Details • PERiskProfileR

Introduction

The FMF risk calculator is developed by the Fetal Medicine Foundation and the underlying model is published in the following papers: (Wright et al. 2015; Tan et al. 2018; Wright, Wright, and Nicolaides 2020).

Some details are, however, not well documented and must therefore be considered as experimental from my part.

MoM Calculations

General notes

The MoM values for the FMF calculator are estimated from a model published by Tan et al. (2018). The regression equations produce the log10 expected values, so to get the actual MoM values:

$MoM = \frac{Measured}{10^{result}}.$

Gestational age

The gestational age at which the measurements are taken is used to calculate the MoM values. Note that there are three dates that are used in the calculations:

ga_at
biophysical_at
biochemical_at

In addition, the user provides a variable ga that is the gestational age in weeks at the date ga_at. Note that CRL is not used in the calculations. The gestational age at blood sampling is thus calculated as ga plus the number of weeks between biochemical_at and ga_at (biochemical_at - ga_at). The same approach is used for MAP and UtAPI, but using biophysical_at.

For women with previous pregnancies, the gestational age at delivery for the previous pregnancy is given by the user. The inter-pregnancy interval, however, is calculated as the number of years (in this package: the number of days divided by 365.25) between the previous delivery date and the beginning of the current pregnancy (i.e., ga_at minus ga*7 days).

Truncations

Some of variables affecting the MoMs are truncated. The limits are as follows (haven’t found them reported):

Weight, upper limit: 130 kg
Previous interval, upper limit: 20 years

Variables involved in MoM calculations

	PlGF	UtAPI	MAP	Prior risk
Instrument	x
GA	x	x	x
Weight	x	x	x	Only when no CH
Height			x	x
Age	x	x		Only when > 35
Afro-caribbean	x	x	x	x
South-Asian	x			x
East-Asian	x	x
Mixed	x	x
Smoking	x		x
Chronic hypertension			x	x
Family history of PE			x	Only when no CH
DM-1	x	x	x	Only when no CH
DM-2			x	Only when no CH
DM-2 with insulin	x
ALS or SLE				x (See note below)
In-vitro fertilization	x			x
Parous but not previous PE	x	x	x
Parous with previous PE		x	x	x
Inter-pregnancy interval			Only when no previous PE	Only when no previous PE
GA at previous delivery				x

Prior risk

The variables involved in the calculation of prior risk are given in the table above. The regression model will produce a $\hat{\mu}$ from the provided variables. The $\sigma$ is fixed at $\sigma = 6.8833$ . The prior risk is then calculated as the cummulative probability of the normal distribution with mean $\hat{\mu}$ and standard deviation $\sigma$ at the value of $g$ , where $g$ is the gestational age of interest (in weeks).

Important note: Whereas the published papers states that SLE or APS increase the risk of PE, the online FMF calculator seems to give increased risk only when BOTH SLE AND APS are present.

Truncations

Some variables are truncated in calculation of prior risk. Note that these limits are not the same as for MoM calculations (given above). The limits are as follows:

Maternal age: lower 12 years, upper 55 years
Maternal weight: lower 34 kg, upper 190 kg
Maternal height: lower 127 cm, upper 198 cm
GA at delivery in previous pregnancy: lower 24 weeks, upper 42 weeks
Inter-pregnancy interval: lower 0.25 years, upper 15 years

Posterior risk

The posterior risk $p$ at some gestational week $G$ is calculated as

$p(G) = \frac{\int_{24}^{G} h(g) \cdot \tilde{p}(g) dg}{\int_{24}^{\infty} h(g) \cdot \tilde{p}(g) dg}$

where $\tilde{p}(g)$ is the prior risk at week $g$ (as described above), and $h(g)$ is an adjustment based on MoM of MAP, PlGF and UtAPI (as described below).

Important: In practice, the integral diverged for some inputs when the upper limit was $\infty$ . Therefore, I have used upper level 1e3. This seems to work fine (see validation).

The adjustment $h(g)$ is only calculated from the MoMs (and not other variables) and given by the multivariate normal distribution

emdbook::dmvnorm(
      < measured MoM for MAP, UtAPI, PlGF >,
      mu = < mu for MAP, UtAPI, PlGF >,
      Sigma = < Covariance Matrix >
    )

where the first input is the log10 of the MoMs for MAP, PI and PlGF as calculated above. The $\mu$ for MAP, UtAPI and PlGF is based on gestational age $g$ and the following regression formula:

$\mu = \beta_0 + \beta_1 \cdot g,\,\,\,\,\, g < -\beta_0/\beta_1,$ and $\mu = 0$ when $g \geq -\beta_0/\beta_1$ . The coefficients are

	$\beta_0$	$\beta_1$
MAP	0.088997	-0.0016711
UtAPI	0.5861	-0.014233
PlGF	-0.92352	0.021584

The covariance matrix is as follows:

	MAP	PI	PlGF
MAP	0.00141396	-0.0002726	-0.0001907
PI	-0.0002726	0.01630906	-0.0034539
PlGF	-0.0001907	-0.0034539	0.03147225

Please note: The emdbook::dmvnorm() function is the bottleneck of the package and I haven’t found a good way of improving performance yet.

Truncations

There are limits for the MoM values, and values outside these limits are truncated in the calculations but are still reported un-truncated by the online FMF calculator. The limits are as follows:

Log10 MoM-MAP: lower: -0.1224076, upper: 0.12240759
Log10 MoM-PlGF: lower: -0.5655099, upper: 0.56550992
Log10 MoM-UtAPI: lower: -0.4216152, upper: 0.42161519

References

Tan, M. Y., A. Syngelaki, L. C. Poon, D. L. Rolnik, N. O’Gorman, J. L. Delgado, R. Akolekar, et al. 2018. “Screening for Pre-Eclampsia by Maternal Factors and Biomarkers at 11–13 Weeks’ Gestation.” Ultrasound in Obstetrics & Gynecology 52 (2): 186–95. https://doi.org/10.1002/uog.19112.

Wright, David, Argyro Syngelaki, Ranjit Akolekar, Leona C. Poon, and Kypros H. Nicolaides. 2015. “Competing Risks Model in Screening for Preeclampsia by Maternal Characteristics and Medical History.” American Journal of Obstetrics & Gynecology 213 (1): 62.e1–10. https://doi.org/10.1016/j.ajog.2015.02.018.

Wright, David, Alan Wright, and Kypros H. Nicolaides. 2020. “The Competing Risk Approach for Prediction of Preeclampsia.” American Journal of Obstetrics and Gynecology 223 (1): 12–23.e7. https://doi.org/10.1016/j.ajog.2019.11.1247.