Using Kernel Methods and Model Selection for Prediction of Preterm Birth

07/27/2016 ∙ by Ilia Vovsha, et al. ∙ Columbia University Cooper Union 0

We describe an application of machine learning to the problem of predicting preterm birth. We conduct a secondary analysis on a clinical trial dataset collected by the National In- stitute of Child Health and Human Development (NICHD) while focusing our attention on predicting different classes of preterm birth. We compare three approaches for deriving predictive models: a support vector machine (SVM) approach with linear and non-linear kernels, logistic regression with different model selection along with a model based on decision rules prescribed by physician experts for prediction of preterm birth. Our approach highlights the pre-processing methods applied to handle the inherent dynamics, noise and gaps in the data and describe techniques used to handle skewed class distributions. Empirical experiments demonstrate significant improvement in predicting preterm birth compared to past work.

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1 Introduction

Premature or preterm birth (PTB) is a major long-lasting public health problem with heavy emotional and financial consequences to families and society (March of Dimes, 2012; Conova, 2016). PTB is the leading cause of neonatal mortality and, long-term disabilities. Furthermore, over 26 billion dollars are spent annually on the delivery and care of the 12-13% of infants who are born preterm in the United States (Behrman et al., 2007). A crucial challenge is to identify women who are at the highest risk for very early preterm birth and to develop interventions. Equally important, would be the ability to identify women at the lowest risk to avoid unnecessary and costly interventions. A particularly challenging population to determine PTB risk is first time mothers (nulliparous women) due to the lack of prior pregnancy history.

Prediction of preterm birth represents a compelling application from a machine learning perspective. It has been an exceedingly challenging problem, predominantly due to (1) the inherent complexity of its heterogeneous multifactorial etiology, (2) the temporal dynamics of pregnancy and (3) the lack of approaches capable of integrating and interpreting large multidimensional data.

Risk factors of PTB are heterogenous and include history of PTB, race, age, parity of the mother, bacterial vaginosis, urinary tract infection, smoking, bleeding, cervix length. Most studies to date have examined individual risk factors independently of each other through univariate analyses of their coincidence with PTB. While these studies led to many insights on the PTB problem, current models lack sufficiently good prediction to be used clinically (Mercer et al., 1996). Previous results on this dataset using a multivariate logistic regression model show a sensitivity of 24.2% and 18.2%, and specificity of 28.6% and 33.3%, for nulliparous and multiparous women respectively.

We describe our efforts towards developing multivariate linear and non-linear models that integrate all risk factors for predicting preterm birth.111A preliminary version of this work appeared in  (Vovsha et al., 2014). We use the “Preterm Prediction Study,” a clinical trial dataset collected by the National Institute of Child Health and Human Development (NICHD) – Maternal-Fetal Medicine Units Network (MFMU). We compare three approaches for deriving predictive models: a support vector machine (SVM) approach with linear and non-linear kernels, logistic regression with model selection along with a hand-picked model.

We also focus our attention (as recommended by (NICHD, 2005)) on predicting (1) any kind of preterm birth, (2) spontaneous preterm birth, and (3) predicting preterm birth for nulliparous women. Furthermore, etiologies of preterm birth are believed to be different as pregnancy progresses. Hence, we also derive models at different time points, which represent the three main prenatal visits in the preterm prediction study, that is at 24, 26 and 28 weeks gestation. Our results for the spontaneous preterm birth class at 28 weeks gestation show an improvement of 20% and 30% for sensitivity and specificity respectively as compared to (Mercer et al., 1996). In addition, we obtain approximately sensitivity and specificity across other data classes and time points.

This paper is organized as follows: in Section 2, we provide an overview of the risk factors and state-of-the-art systems for predicting PTB. We describe the Preterm Prediction Study dataset in Section 3 along with our pre-processing methods. We present our approach in Section 4 and our empirical evaluation along with a discussion of our results in Section 5. Finally, we discuss the significance and impact of this study and outline future work in Section 6.

2 Background

In this section, we describe the known risk factors for PTB and review state-of-the-art approaches to devise a risk-scoring system for PTB.

