**Epidemiology**

in Monochorionic Pregnancies" (Bruno Toneto). The pathophysiology of most of these com‐ plications is related to placental angioarchitecture such as twin to twin transfusion syn‐ drome (TTTS). Fetoscopic laser treatment for TTTS represents one of the best applications for fetal surgery, showing great results. Fetoscopic laser photocoagulation has drastically improved the survival rate of fetuses with TTTS when compared to serial amnioreduction. The chapter "Quadruplets and Quintuplets" (Stelios Fiorentzis et al.) shows that preterm birth occurs in nearly 100% of high-order pregnancy twins and in 50% of twins as demon‐ strated in the chapter "Preterm Birth in Twins" (Marcelo Santucci et al.). Perinatal morbidity and mortality in multiple pregnancy is very elevated when compared to singleton pregnan‐ cy. The incidence of twins is only 2–3% of all pregnancies, but it is responsible for 15% of all preterm births with less than 32 weeks. Therefore, several strategies have been proposed to minimize this risk, such as follow-up of cervical length to prevent preterm birth, pessary, progesterone, and tocolysis to postpone birth to use corticosteroids in fetal pulmonary ma‐

After all the intense prenatal care, good assistance during delivery is essential, which brings us to the final stop on this journey: the chapter "Time and Mode of Delivery in Twin Preg‐

Throughout our 10 chapters the book contemplates the most relevant aspects of the multiple pregnancy scenario. Authors from all over the world, who have contributed to this book, know their subjects deeply and offer readers the best from their research experiences.

I would like to thank my wife, Camila, and our children João and Pedro for their support, understanding and love during the journey to complete this mission that will help women

**Julio Elito Jr.**

São Paulo, Brazil

Associate Professor of the Department of Obstetrics

Federal University of São Paulo (UNIFESP)

The book gives the reader a state-of-the-art update on multiple pregnancy.

turation, and magnesium sulfate use for neuroprotection.

nancies" (Eduardo Santana et al.).

VIII Preface

with multiple pregnancy all over the world.

**Chapter 1**

Provisional chapter

**Historical Studies of Hellin's Law**

Historical Studies of Hellin's Law

Additional information is available at the end of the chapter

Theorems, proofs, laws and rules are commonly named according to the presumed discoverer, but often earlier investigators have contributed substantially to the findings. One example of this is Hellin's law, which was named after Hellin, although he was not the first to derive it. In research on twinning and higher multiple maternities, the law has played a central role because it is approximately correct, despite showing discrepancies that are difficult to explain or eliminate. However, most studies are based on empirical rates of multiple maternities. Such studies can only serve to identify errors too large to be characterized as random. It has been mathematically proven that Hellin's law does not hold as a general rule. Consequently, improvements to this law have been proposed. Keywords: twinning rates, triplet rates, quadruplet rates, Stigler's law, maternal age,

DOI: 10.5772/intechopen.79583

During the history of research on multiple maternities, Hellin's law has been applied as a rule of thumb. Consequently, the law contributes to the description of the twinning models. In this paper, we consider how Hellin's law can be tested and used. It is of particular interest to determine why the rates of higher multiple maternities are sometimes too high or too low when Hellin's law is used as a benchmark. The analysis of Fellman and Eriksson [1] of triplet and quadruplet rates indicated that triplet rates are closer to Hellin's law than quadruplet rates. According to the analyses by Fellman and Eriksson [2] of the twinning rate and the transformed triplet rate and quadruplet rate for Sweden (1751–2000), both triplet and quadruplet rates showed excesses after the 1960s. This is mainly caused by the influence of the artificial reproduction technologies, particularly the use of fertility-enhancing drugs. Fellman and Eriksson [2] introduced measures of concordance between triplet rates with Hellin's law.

> © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.79583

Johan Fellman

Johan Fellman

Abstract

temporal trends

1. Introduction

#### **Chapter 1** Provisional chapter

#### **Historical Studies of Hellin's Law** Historical Studies of Hellin's Law

#### Johan Fellman Johan Fellman

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.79583

#### Abstract

Theorems, proofs, laws and rules are commonly named according to the presumed discoverer, but often earlier investigators have contributed substantially to the findings. One example of this is Hellin's law, which was named after Hellin, although he was not the first to derive it. In research on twinning and higher multiple maternities, the law has played a central role because it is approximately correct, despite showing discrepancies that are difficult to explain or eliminate. However, most studies are based on empirical rates of multiple maternities. Such studies can only serve to identify errors too large to be characterized as random. It has been mathematically proven that Hellin's law does not hold as a general rule. Consequently, improvements to this law have been proposed.

