# genetic algorithm .pdf

Nom original:

**genetic-algorithm.pdf**Titre:

**Estimating time to full uterine cervical dilation using genetic algorithm**Auteur:

**Jeong-Kyu Hoh; Kyung-Joon Cha; Moon-Il Park; Mei-Ling Ting Lee; Young-Sun Park**

Ce document au format PDF 1.7 a été généré par Elsevier / Acrobat Distiller 8.0.0 (Windows), et a été envoyé sur fichier-pdf.fr le 15/04/2015 à 15:02, depuis l'adresse IP 83.134.x.x.
La présente page de téléchargement du fichier a été vue 735 fois.

Taille du document: 405 Ko (6 pages).

Confidentialité: fichier public

### Aperçu du document

Kaohsiung Journal of Medical Sciences (2012) 28, 423e428

Available online at www.sciencedirect.com

journal homepage: http://www.kjms-online.com

ORIGINAL ARTICLE

Estimating time to full uterine cervical dilation using

genetic algorithm

Jeong-Kyu Hoh a, Kyung-Joon Cha b, Moon-Il Park a, Mei-Ling Ting Lee c,

Young-Sun Park b,*

a

Department of Obstetrics and Gynecology, College of Medicine, Hanyang University Hospital, Seoul,

South Korea

b

Department of Mathematics, Research Institute of Natural Sciences, Hanyang University, Seoul, South Korea

c

Department of Epidemiology and Biostatistics, Biostatistics and Risk Assessment Center, University

of Maryland, College Park, MD, USA

Received 30 May 2011; accepted 4 October 2011

Available online 9 April 2012

KEYWORDS

Cervical dilation;

Genetic algorithm;

Labor curves;

Nulliparous

Abstract The objectives of this study were to provide new parameters to better understand

labor curves, and to provide a model to predict the time to full cervical dilation (CD). We

studied labor curves using the retrospective records of 594 nulliparas, including at term, spontaneous labor onset, and singleton vertex deliveries of normal birth weight infants. We redefined the parameters of Friedman’s labor curve, and applied a three-parameter model to the

labor curve with a logistic model using the genetic algorithm and the NewtoneRaphson method

to predict the time necessary to reach full CD. The genetic algorithm is more effective than

the NewtoneRaphson method for modeling labor progress, as demonstrated by its higher accuracy in predicting the time to reach full CD. In addition, we predicted the time (11.4 hours) to

reach full CD using the logistic labor curve using the mean parameters (the power of

CD Z 0.97 cm/hours, a midpoint of the active phase Z 7.60 hours, and the initial

CD Z 2.11 cm). Our new parameters and model can predict the time to reach full CD, which

can aid in the forecasting of prolonged labor and the timing of interventions, with the end goal

being normal vaginal birth.

Copyright ª 2012, Elsevier Taiwan LLC. All rights reserved.

* Corresponding author. Department of Mathematics, Research Institute of Natural Sciences, Hanyang University, 17 Haengdang-dong,

Sungdong-gu, Seoul 133-791, South Korea.

E-mail address: pppppys@hanyang.ac.kr (Y.-S. Park).

1607-551X/$36 Copyright ª 2012, Elsevier Taiwan LLC. All rights reserved.

doi:10.1016/j.kjms.2012.02.012

424

Introduction

Labor is the presence of uterine contractions of sufficient

frequency, duration, and intensity to cause demonstrable

effacement and dilation of the cervix [1]. It is a continuum

that culminates in birth. Multiple fixed factors such as

parity, maternal weight, and fetal weight, as well as

commonly employed interventions (e.g., oxytocin

augmentation and epidural use) may significantly affect the

duration of labor [2]. Childbirth is a complex and dynamic

process that incorporates cervical dilation (CD), uterine

contractions, and the descent of the fetal head. CD and the

duration of CD are good diagnostic indicators of prolonged

labor [3e6]. Friedman [7] produced a chart to illustrate the

relationship between CD and the duration of the labor

process and to aid in differentiation between normal and

abnormal labors. He also established a series of definitions

of labor protraction and arrest. These definitions have been

widely adopted and applied in practice in the past halfcentury [8]. However, as there is no universal definition

of “normal” labor, and diagnosing prolonged labor is

inherently difficult [9].

Some studies have argued that the Friedman curve is no

longer appropriate for induced or actively managed labor

[10,11]. As a reassessment of the labor curve, Zhang et al.

[12] used repeated-measures regression with a 10th-order

polynomial function to define an average labor curve,

suggesting that the pattern of labor progression in

contemporary practice differs significantly from the Friedman curve [12]. Vahratian et al. [13] provided an overview

of Friedman’s work, addressed methodological challenges

in studying labor progression, and described the utility of

more advanced statistical methods for studying labor

progression, such as survival analysis, compared with other

approaches. Some of these studies have focused mainly on

assisting in the diagnosis of prolonged labor and the timing

of interventions, with the aim of achieving natural vaginal

birth, but they have not identified useful tools for predicting prolonged labor.

We therefore reconsider full CD in this study, redefine

the parameters of Friedman’s labor curve (e.g., latent and

active phase, deceleration phase), and develop clinically

useful statistical models. We applied a three-parameter

logistic model to the labor curve and redefined the three

parameters of Friedman’s labor curve with a logistic model

using the genetic algorithm (GA) and NewtoneRaphson (NR)

method to predict the time necessary to reach full CD

[14,15]. We also evaluated and compared the performances

of the mathematical inference method (NR) and evolutionary computation method (GA).

To our knowledge, this is the first report of estimating

the time to full uterine CD using the GA.

J.-K. Hoh et al.

February 2009. Inclusion criteria were gestational age

between 38 and 42 weeks, spontaneous onset of labor,

vertex presentation at admission, CD <7 cm at admission,

and duration of labor from admission to delivery >3 hours

[16]. We performed CD measurements at least once per

hour, thereby establishing a consistent data collection. We

excluded cases involving cesarean delivery, labor induction, and/or epidural anesthesia.

This study was conducted with the approval of the

Institutional Review Board Committee of the Hanyang

University Hospital, Seoul, South Korea.

Redefining the parameters of Friedman’s labor

curve

The three-parameter logistic model is defined as follows:

yj Za= 1 þ exp b xj g

where a (>0) is the final size achieved, b (>0) is the scale

parameter, and g is the inflection point on the curve at the

vertical coordinate xj. When xj / N, for all and any yj,

each yj converges to 0 or a. At (xj, yj) Z (g, a/2), this curve

has a maximum slope of ab/4.

We applied an adjusted three-parameter logistic model

with an upper bound set to 10 cm and defined the lower

asymptote as the “initial CD” due to the different dilation

starting times. Dilation at each time (tj, the jth hour after

admission) was defined as yj (cm). The logistic model has an

upper asymptote, yj Z 10 (cm), defined as follows:

ð1Þ

yj Zc þ ð10 cÞ= 1 þ exp a tj b

Additionally, the three parameters (a, b, and c) are

described as follows:

a Z a scale parameter, is related to the maximum slope

(cm/h) at the point of inflection on the labor curve. This

parameter indicates the “power” of the CD, and it can be

used to determine the time it takes to reach full CD, which

is the final objective of our study.

b Z the location parameter at tj Z b (hours). Eq. (1) has

a maximum slope of a (10ec)/4 (cm/h) at the point of

inflection where (tj, yj) Z (b, (10 þ c)/2). This parameter is

“a midpoint of the active phase” in Friedman’s labor curve.

c Z is a lower asymptote, and is the initial CD, giving

a lower asymptote yj Z c (cm) as tj / eN. The upper

asymptote is yj Z 10 (cm) as tj / þ N. It is also used in

estimating CD at admission or before admission.

Fig. 1 shows a logistic labor curve in which a Z 0.92,

b Z 6.83 hours, c Z 0.75 cm, and the maximum slope is

2.13 cm/h.

The following is an example of what the equation, using

the above parameters, would look like:

yj Z0:75 þ ð10 0:75Þ= 1 þ exp 0:9 tj 6:83

ð2Þ

Materials and methods

Research participants

Estimation of a three-parameter logistic model

in the labor curve

We extracted the clinical record data of 594 singleton

nulliparous women in the last months of their pregnancies

who underwent vaginal delivery at Hanyang University

Hospital, Seoul, South Korea, between October 2004 and

GA is the most fundamental and widely known evolutionary

computation currently used in application research. The

most important feature in GA design is chromosome

encoding, as the chromosomes must be mapped to the sets

Estimating time to full cervical dilation

425

Figure 1. Definitions of the three parameters of the logistic

model in the labor curve. Note. The point of inflection

(hours, cm) Z (b, (10 þ c)/2); the maximum slope Z a (10 e

c)/4 Z 0.92 (10 e 0.75)/4 Z 2.13 (cm/hour), a(Z0.92), is

a power of cervical dilation.

of parameters that need to be estimated. We have adopted

a real value representation, rather than a classic binary

representation, for the application of the logistic model

Eq. (1).

When applying the GA (Appendix 1), the number of

chromosomes m was set to 100, and the number of

maximum iterations (i.e., gen) was set to 20,000. In the

selection process, after randomly choosing a number r from

(0, 1), the numerical value [100 r] ([ ] indicates a Gauss

function) was obtained by roulette wheel selection

(number of precision Z 6 and precision integer Z 2). The

arithmetical crossover operator’s weight was set to 0.8, the

crossover rate pc to 0.2, and the mutation rate pm to 0.01

(Appendix 2, Fig. I).

When applying the NR method (Appendix 3), we applied

PROC NLIN of the SAS package (Ver. 9.1; SAS Institute Inc.,

Cary, NC, USA) to the three-parameter logistic models, with

the initial values for each model based on the published SAS

methods described by Rogers et al. [17].

Results

Table 1 presents the baseline characteristics of the overall

study sample. Physicians performed an average of 10.05

Table 1 General characteristics of the study sample

(N Z 594).

Parameters

No. of pelvic examinations

Maternal age (y)

Gestational age at delivery (wk)

Cervical dilation at admission (cm)

Duration of first stage of labor (h)

Birth height (cm)

Birth weight (gm)

1-min Apgar score

5-min Apgar score

Mean SD

10.05

30.32

40.26

2.11

12.01

49.87

3396

6.95

8.88

Data are presented as mean standard deviation (SD).

2.37

2.46

0.11

1.68

5.19

2.16

310

0.25

0.33

pelvic examinations from admission to the first stage of

labor (standard deviation, 2.37). The mean age at the time

of delivery was 30.32 (2.46) years. The CD at the time of

admission was 2.11 (1.68) cm. The mean number of gestational weeks at delivery was 40.26 (0.11), and the first

stage of labor was 12.01 hours (5.19). The average weight

of the newborns was 3396 g (310). The average Apgar scores

were 6.95 (0.25) and 8.88 (0.33) at 1 and 5 minutes,

respectively.

We found that the prediction accuracy (sum of square

error; root mean square error; statistic measuring the

accuracy of forecast, U1; Theil’s inequality coefficient, U )

[18] of GA was higher than that of the NR method, and that

GA was more appropriate than NR in the optimization of the

three-parameter logistic model in the labor curve (Table 2).

As shown in Table 3, the time predicted by GA was closer

to the observed time than that predicted by NR. Hence, the

models estimated by GA can be regarded as more effective

for modeling labor progress than those estimated by NR.

The estimated labor curves at various dilations are given

in Figs. 2A and 2B. In Fig. 2A (top), the first labor curve (a.1)

used only four observed data-points (3 hours after admission), while (a.2) used five observed data-points (4 hours

after admission). In (a.4), the estimated arrival time to CD

(about 10 cm) was about 10.8 hours (root mean square

error Z 0.1), which was approximately the actual arrival

time of the patient (11.0 hours). As shown in Fig. 2B

(bottom), the initial CD of the labor curve (b) was smaller

than that of labor curve (a), and the “active phase” of labor

curve (b) began 7 hours after admission.