Risk Factors for Preterm Birth:

Approximately 30% of preterm deliveries are indicated based on maternal or fetal conditions such as mother’s preeclampsia and intra uterine growth restriction. The remaining 70%, known as spontaneous PTB (SPTB), occur following the onset of spontaneous preterm labor, prelabor Premature Rupture Of the Membranes (pPROM), or cervical insufficiency (Goldenberg et al., 2008). Spontaneous preterm labor is a heterogeneous condition, the final common product of numerous biologic pathways that include immune, inflammatory, neuroendocrine, and vascular processes (Behrman et al., 2007). Epidemiological investigations have largely associated single factors with PTB. Of the many risk factors for preterm labor, a prior history of preterm delivery is the most predictive with a recurrence risk as high as 50% depending on the number and gestational age of previous deliveries (Goldenberg et al., 2008). It has been shown (Goldenberg et al., 1998)

that the odds ratio of SPTB was highest for a positive fetal fibronectin test, followed by short cervix  

(Crane and Hutchens, 2008) and history of prior PTB. However, in practice, prior history of preterm delivery is used as the most predictive indicator of PTB in most clinical settings. Risk factors include race (Goldenberg et al., 2008), low socioeconomic status, extremes in age, single marital status (Smith et al., 2007; Thompson et al., 2006), low pre-pregnancy body mass index, (Hendler et al., 2005), and high-risk behaviors during pregnancy (e.g. tobacco, cocaine and heroin use). Psychological factors (Grote et al., 2010), (Zhu et al., 2010), and obstetrical conditions (Goldenberg et al., 2000; Gotsch et al., 2007; Romero et al., 2006; Tita and Andrews, 2010) are also known to increase the risk of PTB. Additional risk factors include closely spaced gestations (Conde-Agudelo et al., 2006), multiple gestations (Goldenberg et al., 2008), assisted reproductive technologies (Allen et al., 2006), exposure to tobacco smoke (Kharrazi et al., 2004; Jaakkola et al., 2001), and genetic factors (Porter et al., 1997; Winkvist et al., 1998). Those judged at risk for PTB are typically treated by prenatal administration of progesterone 17 OHPC (IM progesterone) (Acog, 2008; Flood and D. Malone, 2012). However, pregnant nulliparous women are often not treated due to the lack of prior pregnancy history.

Risk Scoring Systems for Predicting Preterm Birth:

In the late 1960’s, Papiernik proposed an empirical method for estimating the risk of premature delivery

(Papiernik-Berkhauer, 1969). In this approach, maternal characteristics are grouped into four series of comparable variables (social status, obstetric history, work conditions, pregnancy characteristics) in a two-dimensional table. Point values varying from 1 to 5 according to the degree of their importance are assigned to all characteristics. The sum of the points gives the risk of Premature delivery. Papiernik’s risk table was later modified by Creasy et al. and used in the risk of preterm delivery (RPD) system proposed in (Creasy et al., 1980) (Appendix, Table 4). Further assessment of the prediction performance of Creasy’s table (Edenfield et al., 1995) on another population has shown low performance.

Another graded risk system was proposed (Mercer et al., 1996) in the context of the NICHD MFMU preterm prediction study. The results of a multivariate logistic regression were modest with sensitivity of 24.2% and 18.2%; specificity of 28.6% and 33.3%, respectively for nulliparous and multiparous women. This constitutes our baseline for comparison.

Goodwin et al. (2001) have explored the use of data mining techniques to predict preterm labor. They have identified seven demographic variables that predict preterm birth. While these results are interesting, there are concerns whether the sampling of a particular demographic would be representative of more general population. Furthermore, the experiment procedure is unclear – for example, the Area Under Curve (AUC) could have been obtained on a validation set or an unseen test set; consequently it is difficult to reproduce their results. Courtney et al. (2008) describe a secondary analysis showing that the demographic preterm prediction model generated in (Goodwin et al., 2001) generalizes to a broader population with a modest accuracy. Today, there is no widely tested risk scoring/prediction system that combines PTB factors (Davey et al., 2011).

Our models differ from the previous work as follows: (1) the dataset we study represents a diverse population from ten medical centers across the US, (2) we derive predictive models at different stages in pregnancy, (3) we derive models for specific classes of patients, namely nulliparous women and also for spontaneous PTB, and (4) the procedure we use to evaluate our models is robust and reproducible.

3 The Preterm Prediction Study Data

We have obtained the released data set for the Preterm Prediction Study, performed by the NICHD Maternal Fetal Medicine Units (MFMU) Network between 1992 to 1994. This study is an observational prospective study of 3,073 women with singleton pregnancies recruited at less than 24 weeks gestational age. Of the women enrolled, 2,929 participated in the study at the 10 participating MFMU centers across the United States between October 1992 and July 1994. There were 1,711 multiparous and 1,218 nulliparous women. The incidence of spontaneous preterm birth was 10.3% overall 8.2% for nulliparous and 11.9% for multiparous women (Mercer et al., 1996). Henceforth, we will refer to this data as the MFMU data. Participating women in this study were followed up by research nurses during four visits at 24 (time T0), 26 (time T1), 28 (time T3) and 30 (time T4) weeks gestation for screening tests. The MFMU data timeline is illustrated in Figure 1. The data collected from all visits Maternal Fetal Medicine Units Network (1994) has over 400 variables in all. These include demographic, behavioral, medical history, previous and current pregnancy history, digital cervical examination, vaginal ultrasound, cervical and vaginal fetal fibronectin, KOH prep for yeast tests, and a psychosocial questionnaire. The detailed outcome of the pregnancies is as follows for spontaneous PTB 32 weeks (2%), 35 weeks (4%), 37 weeks (10%); indicated PTB 37 weeks (4%). The Preterm prediction cohort singletons was released only in April 2007 under the study title: Screening for Risk Factors for Spontaneous Preterm Delivery in Singletons and Twins (MFM, 2007).

Acronym Description Acronym Description
DMG Demographics and Home Life CRVM Cervical Measurements V1
PPH Previous Pregnancy History CRVM3 Cervical Measurements V3
PPHD Previous Pregnancy History Detail FFN Fetal Fibronectin Analysis V1
OBST Obstetrical and Medical Complications FFN2 Fetal Fibronectin Analysis V2
SAD Substance Use V1 FFN3 Fetal Fibronectin Analysis V3
SAD3 Substance Use V3 FFN4 Fetal Fibronectin Analysis V4
CPH Current Pregnancy History V1 BUA Blood and Urine Analysis V1
CPH3 Current Pregnancy History V3 BUA3 Blood and Urine Analysis V3
JOB Current or Last Job PSYCH Psychological Questionnaire
INFEC Infections During This Pregnancy V1 VISIT2 Yeast and Intercourse Variables V2
INFEC3 Infections During This Pregnancy V3 VISIT4 Yeast and Intercourse Variables V4
MEDT Medications and Treatments V1 OUTM Pregnancy Outcome, Maternal Data
MEDT3 Medications and Treatments V3 OUTN Pregnancy Outcome, Neonatal Data
SYMP Symptoms During Previous Week V1 OUTS Pregnancy Outcome Status
SYMP3 Symptoms During Previous Week V3 IPRE Indicated Preterm Birth Reasons
CPM Current Pregnancy Measurements V1 CHORS Chorioamnionitis Suspected
CPM3 Current Pregnancy Measurements V3 PDELM Preterm Delivery, Maternal Data
SPEC Specimen Collection V1 PDELC Preterm Delivery, Clinical Data
SPEC3 Specimen Collection V3
Figure 1: Illustration of MFMU data timeline and description of the set of feature groups. The numbers at the bottom of the diagram indicate the number of patients that reached that point in time of the study. These numbers decrease with time for several possible reasons including: patients withdrawing from study/delivered/lost to follow up/skipped major visit etc. The last number (3001) indicates the total number of patients with known pregnancy outcomes.
Table 1: (Left) CPM group features; (Bottom) Right group features. From left to right: feature number in the group, name, feature number in the raw data, type, range, number of missing values, processing flag, description.

The MFMU data is a very rich and highly structured dataset. As a result, multiple processing steps are required. We face several challenges, including the complexity of data, missing data and skewed class distribution (addressed in Section 4). For reproducibility purposes, we describe our preprocessing steps in considerable detail in Vovsha et al. (2013).

Complexity of Data:

We handle the complexity of the data by organizing features into groups (according to the original questionnaire) as depicted in Figure 1. At each visit, a set of feature groups is collected. We focus our study on the three major visits at time T0, T1 and T3.