DOI: 10.5772/intechopen.79583

Keywords: twinning rates, triplet rates, quadruplet rates, Stigler's law, maternal age, temporal trends

#### 1. Introduction

During the history of research on multiple maternities, Hellin's law has been applied as a rule of thumb. Consequently, the law contributes to the description of the twinning models. In this paper, we consider how Hellin's law can be tested and used. It is of particular interest to determine why the rates of higher multiple maternities are sometimes too high or too low when Hellin's law is used as a benchmark. The analysis of Fellman and Eriksson [1] of triplet and quadruplet rates indicated that triplet rates are closer to Hellin's law than quadruplet rates. According to the analyses by Fellman and Eriksson [2] of the twinning rate and the transformed triplet rate and quadruplet rate for Sweden (1751–2000), both triplet and quadruplet rates showed excesses after the 1960s. This is mainly caused by the influence of the artificial reproduction technologies, particularly the use of fertility-enhancing drugs. Fellman and Eriksson [2] introduced measures of concordance between triplet rates with Hellin's law.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Regression analyses of twinning and triplet rates yield rather good fits with respect to Hellin's law, but deficiencies in the triplet rates are commonly present. According to Hellin's law, historical data show deficiencies in triplet rates, but recent data reveal excesses, especially among older mothers. The excesses obtained are in good agreement with other studies of recent data. Here, we pay special attention to the use of Hellin's law in investigations of multiple maternities.

Advancement of Science, at the end of which he had contributed to the creation of a section devoted to statistics. The idea to organize a congress, the main objective of which was to lay down a common foundation for statistical data to enable international comparisons, was presented by

Historical Studies of Hellin's Law

5

http://dx.doi.org/10.5772/intechopen.79583

bring together at a congress in Brussels the persons, who in various countries, are dealing specifically with statistics, in order to give their works a common impulse, and to adopt, for the computations, uniform grounds which will allow for comparison of observations and results.

Furthermore, Droesbeke describes the congress programme and stressed the content of the

It is to be hoped that the works which belongs to this science will now be taken on, in every State, following the bases which have been laid down during the Congress of Brussels. It is not any more a theoretical wish, to see the states adopt uniform bases for scientific works in order to make the results comparable; the opportunity of implementation of the idea has been proclaimed; the framework has been chosen and the reading of the report […] will demonstrate what is allowed to expect from the wisdom, maturity, perfect intelligence and good harmony

Finally, Droesbeke listed the Statistical Congresses during the nineteenth century that followed

Recently, Randeraad [8] directed attention to and even criticism of the international statistical congresses in the second half of the nineteenth century. He stated that it would be overly simplistic to assume that they were an outright success. In fact, no more congresses were held

More importantly, by then it was clear that the aspirations of the early congresses had been too high. International uniformity in statistics was evidently not a goal that could be reached overnight. Much of this failure to bring about rapid change can be explained by the difficulties in realizing effective knowledge transfers, in other words effective communication, in an age that was not fully prepared for truly international activities. It has been shown that the second half of the nineteenth century was a period of numerous experiments in internationalism, but

In most countries, the registers were deemed lacking in essential facts; those of Belgium and Sweden were perhaps the most detailed for scientific inquiries [3]. Arosenius [9] presented a detailed study of the emergence of the official statistics of Sweden. His presentation shows just how difficult the development of the process is until an official statistics of modern proficiency

Already in the eighteenth century, Wargentin published demographic data for Sweden. However, he did not pay any attention to twinning and higher multiple maternities [10]. Berg [11] published a comprehensive study of multiple maternities. He analyzed the rates of multiple maternities in Sweden from 1776 to 1878. He also presented corresponding data for several

at the same time rampant nationalism nipped many initiatives in the bud.

Quetelet 1851. He offered to

the first one in Brussels.

is born.

(Bulletin of the Commission, 1853, p. 106).

which presided over the deliberations of the Congress.

congress according to Quetelet's words:

after 1876. Furthermore, he stressed that:
