
#> 91    N   F  6.38  6.78  7.63  8.55  9.54 10.62  11.18
#> 92    N   F  6.68  7.10  7.99  8.95  9.99 11.12  11.72
#> 93    N   F  6.95  7.38  8.30  9.30 10.39 11.56  12.19
#> 94    N   F  7.21  7.65  8.60  9.63 10.76 11.98  12.63
#> 95    N   F  7.45  7.90  8.88  9.94 11.10 12.37  13.04
#> 96    N   F  7.67  8.14  9.13 10.23 11.43 12.74  13.44
#> 97    N   F  7.86  8.34  9.37 10.50 11.74 13.11  13.83
#> 98    N   F  8.05  8.54  9.59 10.75 12.02 13.42  14.17
#> 99    N   F  8.24  8.74  9.82 11.00 12.30 13.74  14.51
#> 100   N   F  8.85  9.38 10.52 11.78 13.18 14.73  15.57
#> 101   N   F  9.79 10.36 11.62 13.02 14.59 16.35  17.30
#> 102   N   F 10.59 11.21 12.58 14.12 15.86 17.83  18.91
#> 103   N   F 11.39 12.06 13.52 15.19 17.09 19.26  20.45
#> 104   N   F 12.18 12.89 14.47 16.28 18.36 20.76  22.10
#> 105   N   F 12.98 13.74 15.45 17.42 19.72 22.40  23.91
#> 106   N   F 13.83 14.64 16.47 18.60 21.10 24.07  25.75
#> 107   N   F 14.67 15.54 17.50 19.82 22.57 25.87  27.76
#> 108   N   F 15.54 16.47 18.57 21.08 24.09 27.76  29.89
#> 109   N   F 16.39 17.38 19.64 22.37 25.69 29.79  32.21
#> 110   N   F 17.28 18.33 20.74 23.68 27.30 31.82  34.52
#> 111   N   F 18.14 19.26 21.85 25.03 28.99 34.02  37.07
#> 112   N   F 19.08 20.26 23.02 26.43 30.73 36.25  39.64
#> 113   N   F 19.97 21.24 24.18 27.86 32.54 38.65  42.44
#> 114   N   F 20.86 22.20 25.35 29.30 34.38 41.11  45.32
#> 115   N   F 21.78 23.20 26.54 30.76 36.22 43.51  48.12
#> 116   N   F 22.66 24.16 27.73 32.25 38.15 46.09  51.15
#> 117   N   F 23.59 25.18 28.97 33.79 40.10 48.62  54.07
#> 118   N   F 24.55 26.25 30.28 35.43 42.17 51.29  57.12
#> 119   N   F 25.53 27.36 31.69 37.23 44.48 54.28  60.53
#> 120   N   F 26.65 28.62 33.29 39.24 47.00 57.39  63.97
#> 121   N   F 27.85 29.99 35.06 41.48 49.79 60.77  67.64
#> 122   N   F 29.23 31.56 37.07 43.99 52.84 64.35  71.44
#> 123   N   F 30.74 33.29 39.29 46.77 56.22 68.31  75.64
#> 124   N   F 32.59 35.35 41.80 49.77 59.69 72.17  79.61
#> 125   N   F 34.62 37.58 44.46 52.87 63.22 76.06  83.62
#> 126   N   F 36.88 40.00 47.20 55.94 66.59 79.64  87.25
#> 127   N   F 39.20 42.43 49.87 58.82 69.65 82.80  90.42
#> 128   N   F 41.54 44.84 52.41 61.45 72.32 85.43  92.98
#> 129   N   F 43.65 47.01 54.66 63.77 74.67 87.77  95.30
#> 130   N   F 45.58 48.96 56.64 65.75 76.61 89.61  97.06
#> 131   N   F 47.22 50.62 58.32 67.43 78.26 91.18  98.58
#> 132   N   F 48.71 52.11 59.79 68.85 79.59 92.38  99.68
#> 133   N   F 49.95 53.35 61.02 70.06 80.75 93.45 100.70
#> 134   N   F 51.07 54.47 62.12 71.10 81.70 94.27 101.43
#> 135   N   F 52.01 55.41 63.06 72.04 82.62 95.15 102.28
#> 136   N   F 52.90 56.30 63.94 72.89 83.43 95.89 102.98
#> 137   N   F 53.88 57.26 64.84 73.70 84.10 96.37 103.33
#> 138   N   F 54.73 58.10 65.67 74.49 84.83 97.02 103.92
#> 139   N   F 55.58 58.95 66.50 75.28 85.56 97.65 104.50
#> 140   N   F 55.58 58.95 66.50 75.28 85.56 97.65 104.50
#> 141   T   M  2.58  2.77  3.15  3.55  3.97  4.40   4.62
#> 142   T   M  2.73  2.93  3.33  3.75  4.19  4.65   4.89
#> 143   T   M  2.87  3.08  3.50  3.94  4.40  4.89   5.14
#> 144   T   M  3.01  3.22  3.67  4.13  4.62  5.12   5.39
#> 145   T   M  3.16  3.38  3.84  4.33  4.84  5.37   5.65
#> 146   T   M  3.31  3.54  4.02  4.53  5.06  5.62   5.91
#> 147   T   M  3.46  3.70  4.20  4.72  5.27  5.85   6.15
#> 148   T   M  3.61  3.86  4.37  4.92  5.50  6.10   6.41
#> 149   T   M  3.75  4.01  4.54  5.11  5.71  6.34   6.66
#> 150   T   M  3.89  4.16  4.71  5.30  5.92  6.57   6.91
#> 151   T   M  4.03  4.30  4.87  5.48  6.12  6.80   7.15
#> 152   T   M  4.30  4.59  5.19  5.84  6.53  7.25   7.63
#> 153   T   M  4.56  4.86  5.51  6.19  6.92  7.69   8.09
#> 154   T   M  4.81  5.13  5.80  6.51  7.27  8.07   8.49
#> 155   T   M  5.05  5.38  6.07  6.82  7.62  8.46   8.90
#> 156   T   M  5.27  5.61  6.33  7.11  7.94  8.83   9.29
#> 157   T   M  5.48  5.83  6.58  7.39  8.25  9.18   9.66
#> 158   T   M  5.68  6.04  6.82  7.65  8.54  9.50  10.01
#> 159   T   M  5.86  6.23  7.03  7.89  8.81  9.80  10.33
#> 160   T   M  6.03  6.42  7.24  8.12  9.07 10.10  10.63
#> 161   T   M  6.38  6.78  7.63  8.55  9.54 10.62  11.18
#> 162   T   M  6.68  7.10  7.99  8.95  9.99 11.12  11.72
#> 163   T   M  6.95  7.38  8.30  9.30 10.39 11.56  12.19
#> 164   T   M  7.21  7.65  8.60  9.63 10.76 11.98  12.63
#> 165   T   M  7.45  7.90  8.88  9.94 11.10 12.37  13.04
#> 166   T   M  7.67  8.14  9.13 10.23 11.43 12.74  13.44
#> 167   T   M  7.86  8.34  9.37 10.50 11.74 13.11  13.83
#> 168   T   M  8.05  8.54  9.59 10.75 12.02 13.42  14.17
#> 169   T   M  8.24  8.74  9.82 11.00 12.30 13.74  14.51
#> 170   T   M  8.85  9.38 10.52 11.78 13.18 14.73  15.57
#> 171   T   M  9.79 10.36 11.62 13.02 14.59 16.35  17.30
#> 172   T   M 10.59 11.21 12.58 14.12 15.86 17.83  18.91
#> 173   T   M 11.39 12.06 13.52 15.19 17.09 19.26  20.45
#> 174   T   M 12.18 12.89 14.47 16.28 18.36 20.76  22.10
#> 175   T   M 12.98 13.74 15.45 17.42 19.72 22.40  23.91
#> 176   T   M 13.83 14.64 16.47 18.60 21.10 24.07  25.75
#> 177   T   M 14.67 15.54 17.50 19.82 22.57 25.87  27.76
#> 178   T   M 15.54 16.47 18.57 21.08 24.09 27.76  29.89
#> 179   T   M 16.39 17.38 19.64 22.37 25.69 29.79  32.21