Since features are obtained from various sources, they are not always uniform. We undertake several processing steps to convert the data into a standard numerical format suitable for off-the-shelf machine learning algorithms. In particular, Yes/No features are converted to binary (1/0) values, categorical features are converted to a set of binary features, unusual values (e.g., “”, “2-3”) are replaced with reasonable approximations (4, 2.5 respectively), and features with arbitrary ranges are normalized to the [0,1] interval. We review each feature with non-standard values manually and decide what is the most appropriate processing step.

For example, consider some of the features from the “DMG” group (Table 1). The BPPHONE (has home phone) and BPCAR (use of car) are Yes/No features, BPMARITL (marital status) is a categorical feature with four categories, and the AGEMOM (age of mother) and SCHOOLYR (total years of schooling) features both have unusual values and different integer ranges. We replace unusual values in the the last two features (AGEMOM, SCHOOLYR) by rounding off from below and from above, e.g., for AGEMOM, “” is replaced with 17 and “” is replaced with 40.

Furthermore, PTB data is characterized by complex interdependencies among its features (physiological as well as socio-economic) which contributes to the difficulty of accurate prediction of PTB. We propose that use of non-linear methods like using the RBF kernel would pick up on these complex non-linear interdependencies and improve the prediction accuracy. We also propose to use logistic regression with model selection to automatically include whole groups of co-advisorlinear predictors and hence take into account this aspect of the data.

Missing Data:

Our main objective in this work is to retain as many features and examples as possible. Hence, we prefer to fill in (complete) values rather than delete features. Since a substantial number of features is missing, we follow a simplified approach and treat features equally whether they are randomly or structurally absent. Most missing values can be reasonably completed by inserting a default value (e.g., ‘No’ or 0), the most common value (for categorical features), or the mean value (for numeric features). However, some features require non-trivial processing steps, and for those we sometimes include the range, mean or median, and other features in the computation as well.

As a concrete example, consider the features from the “INFEC” group. All 10 features in this group are Yes/No features that can be structurally absent if the patient did not report any infections during pregnancy. As such, we complete any missing values with the default ‘No’ value. On the other hand, the features from the “CPM” group are all numbers from some range of values (Table 1). All 11 of these features can be randomly missing due to the patient not undertaking a test or measurement not being reported after a visit. For several of these features (1-4), we prefer to complete the missing values with the mean of the actual responses. However, other features (5-7) have too many missing values (as shown in Table 1

, column 6), and so we (reluctantly) remove these features from the dataset. Finally, some features (9-11) have particular meaning (weight, height at different points in the pregnancy), and hence we apply non-trivial processing steps to impute the value from the available information. For example, if the weight is not measured during visit 1, then we set feature 10 (

WEIGHTV1) to the weight before pregnancy (feature 11) plus the average difference between the weights of all mothers at visit 1 and their weights before pregnancy.

4 Method for Prediction of PTB

In this section, we consider support vector machines (SVMs) and regression methods with model selection. We frame PTB as a binary classification problem, where patients who deliver a baby preterm (full-term) are assigned the positive (negative) class respectively. At every tick , each patient (example) is described by a complete feature vector (see Section 3) and a label , .

To validate our results, we repeat the following procedure throughout: each dataset is randomly divided into train and test sets with an 80/20 ratio, and each class is split proportionally between the sets. We then apply 5-fold cross-validation (CV) to the train set to determine the best model and optimal parameters (if any). The best model is tested on the (unseen) test set, and confusion matrices for various subsets of the data are recorded.

The metrics used are sensitivity (the percent of positive instances that are correctly predicted as positive), specificity (the percent of negative instances that are correctly predicted as negative) and the geometric mean (the square root of the product of the specificity and sensitivity).

Support Vector Machines

We use support vector machines (SVMs) that belong to the family of maximum margin classifiers

(Vapnik, 1995). The standard approach is to solve the soft-margin formulation (Boser et al., 1992; Cortes and Vapnik, 1995):

where is a positive constant determining the tradeoff between maximizing the margin and minimizing the misclassifications. The ’s are slack variables that allow to calculate the misclassifications. An example is misclassified if its corresponding slack variable . A margin error occurs if . A large C corresponds to assigning a higher penalty to errors. This is useful, since in practice, data is rarely linearly separable. Typically, the SVM produces a classifier that labels examples with .