Fig. 3 shows various patterns of estimated labor curves

to full dilation by GA. The time to reach full CD in curve (b)

was longer than in curve (a) (5.4 vs. 13.6 hours), although

the CD on admission in curve (b) was bigger than curve (a)

(1 vs. 5 cm).

Discussion

In general, measuring CD can be subjective, and such

measurements are only estimates because observations are

rounded to the nearest centimeter [19]. This measure,

although generally accepted, may not be precise and there

are no reported trials of either interobserver or intraobserver reproducibility. Women are admitted into labor

and delivery at various levels of CD, and it is difficult to

predict the chances of a normal vaginal delivery and the

duration of labor in the first stage [2,20]. A nonparametric

method might also provide a direct fit to the data, but the

disadvantage of such methods is the inefficient use of

individual data on labor progression, in the sense that

estimates assume a cluster of points at neighboring dilations [21].

Friedman’s labor curve was derived from observations of

CD and fetal station plotted against time elapsed from the

onset of labor (in hours). The typical S-shaped curve for

most laboring women defines the normal limits for labors

with healthy outcomes or for identifying abnormal labor.

However, the management of labor and delivery has

changed since Friedman’s series of publications on evaluating labor in clinical practice. Specifically, there has been

an increased use of obstetric interventions during labor and

426

Table 2

method.

J.-K. Hoh et al.

Comparisons of estimated parameters and prediction accuracies for the genetic algorithm and the NewtoneRaphson

Parameters

Genetic algorithm

Mean SE

Scale parameter a

Location parameter b (h)

Lower asymptote c (cm)

Maximal slope (cm/h)

SSE

RMSE

U1

U

0.97

7.60

2.11

1.83

2.01

0.39

0.05

0.03

0.08

0.11

0.03

0.16

0.04

0.10

0.01

0.00

NewtoneRaphson

Median (range)

1.00

7.50

2.50

1.54

1.84

0.37

0.05

0.02

(0.33e9.97)

(0.99e16.80)

(0.00e6.57)

(0.70e21.12)

(0.00e4.91)

(0.00e5.52)

(0.00e1.10)

(0.00e0.41)

Mean SE

0.88

7.22

2.62

1.25

13.74

0.67

0.09

0.05

0.16

3.02

0.05

0.27

2.02

0.14

0.01

0.00

Median (range)

1.04

7.73

2.75

1.78

3.95

0.47

0.06

0.03

(0.33e32.54)

(0.93e775.90)

(0.00e6.92)

(0.62e65.09)

(0.00e287.00)

(0.00e5.55)

(0.00e1.10)

(0.00e0.43)

RMSE Z root mean square error; SE Z standard error; SSE Z sum of square error; U1 Z statistic measuring the accuracy of the forecast;

U Z Theil’s inequality coefficient.

delivery [22,23]. The debate over whether the deceleration

phase described by Friedman actually exists remains

unsettled [24].

Hoskins and Gomez [25] determined that abnormalities

in the Friedman curve were not useful predictors for

operative delivery in pregnancies complicated by fetal

macrosomia. Zhang et al. [12] found that the labor curve of

1329 ethnically diverse, nulliparous women differed markedly from the Friedman curve. Using repeated-measures

regression analysis, the duration of labor for fetal descent

at various stations, rate of CD at each phase of labor, were

described and compared with the Friedman curve. It was

noted that the cervix dilated substantially more slowly in

the active phase of the first stage of labor, taking approximately 5.5 hours to dilate from 4 to 10 cm compared with

2.5 hours in the Friedman model. Zhang et al. did not find

evidence of a deceleration (transition) phase in this study.