#> 180   T   M 17.28 18.33 20.74 23.68 27.30 31.82  34.52
#> 181   T   M 18.14 19.26 21.85 25.03 28.99 34.02  37.07
#> 182   T   M 19.08 20.26 23.02 26.43 30.73 36.25  39.64
#> 183   T   M 19.97 21.24 24.18 27.86 32.54 38.65  42.44
#> 184   T   M 20.86 22.20 25.35 29.30 34.38 41.11  45.32
#> 185   T   M 21.78 23.20 26.54 30.76 36.22 43.51  48.12
#> 186   T   M 22.66 24.16 27.73 32.25 38.15 46.09  51.15
#> 187   T   M 23.59 25.18 28.97 33.79 40.10 48.62  54.07
#> 188   T   M 24.55 26.25 30.28 35.43 42.17 51.29  57.12
#> 189   T   M 25.53 27.36 31.69 37.23 44.48 54.28  60.53
#> 190   T   M 26.65 28.62 33.29 39.24 47.00 57.39  63.97
#> 191   T   M 27.85 29.99 35.06 41.48 49.79 60.77  67.64
#> 192   T   M 29.23 31.56 37.07 43.99 52.84 64.35  71.44
#> 193   T   M 30.74 33.29 39.29 46.77 56.22 68.31  75.64
#> 194   T   M 32.59 35.35 41.80 49.77 59.69 72.17  79.61
#> 195   T   M 34.62 37.58 44.46 52.87 63.22 76.06  83.62
#> 196   T   M 36.88 40.00 47.20 55.94 66.59 79.64  87.25
#> 197   T   M 39.20 42.43 49.87 58.82 69.65 82.80  90.42
#> 198   T   M 41.54 44.84 52.41 61.45 72.32 85.43  92.98
#> 199   T   M 43.65 47.01 54.66 63.77 74.67 87.77  95.30
#> 200   T   M 45.58 48.96 56.64 65.75 76.61 89.61  97.06
#> 201   T   M 47.22 50.62 58.32 67.43 78.26 91.18  98.58
#> 202   T   M 48.71 52.11 59.79 68.85 79.59 92.38  99.68
#> 203   T   M 49.95 53.35 61.02 70.06 80.75 93.45 100.70
#> 204   T   M 51.07 54.47 62.12 71.10 81.70 94.27 101.43
#> 205   T   M 52.01 55.41 63.06 72.04 82.62 95.15 102.28
#> 206   T   M 52.90 56.30 63.94 72.89 83.43 95.89 102.98
#> 207   T   M 53.88 57.26 64.84 73.70 84.10 96.37 103.33
#> 208   T   M 48.33 50.76 56.51 63.85 73.58 87.13  96.14
#> 209   T   F  2.46  2.63  2.97  3.34  3.74  4.16   4.39
#> 210   T   F  2.59  2.76  3.12  3.51  3.93  4.38   4.62
#> 211   T   F  2.73  2.90  3.28  3.69  4.13  4.60   4.85
#> 212   T   F  2.85  3.04  3.43  3.86  4.32  4.82   5.08
#> 213   T   F  2.98  3.17  3.58  4.03  4.51  5.03   5.30
#> 214   T   F  3.11  3.32  3.74  4.21  4.71  5.26   5.54
#> 215   T   F  3.25  3.46  3.90  4.38  4.90  5.46   5.76
#> 216   T   F  3.38  3.60  4.06  4.56  5.10  5.68   5.99
#> 217   T   F  3.51  3.74  4.21  4.73  5.29  5.90   6.22
#> 218   T   F  3.65  3.88  4.37  4.90  5.48  6.10   6.43
#> 219   T   F  3.78  4.02  4.52  5.07  5.67  6.31   6.66
#> 220   T   F  4.03  4.28  4.82  5.40  6.04  6.73   7.10
#> 221   T   F  4.28  4.54  5.11  5.72  6.39  7.12   7.50
#> 222   T   F  4.52  4.79  5.38  6.03  6.74  7.50   7.91
#> 223   T   F  4.74  5.03  5.64  6.32  7.06  7.87   8.30
#> 224   T   F  4.96  5.25  5.89  6.59  7.36  8.19   8.64
#> 225   T   F  5.16  5.46  6.12  6.85  7.65  8.52   8.98
#> 226   T   F  5.35  5.66  6.35  7.10  7.93  8.83   9.32
#> 227   T   F  5.54  5.86  6.56  7.33  8.18  9.10   9.60
#> 228   T   F  5.71  6.04  6.76  7.55  8.42  9.38   9.89
#> 229   T   F  6.02  6.36  7.12  7.95  8.87  9.88  10.43
#> 230   T   F  6.30  6.66  7.45  8.32  9.28 10.35  10.92
#> 231   T   F  6.56  6.94  7.76  8.66  9.66 10.78  11.38
#> 232   T   F  6.82  7.21  8.04  8.97 10.00 11.14  11.76
#> 233   T   F  7.04  7.44  8.30  9.27 10.35 11.55  12.20
#> 234   T   F  7.25  7.66  8.55  9.55 10.66 11.90  12.57
#> 235   T   F  7.46  7.88  8.79  9.81 10.95 12.23  12.92
#> 236   T   F  7.65  8.08  9.01 10.06 11.23 12.54  13.26
#> 237   T   F  7.84  8.27  9.23 10.30 11.50 12.85  13.58
#> 238   T   F  8.41  8.88  9.90 11.06 12.37 13.84  14.65
#> 239   T   F  9.35  9.87 11.02 12.32 13.81 15.51  16.45
#> 240   T   F 10.23 10.80 12.07 13.52 15.19 17.12  18.20
#> 241   T   F 11.06 11.68 13.07 14.68 16.55 18.74  19.97
#> 242   T   F 11.86 12.54 14.05 15.82 17.90 20.36  21.77
#> 243   T   F 12.64 13.37 15.01 16.94 19.24 21.99  23.57
#> 244   T   F 13.38 14.16 15.94 18.05 20.59 23.68  25.48
#> 245   T   F 14.15 14.99 16.90 19.21 22.02 25.48  27.53
#> 246   T   F 14.96 15.86 17.92 20.44 23.54 27.42  29.75
#> 247   T   F 15.80 16.76 19.01 21.77 25.22 29.62  32.29
#> 248   T   F 16.72 17.76 20.18 23.19 27.00 31.92  34.96
#> 249   T   F 17.61 18.74 21.37 24.68 28.93 34.55  38.07
#> 250   T   F 18.55 19.76 22.61 26.22 30.92 37.24  41.26
#> 251   T   F 19.50 20.79 23.87 27.80 32.98 40.03  44.59
#> 252   T   F 20.39 21.78 25.11 29.40 35.12 43.02  48.19
#> 253   T   F 21.31 22.80 26.39 31.04 37.28 46.00  51.76
#> 254   T   F 22.24 23.85 27.71 32.75 39.55 49.10  55.43
#> 255   T   F 23.21 24.94 29.09 34.52 41.85 52.15  58.97
#> 256   T   F 24.16 26.03 30.52 36.40 44.34 55.48  62.85
#> 257   T   F 25.28 27.29 32.13 38.46 46.96 58.77  66.50
#> 258   T   F 26.52 28.70 33.93 40.73 49.78 62.19  70.19
#> 259   T   F 28.05 30.39 36.00 43.21 52.69 65.44  73.53
#> 260   T   F 29.93 32.41 38.30 45.80 55.49 68.27  76.23
#> 261   T   F 32.00 34.58 40.67 48.32 58.08 70.76  78.54
#> 262   T   F 34.15 36.78 42.95 50.64 60.37 72.87  80.48
#> 263   T   F 36.26 38.89 45.06 52.70 62.33 74.66  82.15
#> 264   T   F 38.19 40.81 46.92 54.48 64.00 76.21  83.65
#> 265   T   F 39.83 42.43 48.48 56.00 65.49 77.74  85.24
#> 266   T   F 41.24 43.81 49.82 57.29 66.77 79.10  86.71
#> 267   T   F 42.42 44.98 50.93 58.37 67.86 80.31  88.08
#> 268   T   F 43.48 46.00 51.90 59.28 68.74 81.24  89.10
#> 269   T   F 44.23 46.75 52.64 60.04 69.59 82.33  90.42
#> 270   T   F 44.99 47.48 53.33 60.70 70.24 83.04  91.22
#> 271   T   F 45.58 48.07 53.90 61.27 70.85 83.81  92.14
#> 272   T   F 46.14 48.61 54.43 61.79 71.41 84.48  92.95
#> 273   T   F 46.63 49.10 54.90 62.25 71.89 85.06  93.64
#> 274   T   F 47.11 49.56 55.34 62.68 72.33 85.57  94.24
#> 275   T   F 47.55 49.99 55.75 63.08 72.73 86.03  94.77
#> 276   T   F 47.90 50.34 56.11 63.47 73.20 86.71  95.66
#> 277   T   F 48.33 50.76 56.51 63.85 73.58 87.13  96.14
#> 278   M   M  2.46  2.63  2.97  3.34  3.74  4.16   4.39
#> 279   M   M  2.59  2.76  3.12  3.51  3.93  4.38   4.62
#> 280   M   M  2.73  2.90  3.28  3.69  4.13  4.60   4.85
#> 281   M   M  2.85  3.04  3.43  3.86  4.32  4.82   5.08
#> 282   M   M  2.98  3.17  3.58  4.03  4.51  5.03   5.30
#> 283   M   M  3.11  3.32  3.74  4.21  4.71  5.26   5.54
#> 284   M   M  3.25  3.46  3.90  4.38  4.90  5.46   5.76
#> 285   M   M  3.38  3.60  4.06  4.56  5.10  5.68   5.99
#> 286   M   M  3.51  3.74  4.21  4.73  5.29  5.90   6.22
#> 287   M   M  3.65  3.88  4.37  4.90  5.48  6.10   6.43
#> 288   M   M  3.78  4.02  4.52  5.07  5.67  6.31   6.66
#> 289   M   M  4.03  4.28  4.82  5.40  6.04  6.73   7.10
#> 290   M   M  4.28  4.54  5.11  5.72  6.39  7.12   7.50
#> 291   M   M  4.52  4.79  5.38  6.03  6.74  7.50   7.91
#> 292   M   M  4.74  5.03  5.64  6.32  7.06  7.87   8.30
#> 293   M   M  4.96  5.25  5.89  6.59  7.36  8.19   8.64
#> 294   M   M  5.16  5.46  6.12  6.85  7.65  8.52   8.98
#> 295   M   M  5.35  5.66  6.35  7.10  7.93  8.83   9.32
#> 296   M   M  5.54  5.86  6.56  7.33  8.18  9.10   9.60
#> 297   M   M  5.71  6.04  6.76  7.55  8.42  9.38   9.89
#> 298   M   M  6.02  6.36  7.12  7.95  8.87  9.88  10.43
#> 299   M   M  6.30  6.66  7.45  8.32  9.28 10.35  10.92
#> 300   M   M  6.56  6.94  7.76  8.66  9.66 10.78  11.38
#> 301   M   M  6.82  7.21  8.04  8.97 10.00 11.14  11.76
#> 302   M   M  7.04  7.44  8.30  9.27 10.35 11.55  12.20
#> 303   M   M  7.25  7.66  8.55  9.55 10.66 11.90  12.57
#> 304   M   M  7.46  7.88  8.79  9.81 10.95 12.23  12.92
#> 305   M   M  7.65  8.08  9.01 10.06 11.23 12.54  13.26
#> 306   M   M  7.84  8.27  9.23 10.30 11.50 12.85  13.58
#> 307   M   M  8.41  8.88  9.90 11.06 12.37 13.84  14.65
#> 308   M   M  9.35  9.87 11.02 12.32 13.81 15.51  16.45
#> 309   M   M 10.23 10.80 12.07 13.52 15.19 17.12  18.20
#> 310   M   M 11.06 11.68 13.07 14.68 16.55 18.74  19.97
#> 311   M   M 11.86 12.54 14.05 15.82 17.90 20.36  21.77
#> 312   M   M 12.64 13.37 15.01 16.94 19.24 21.99  23.57
#> 313   M   M 13.38 14.16 15.94 18.05 20.59 23.68  25.48
#> 314   M   M 14.15 14.99 16.90 19.21 22.02 25.48  27.53
#> 315   M   M 14.96 15.86 17.92 20.44 23.54 27.42  29.75
#> 316   M   M 15.80 16.76 19.01 21.77 25.22 29.62  32.29
#> 317   M   M 16.72 17.76 20.18 23.19 27.00 31.92  34.96
#> 318   M   M 17.61 18.74 21.37 24.68 28.93 34.55  38.07
#> 319   M   M 18.55 19.76 22.61 26.22 30.92 37.24  41.26
#> 320   M   M 19.50 20.79 23.87 27.80 32.98 40.03  44.59
#> 321   M   M 20.39 21.78 25.11 29.40 35.12 43.02  48.19
#> 322   M   M 21.31 22.80 26.39 31.04 37.28 46.00  51.76
#> 323   M   M 22.24 23.85 27.71 32.75 39.55 49.10  55.43
#> 324   M   M 23.21 24.94 29.09 34.52 41.85 52.15  58.97
#> 325   M   M 24.16 26.03 30.52 36.40 44.34 55.48  62.85
#> 326   M   M 25.28 27.29 32.13 38.46 46.96 58.77  66.50
#> 327   M   M 26.52 28.70 33.93 40.73 49.78 62.19  70.19
#> 328   M   M 28.05 30.39 36.00 43.21 52.69 65.44  73.53
#> 329   M   M 29.93 32.41 38.30 45.80 55.49 68.27  76.23
#> 330   M   M 32.00 34.58 40.67 48.32 58.08 70.76  78.54
#> 331   M   M 34.15 36.78 42.95 50.64 60.37 72.87  80.48
#> 332   M   M 36.26 38.89 45.06 52.70 62.33 74.66  82.15
#> 333   M   M 38.19 40.81 46.92 54.48 64.00 76.21  83.65
#> 334   M   M 39.83 42.43 48.48 56.00 65.49 77.74  85.24
#> 335   M   M 41.24 43.81 49.82 57.29 66.77 79.10  86.71
#> 336   M   M 42.42 44.98 50.93 58.37 67.86 80.31  88.08
#> 337   M   M 43.48 46.00 51.90 59.28 68.74 81.24  89.10
#> 338   M   M 44.23 46.75 52.64 60.04 69.59 82.33  90.42
#> 339   M   M 44.99 47.48 53.33 60.70 70.24 83.04  91.22
#> 340   M   M 45.58 48.07 53.90 61.27 70.85 83.81  92.14
#> 341   M   M 46.14 48.61 54.43 61.79 71.41 84.48  92.95
#> 342   M   M 46.63 49.10 54.90 62.25 71.89 85.06  93.64
#> 343   M   M 47.11 49.56 55.34 62.68 72.33 85.57  94.24
#> 344   M   M 47.55 49.99 55.75 63.08 72.73 86.03  94.77
#> 345   M   M 48.33 50.76 56.51 63.85 73.58 87.13  96.14
#> 346   M   F  2.46  2.63  2.97  3.34  3.74  4.16   4.39
#> 347   M   F  2.59  2.76  3.12  3.51  3.93  4.38   4.62
#> 348   M   F  2.73  2.90  3.28  3.69  4.13  4.60   4.85
#> 349   M   F  2.85  3.04  3.43  3.86  4.32  4.82   5.08
#> 350   M   F  2.98  3.17  3.58  4.03  4.51  5.03   5.30
#> 351   M   F  3.11  3.32  3.74  4.21  4.71  5.26   5.54
#> 352   M   F  3.25  3.46  3.90  4.38  4.90  5.46   5.76
#> 353   M   F  3.38  3.60  4.06  4.56  5.10  5.68   5.99
#> 354   M   F  3.51  3.74  4.21  4.73  5.29  5.90   6.22
#> 355   M   F  3.65  3.88  4.37  4.90  5.48  6.10   6.43
#> 356   M   F  3.78  4.02  4.52  5.07  5.67  6.31   6.66
#> 357   M   F  4.03  4.28  4.82  5.40  6.04  6.73   7.10
#> 358   M   F  4.28  4.54  5.11  5.72  6.39  7.12   7.50
#> 359   M   F  4.52  4.79  5.38  6.03  6.74  7.50   7.91
#> 360   M   F  4.74  5.03  5.64  6.32  7.06  7.87   8.30
#> 361   M   F  4.96  5.25  5.89  6.59  7.36  8.19   8.64
#> 362   M   F  5.16  5.46  6.12  6.85  7.65  8.52   8.98
#> 363   M   F  5.35  5.66  6.35  7.10  7.93  8.83   9.32
#> 364   M   F  5.54  5.86  6.56  7.33  8.18  9.10   9.60
#> 365   M   F  5.71  6.04  6.76  7.55  8.42  9.38   9.89
#> 366   M   F  6.02  6.36  7.12  7.95  8.87  9.88  10.43
#> 367   M   F  6.30  6.66  7.45  8.32  9.28 10.35  10.92
#> 368   M   F  6.56  6.94  7.76  8.66  9.66 10.78  11.38
#> 369   M   F  6.82  7.21  8.04  8.97 10.00 11.14  11.76
#> 370   M   F  7.04  7.44  8.30  9.27 10.35 11.55  12.20
#> 371   M   F  7.25  7.66  8.55  9.55 10.66 11.90  12.57
#> 372   M   F  7.46  7.88  8.79  9.81 10.95 12.23  12.92
#> 373   M   F  7.65  8.08  9.01 10.06 11.23 12.54  13.26
#> 374   M   F  7.84  8.27  9.23 10.30 11.50 12.85  13.58
#> 375   M   F  8.41  8.88  9.90 11.06 12.37 13.84  14.65
#> 376   M   F  9.35  9.87 11.02 12.32 13.81 15.51  16.45
#> 377   M   F 10.23 10.80 12.07 13.52 15.19 17.12  18.20
#> 378   M   F 11.06 11.68 13.07 14.68 16.55 18.74  19.97
#> 379   M   F 11.86 12.54 14.05 15.82 17.90 20.36  21.77
#> 380   M   F 12.64 13.37 15.01 16.94 19.24 21.99  23.57
#> 381   M   F 13.38 14.16 15.94 18.05 20.59 23.68  25.48
#> 382   M   F 14.15 14.99 16.90 19.21 22.02 25.48  27.53
#> 383   M   F 14.96 15.86 17.92 20.44 23.54 27.42  29.75
#> 384   M   F 15.80 16.76 19.01 21.77 25.22 29.62  32.29
#> 385   M   F 16.72 17.76 20.18 23.19 27.00 31.92  34.96
#> 386   M   F 17.61 18.74 21.37 24.68 28.93 34.55  38.07
#> 387   M   F 18.55 19.76 22.61 26.22 30.92 37.24  41.26
#> 388   M   F 19.50 20.79 23.87 27.80 32.98 40.03  44.59
#> 389   M   F 20.39 21.78 25.11 29.40 35.12 43.02  48.19
#> 390   M   F 21.31 22.80 26.39 31.04 37.28 46.00  51.76
#> 391   M   F 22.24 23.85 27.71 32.75 39.55 49.10  55.43
#> 392   M   F 23.21 24.94 29.09 34.52 41.85 52.15  58.97
#> 393   M   F 24.16 26.03 30.52 36.40 44.34 55.48  62.85
#> 394   M   F 25.28 27.29 32.13 38.46 46.96 58.77  66.50
#> 395   M   F 26.52 28.70 33.93 40.73 49.78 62.19  70.19
#> 396   M   F 28.05 30.39 36.00 43.21 52.69 65.44  73.53
#> 397   M   F 29.93 32.41 38.30 45.80 55.49 68.27  76.23
#> 398   M   F 32.00 34.58 40.67 48.32 58.08 70.76  78.54
#> 399   M   F 34.15 36.78 42.95 50.64 60.37 72.87  80.48
#> 400   M   F 36.26 38.89 45.06 52.70 62.33 74.66  82.15
#> 401   M   F 38.19 40.81 46.92 54.48 64.00 76.21  83.65
#> 402   M   F 39.83 42.43 48.48 56.00 65.49 77.74  85.24
#> 403   M   F 41.24 43.81 49.82 57.29 66.77 79.10  86.71
#> 404   M   F 42.42 44.98 50.93 58.37 67.86 80.31  88.08
#> 405   M   F 43.48 46.00 51.90 59.28 68.74 81.24  89.10
#> 406   M   F 44.23 46.75 52.64 60.04 69.59 82.33  90.42
#> 407   M   F 44.99 47.48 53.33 60.70 70.24 83.04  91.22
#> 408   M   F 45.58 48.07 53.90 61.27 70.85 83.81  92.14
#> 409   M   F 46.14 48.61 54.43 61.79 71.41 84.48  92.95
#> 410   M   F 46.63 49.10 54.90 62.25 71.89 85.06  93.64
#> 411   M   F 47.11 49.56 55.34 62.68 72.33 85.57  94.24
#> 412   M   F 47.55 49.99 55.75 63.08 72.73 86.03  94.77
#> 413   M   F 47.90 50.34 56.11 63.47 73.20 86.71  95.66
#> 414   M   F 48.33 50.76 56.51 63.85 73.58 87.13  96.14

# P85 of BMI in 5-8 year old Dutch boys and girls
e <- expand.grid(age=5:8, sex=c("M","F"))
w <- z2y(z=rep(qnorm(0.85),nrow(e)), x=e$age, sex=e$sex, ref=nl4.bmi)
w <- matrix(w, nrow=2, byrow=TRUE)
dimnames(w) <- list(c("boys","girls"),5:8)
w
#>            5      6      7      8
#> boys  17.152 17.282 17.508 17.857
#> girls 17.090 17.386 17.837 18.327

# data transformation of height z-scores to cm-scale
z <- c(-1.83, 0.09, 2.33, 0.81, -1.20)
x <- c(8.33,  0.23, 19.2, 24.3, 10)
sex <- c("M", "M", "F", "M", "F")
round(z2y(z=z, x=x, sex=sex, ref=nl4.hgt), 1)
#> [1] 123.8  60.7 185.3 189.7 135.6

# interpolate published height standard 
# to daily values, days 0-31, boys
# on centiles -2SD, 0SD and +2SD 
days <- 0:31
sds  <- c(-2, 0, +2)
z    <- rep(sds, length(days))
x    <- rep(round(days/365.25,4), each=length(sds))
w    <- z2y(z, x, sex="M", ref=nl4.hgt)
w    <- matrix(w, ncol=length(sds), byrow=TRUE)
dimnames(w) <- list(days, sds)
w
#>        -2      0      2
#> 0  47.163 51.320 55.477
#> 1  47.265 51.430 55.594
#> 2  47.371 51.543 55.716
#> 3  47.474 51.653 55.833
#> 4  47.580 51.767 55.954
#> 5  47.682 51.877 56.071
#> 6  47.784 51.986 56.188
#> 7  47.890 52.100 56.310
#> 8  47.993 52.210 56.427
#> 9  48.096 52.321 56.545
#> 10 48.203 52.435 56.667
#> 11 48.305 52.545 56.785
#> 12 48.412 52.659 56.907
#> 13 48.515 52.770 57.024
#> 14 48.618 52.880 57.142
#> 15 48.727 52.995 57.264
#> 16 48.832 53.106 57.381
#> 17 48.937 53.217 57.498
#> 18 49.046 53.333 57.619
#> 19 49.151 53.444 57.736
#> 20 49.260 53.559 57.857
#> 21 49.366 53.670 57.974
#> 22 49.469 53.781 58.093
#> 23 49.577 53.896 58.216
#> 24 49.681 54.007 58.334
#> 25 49.784 54.118 58.453
#> 26 49.892 54.234 58.576
#> 27 49.996 54.345 58.694
#> 28 50.103 54.460 58.817
#> 29 50.213 54.573 58.933
#> 30 50.324 54.686 59.049
#> 31 50.438 54.803 59.169