While labor curves may provide graphical depictions of

labor progression that are easier for physicians to visualize

in clinical practice, they are difficult to construct and

interpret accurately. They also have limited clinical utility,

especially for determining whether labor deviates from the

normal progression (e.g., duration of normal first stage

labor) [26].

In contrast, our model provides detailed real-time

information regarding the duration of CD, requiring only

three observed data-points (i.e., known onset of labor);

this has not been achieved in previous studies. Based on this

information, the model calculates latent and active phase

duration, maximum slope, deceleration phase duration,

and overall first stage duration.

The calibration (inverse estimation) of the latent (onset

of labor to 4 cm dilation) and active (4e10 cm) phases [27]

can be easily performed by using Eq. (3), which is induced

by Eq. (1) in the section “Redefining the parameters of

Friedman’s labor curve”:

tj Zð 1=aÞ loge 10 yj

ð3Þ

yj c þ b

For example, in Fig. 1 we can calculate the latent (6.16

hours; tj Z (e1/0.92) loge[(10 e 4.0)/(4.0e0.75)] þ 6.83)

and active phases (4.81 hours; Dtj Z 10.97 e 6.16) of the

first stage of labor. We also predict the time (11.4 hours) to

reach full CD using the logistic labor curve with mean

parameters (i.e., a Z 0.97, b Z 7.60, and c Z 2.11; Table 2).

Comparing the estimates of duration of labor across

studies, especially for the first stage, is difficult for several

reasons (e.g., different starting points to calculate the

duration of labor, variation in sample restriction, exclusion

of induced labor and cesarean deliveries) [28].

We are convinced that such biases could be reduced by

introducing mathematical modeling and a method known

for accuracy (the logistic and GA models, respectively). In

this research, we applied the three-parameter logistic

model to labor curves. Obviously, three measurements

obtained within a couple of hours of admission will not

yield a satisfactory “prediction accuracy.” Thus, a fourth

and a fifth addition of observed data-points to the above

Table 3 Comparison of predicted time to full cervical dilation (10 cm)a estimated by the genetic algorithm and the

NewtoneRaphson methods.

Parameters

Genetic algorithm

b

Time prediction (h)

MAE

MSE

NewtoneRaphson

Mean SE

Median (range)

Mean SE

Median (range)

11.44 0.11

0.50 0.02

0.45 0.02

11.75 (5.0e19.0)

0.31 (0.00e2.00)

0.05 (0.00e4.00)

12.17 0.34

0.92 0.15

3.02 1.48

12.00 (3.0e23.00)

0.88 (0.00e5.00)

0.32 (0.00e25.00)

MAE Z mean absolute error; MSE Z mean squared error; SE Z standard error.

a

Full cervical dilation (CD) is approximately 10 cm if the estimate of CD 9.8 cm.

b

95% confidence interval; genetic algorithm Z (11.22e11.68) versus NewtoneRaphson Z (12.43e12.91).

Estimating time to full cervical dilation

427

Figure 2. Estimated labor curves calculated using the genetic algorithm for (A) (a.1) 3 hours, (a.2) 4 hours, (a.3) 5 hours, and

(a.4) 6 hours of observation; (B) (b.1) 3 hours, (b.2) 4 hours, (b.3) 5 hours, and (b.4) 8 hours of observation after admission. Note.

(a.1) the first estimated labor curve used only four observed data-points (n Z 4, B; RMSE Z 2.4), and the 10 cm* arrival time was

approximately 7.8 hours (true, 11.0 hours), (a.4) n Z 7, 10.8 hours (RMSE Z 0.1); (b.1) n Z 4, 19.5 hours (RMSE Z 0.1; true, 19.0

hours), (b.4) n Z 9, about 18.7 hours (RMSE Z 0.1). * Full CD is approximately 10 cm if the estimate of CD 9.8 cm. CD Z cervical

dilation; RMS Z root mean square error.

steps will produce a more accurate result. The number of

parameters used in our study, 3 (a, b, and c), is chosen as

a minimum number of nonlinear model to explain the labor

curve. Using our three parameters not only enables users to

calculate the parameters currently used but also to

calculate the time to full uterine CD, and even the overall

duration of first stage using the time calculated. As for

predictive accuracy, we found that the parameters from

GA were closer to the optimal solution, and that GA was

better than the NR method at solving optimization problems. GA is more effective than NR for modeling labor

progress, as demonstrated by its higher accuracy in predicting the time to reach full CD. Our study focused on

estimating the time to full uterine CD using the GA, which

Figure 3. Estimated labor curves to full CD (approximately 10 cm of cervical dilation)* according to the genetic algorithm. (a) 5.4

hours, (b) 13.6 hours, (c) mean Z 11.4 hours (i.e., labor curve with a Z 0.97, b Z 7.60, c Z 2.11 in Table 3), (d) 20.0 hours, and (e)

17.8 hours. *Full cervical dilation (CD) is approximately 10 cm if the estimate of CD 9.8 cm.

428

is prioritized to any other, in order to figure out the “labor

mechanism.” In the future, we will be able to provide

direct “criteria for normal labor” subjected to greater data

further proving the model to be a useful one in prediction

of prolonged labor.

Our research had the following limitations. First, we

were unable to confirm that delays in the progression of

labor were actually associated with increases in incidence

of cesarean delivery, augmentation of labor, or number of

vaginal examinations [29]. Second, we were unable to

demonstrate whether there were any similarities between

the duration of labor and the pattern of labor progress

among nulliparous and multiparous mothers [30]. Finally,

our sample was drawn from a single tertiary care hospital in

South Korea, which may limit the generalizability of our

results. Regarding the problem of having study participants

from a hospital, we plan to conduct a more extensive

research through a multicenter study in the future.

In conclusion, we have developed a three-parameter

logistic model to predict the time to reach full dilation. This

model may be useful for diagnosis of prolonged labor and

the timing of interventions, and may facilitate the

achievement of normal vaginal birth.

Acknowledgments

This work was supported by the Cluster Research Fund of

Hanyang University (HY-2009) and Basic Science Research

Program through the NRF of Korea funded by the Ministry of

Education, Science and Technology (No. 2010-0005140).

Supplementary data

Supplementary data related to this article can be found

online at doi:10.1016/j.kjms.2012.02.012.

References

[1] American College of Obstetrics and Gynecology Committee on

Practice BulletinsdObstetrics. ACOG practice bulletin

number 49, December 2003: dystocia and augmentation of

labor. Obstet Gynecol 2003;102:1445e54.

[2] Neal JL, Lowe NK, Ahijevych KL, Patrick TE, Cabbage LA,

Corwin EJ. “Active labor” duration and dilation rates among

low-risk, nulliparous women with spontaneous labor onset:

a systematic review. J Midwifery Womens Health 2010;55:

308e18.

[3] Friedman EA. The graphic analysis of labor. Am J Obstet

Gynecol 1954;68:1568e75.

[4] Friedman EA. Primigravid labor: a graphicostatistical analysis.

Obstet Gynecol 1955;6:567e89.

[5] Cardozo LD, Gibb DM, Studd JW, Vasant RV, Cooper DJ.

Predictive value of cervimetric labor pattern in primigravidae.

Br J Obstet Gynaecol 1982;89:33e8.

[6] Go

´mez Laencina AM, Sa

´nchez FG, Gimenez JH, Martı´nez MS,

Valverde Martı´nez JA, Vizcaı´no VM. Comparison of ultrasonographic cervical length and the Bishop score in predicting

successful labor induction. Acta Obstet Gynecol Scand 2007;

86:799e804.

[7] Friedman EA. Labor: clinical evaluation and management. 2nd

ed. New York: Appleton-Century-Crofts; 1978. p. 23.

J.-K. Hoh et al.

[8] American College of Obstetricians and Gynecologists. Dystocia

and augmentation of labor. Washington (DC): The College

Technical bulletin; 1995. No. 218.

[9] Lavender T, Hart A, Walkinshaw S, Campbell E, Alfirevic Z.

Progress of first stage of labour for multiparous women: an

observational study. Br J Obstet Gynaecol 2005;112:1663e5.

[10] Rinehart BK, Terrone DA, Hudson C, Isler CM, Larmon JE,

Perry Jr KG. Lack of utility of standard labor curves in the

prediction of progression during labor induction. Am J Obstet

Gynecol 2000;182:1520e6.

[11] Impey L, Hobson J, O’herlihy C. Graphic analysis of actively

managed labor: prospective computation of labor progress in

500 consecutive nulliparous women in spontaneous labor at

term. Am J Obstet Gynecol 2000;183:438e43.

[12] Zhang J, Troendle JF, Yancey MK. Reassessing the labor curve

in nulliparous women. Am J Obstet Gynecol 2002;187:824e8.

[13] Vahratian A, Troendle JF, Siega-Riz AM, Zhang J. Methodological challenges in studying labor progression in contemporary practice. Paediatr Perinat Epidemiol 2006;20:72e8.

[14] Chambers LD. Practical handbook of genetic algorithms: new

frontiers. Boca Raton, FL: Chemical Rubber Company Press;

1995.

[15] Boyer CB, Merzbacher UC. A History of mathematics. 2nd ed.

New York: Wiley; 1991.

[16] Suzuki R, Horiuchi S, Ohtsu H. Evaluation of the labor curve in

nulliparous Japanese women. Am J Obstet Gynecol 2010;203:

e1e6.

[17] Rogers SR, Pesti GM, Marks HL. Comparison of three nonlinear

regression models for describing broiler growth curves.

Growth 1987;51:229e39.

[18] Bliemel F. Theil’s forecast accuracy coefficient: a clarification. J Marketing Res 1973;10:444e6.

[19] Hoffman MK, Vahratian A, Sciscione AC, Troendle JF, Zhang J.

Comparison of labor progression between induced and noninduced multiparous women. Obstet Gynecol 2006;107:

1029e34.

[20] Holmes P, Oppenheimer LW, Wen SW. The relationship

between cervical dilatation at initial presentation in labour

and subsequent intervention. Br J Obstet Gynaecol 2001;108:

1120e4.

[21] Arunajadai SG. A nonlinear model for highly unbalanced

repeated time-to-event data: application to labor progression. Stat Med 2010;29:2709e22.

[22] Martin JA, Hamilton BE, Sutton PD, Ventura SJ, Menacker F,

Munson ML. Births: final data for 2002. National Vital Statistics

Reports 2003;52:1e27.

[23] Zhang J, Yancey MK, Henderson CE. U.S. national trends in

labor induction, 1989e1998. J Reprod Med 2002;47:120e4.

[24] Kelly G, Peaceman AM, Colangelo L, Rademaker A. Normal

nulliparous labor: are Friedman’s definitions still relevant? Am

J Obstet Gynecol 2001;182:S129.

[25] Hoskins I, Gomez J. Use of abnormalities in the Friedman

curve as a predictor of operative delivery in macrosomic

babies. J Perinatol 1998;18:381e3.

[26] Gross MM, Drobnic S, Keirse MJ. Influence of fixed and timedependent factors on duration of normal first stage labor.

Birth 2005;32:27e33.

[27] Bergsjo P, Bakketeig L, Eikhom SN. Duration of labour with

spontaneous onset. Acta Obstet Gynecol Scand 1979;58:

129e34.

[28] Vahratian A, Hoffman MK, Troendle JF, Zhang J. The impact of

parity on course of labor in a contemporary population. Birth

2006;33:12e7.

[29] Orji EO. Evaluating progress of labor in nulliparas and multiparas using the modified WHO partograph. Int J Gynecol

Obstet 2008;102:249e52.

[30] Bogaert Van. The multigravid partogram: should it be

customized? J Obst Gynecol 2004;12:881e5.

## Télécharger le fichier (PDF)

genetic-algorithm.pdf (PDF, 405 Ko)