To account for the large discrepancy between the number of examples in each class, we scale the hinge loss penalty from the cost function proportionally to the size of each class. The cost function is thus a slightly modified version of the soft-margin SVM formulation:

By assigning different misclassification costs, we can give equal overall weight to each class in measuring performance. In order to avoid tuning two cost parameters, we set:
where () is the number of positive (negative) examples (Ben-Hur and Weston, 2010)

. In our experiments, we use an SVM with linear, polynomial of degree 2 and 3 along with a radial basis function (RBF) kernels.

Logistic and Lasso Regression:

The regression study in this paper is motivated by the desire to create a meaningful baseline model to evaluate the performance of linear models in this problem space and assess the benefit of model selection methodologies. We consider two logistic regression model selection methodologies: lasso regression and elastic net regression (Zou and Hastie, 2005; Tibshirani, 1996). Lasso regression uses an (

norm) penalty to encourage sparse solutions and perform a level of feature selection. Elastic net regression combines the sparsity induction of the

norm to eliminate the trivial covariates, while using the ridge regression

norm to automatically include whole groups of collinear predictors once a single covariate is added (Zou and Hastie, 2005).

Since the class distribution is skewed towards the negative (full term) class (skewed distribution challenge from the previous section), we use oversampling techniques to achieve 1:1 levels of negative to positive examples. Specifically, we use the adaptive synthetic (ADASYN) sampling approach (He et al., 2008) to adaptively generating minority data to balance the dataset.

The Creasy Baseline:

We implemented the risk of preterm delivery score proposed by Creasy, as discussed in Section 2, in order to provide a baseline for comparison. In Creasy’s system, patients were initially screened, and then given a follow up screening at 26 to 28 weeks’ gestation. This follow up screening provided additional information on the pregnancy and improved the accuracy of the risk of preterm delivery (RPD) system (Creasy et al., 1980). Similarly, our implementation had an initial screening at T0 and then added information at the T1 and T3 time points. Our implementation had two key differences to the RPD system.

In RPD, patients are given a risk score based on factors involving socioeconomic status, past history, daily habits and status of the pregnancy. Consider for instance a mother who encountered DES (diethylstilbestrol) exposure, has a very low socioeconomic status, and is diagnosed with hypertension. This patient is assigned a score of 5 in our implementation. We manually classified these factors into three feature categories. In the first category, features did not require any modification and are used as is, such as having two children at home or hypertension. The second category of factors were simply discounted because they were either no longer prevalent (DES exposure) or the dataset lacked information on that feature (head being engaged). In the third category, features were ambiguous. For example, Creasy does not provide a clear distinction between low socioeconomic status and very low socioeconomic status. In order to compensate, we assigned a reasonable definition so that their score could be taken into account. The RPD scoring system as well as the mapping we developed of RPD risk score factors to MFMU features are available in the Appendix (Tables 4, and 5).

In RPD, the numerical risk factor is then translated into low, medium, or high risk of PTB, whereas SVM and regression methodologies are marked as only low or high risk. We modified RPD by eliminating the medium category. We ran the analysis twice, using seven and thirteen points as our boundary between low and high risk (respectively marked Creasy-7 and Creasy-13 in Table 3). A cut-off of seven points agreed with Creasy’s definition of medium risk, but did not produce a similar distribution of PTB patients found in (Creasy et al., 1980), whereas a cut-off of thirteen produced a similar distribution.

5 Empirical Evaluation

Results:

For each of the three problems above, we derive prediction models at different time points (ticks). Each tick (T0, T1, T3) represents a critical point (major visit) at which information is collected. In Table 2, we list the ratio of positive to negative examples in each dataset and the number of features at each tick.

We use the glmnet package to run our regression experiments. The package implements coordinate descent to train the elastic net and lasso models (Friedman et al., 2010). We display results for models with weighting factor only, as there is little difference in performance between using and

. We use the sklearn package for random forest and used the ”class weight” parameter to handle the data imbalance. We obtain our SVM models with modified code based on the LIBSVM package

(Chang and Lin, 2011).

T0 T1 T3
Feature count 50 205 316
All data 434 / 2,568 423 / 2,506 334 / 2,215
Spontaneous only 309 / 2,568 302 / 2,506 240 / 2,215
Nulliparous only 156 / 1,087 153 / 1,065 112 / 951
Table 2: Class size and feature count

We present our results in Table 3

. For each algorithm, we show the sensitivity, specificity, and geometric mean (g-mean) performance measures (rounded off to two decimal places) on the unseen test set, averaged over five runs plus-minus the standard deviation.

Sensitivity Specificity g-mean
T0 T1 T3 T0 T1 T3 T0 T1 T3
Preterm vs. Fullterm, All data
Lasso 0.59 0.52 0.50 0.59 0.67 0.73 0.59 0.02 0.59 0.02 0.60 0.03
Elastic Net 0.59 0.51 0.50 0.59 0.67 0.73 0.59 0.02 0.59 0.02 0.60 0.03
Linear SVM 0.40 0.43 0.45 0.83 0.82 0.84 0.58 0.04 0.59 0.02 0.62 0.03
Poly. SVM d2 0.56 0.62 0.67 0.63 0.65 0.66 0.59 0.03 0.64 0.01 0.6 0.04
Poly. SVM d3 0.55 0.27 0.23 0.62 0.87 0.93 0.57 0.03 0.49 0.02 0.46 0.07
RBF SVM 0.58 0.55 0.59 0.62 0.72 0.72 0.60 0.04 0.63 0.03 0.65 0.03
Random Forest 0.3 0.3 0.3 0.86 0.88 0.93 0.51 0.07 0.48 0.09 0.5 0.1
Creasy-7 0.30 0.22 0.21 0.88 0.91 0.93 0.52 0.04 0.45 0.03 0.44 0.03
Creasy-13 0.29 0.31 0.31 0.86 0.89 0.91 0.50 0.04 0.52 0.06 0.53 0.03

Preterm vs. Fullterm, Spontaneous only
Lasso 0.53 0.35 0.36 0.54 0.66 0.67 0.53 0.02 0.48 0.04 0.48 0.05
Elastic Net 0.52 0.36 0.36 0.55 0.65 0.67 0.53 0.03 0.48 0.04 0.49 0.05
Linear SVM 0.50 0.53 0.47 0.50 0.51 0.57 0.49 0.02 0.52 0.03 0.52 0.02
Poly. SVM d2 0.56 0.44 0.41 0.48 0.58 0.6 0.51 0.03 0.5 0.02 0.49 0.03
Poly. SVM d3 0.42 0.17 0.02 0.62 0.86 0.93 0.51 0.01 0.38 0.08 0.11 0.1
RBF SVM 0.40 0.40 0.43 0.59 0.60 0.58 0.49 0.04 0.49 0.04 0.50 0.02
Random Forest 0.08 0.03 0.03 0.95 0.97 0.98 0.2 0.1 0.13 0.1 0.14 0.1
Creasy-7 0.09 0.10 0.10 0.88 0.89 0.92 0.28 0.03 0.30 0.02 0.30 0.03
Creasy-13 0.07 0.11 0.08 0.88 0.90 0.91 0.25 0.08 0.30 0.05 0.26 0.07



Preterm vs. Fullterm, Nulliparous only
Lasso 0.36 0.35 0.31 0.58 0.68 0.75 0.46 0.06 0.48 0.05 0.47 0.11
Elastic Net 0.35 0.35 0.30 0.58 0.69 0.76 0.45 0.07 0.49 0.06 0.47 0.06
Linear SVM 0.40 0.40 0.42 0.59 0.60 0.66 0.48 0.03 0.49 0.06 0.52 0.07
Poly. SVM d2 0.49 0.38 0.38 0.46 0.63 0.73 0.46 0.04 0.48 0.04 0.52 0.05
Poly. SVM d3 0.38 0.15 0.18 0.61 0.88 0.93 0.48 0.05 0.36 0.05 0.4 0.06
RBF SVM 0.41 0.34 0.42 0.64 0.64 0.68 0.50 0.05 0.46 0.06 0.53 0.08
Random Forest 0.12 0.09 0.03 0.92 0.93 0.98 0.31 0.09 0.25 0.14 0.14 0.1
Creasy-7 0.02 0.13 0.13 0.87 0.88 0.92 0.06 0.13 0.34 0.05 0.35 0.05
Creasy-13 N/A 0.10 0.14 N/A 0.88 0.90 N/A N/A 0.22 0.21 0.27 0.25

Table 3: Average test rates for all algorithms at each tick

Observations:

As we stated in Section 2, the test error of a multivariate logistic regression model was modest (Mercer et al., 1996) with sensitivity of 24.2% and 18.2%; specificity of 28.6% and 33.3%, respectively for nulliparous and multiparous women. This constitutes our baseline for comparison. Our results for the spontaneous preterm birth class at 28 weeks gestation using linear SVMs are 47% sensitivity and 57% specificity showing an improvement of 20% and 30% respectively as compared to (Mercer et al., 1996). In addition, we obtain approximately sensitivity and specificity across other data classes and time points.

We observe that SVM with a non-linear (RBF) kernel performs slightly better than linear SVM for the full data. We believe that a larger data set would highlight the advantage of the non-linear method more prominently. When we consider the entire (full) dataset, the linear/RBF SVM performs better with increasing ticks (T0 to T3 i.e., as the pregnancy progresses). This reflects our intuition that as we increasingly obtain more information (features) about each patient (example), we expect to better discriminate between them. SVMs for spontaneous and nulliparous data can sometimes lead to a poor performance. For instance the g-mean for polynomial SVMs with degree 3 for T3 is 0.11

0.1. We consider the nulliparous data only to be the most difficult of the three datasets. This is especially clear at T0 when most of the critical features are derived from previous pregnancy history which is not available for nulliparous women. The high number of support vectors (not shown in the tables) required for the SVMs solution throughout the SVMs runs (across ticks, kernels, data) indicates that the preferable decision rule is approximately linear. In other words, under-fitting the data (small C value) generalizes better to unseen examples. We observe a poor performance of the Random Forest method, probably due to overfitting of decision trees on this kind of data. We have also shown that the

machine-picked linear model presented in this paper outperforms Creasy table (Creasy et al., 1980) hand-picked model. In summary, our study demonstrates that model selection and non linear kernels are promising approaches for prediction of PTB.

6 Significance and Impact

Preterm birth is a challenging and complex real world problem that pushes the boundary of machine learning state-of-the-art methodologies. Today, there does not exist an effective prediction system to identify women at risk of PTB to prevent this adverse pregnancy outcome. Specifically, nulliparous women (first time mothers-to-be) remain the most vulnerable population.

We present a comprehensible and reproducible study that demonstrates that more accurate prediction of preterm birth is not an elusive task. Our best performing algorithms attained (balanced) accuracy rates of 60%. We have demonstrated significant improvement compared to previous prediction performance on the same type of data and developed models that integrate heterogenous risk factors.

For future work, we plan to conduct larger scale experiments on other sources of data to study preterm birth including existing datasets and other data collected from electronic health records at a large urban hospital.

Acknowledgment

We thank the reviewers for their helpful comments. This work is partially funded by the National Science Foundation (NSF) under agreement number IIS-1454855 and IIS-1454814. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect those of the National Science Foundation.

We also acknowledge the assistance of NICHD, the MFMU Network, and the Protocol Subcommittee in making the database available on behalf of the project. The contents of this paper represent the views of the authors and do not represent the views of the Eunice Kennedy Shriver National Institute of Child Health and Human Development Maternal-Fetal Medicine Units Network or the National Institutes of Health.

The authors are very thankful to Dr. Tara Randis and Dr. Mary McCord for their invaluable contributions on preterm birth background and insightful discussions in an early stage of this project.

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Appendix

Table 4 shows the Risk of Preterm Delivery system (RPD) Creasy et al. (1980). This scoring system is a modification of the CPDR system proposed in Papiernik-Berkhauer (1969). The final score is computed by addition of the number of points given any item. A final score between 0 and 5 is classified as low risk; a score between 6 and 9 as medium risk and any score higher or equal to 10 deemed as high risk score for preterm birth.

Points Socioeconomic status Past history Daily habits Current pregnancy
1 2 children at home 1 abortion Work outside home Unusual fatigue
Low socioeconomic status Less than 1 year since last birth
2 Younger than 20 years Older than 40 years 2 abortions More than 10 cigarettes per day Less than 13 kg gain by 32 weeks’ gestation
Single parent Albuminuria
Hypertension
Bacteriuria
3 Very low socioeconomic 3 abortions Heavy work Breech at 32 weeks
status Long tiring trip Weight loss of 2 kg
Shorter than 150 cm Head engaged
Lighter than 45 kg Febrile illness
4 Younger than 18 years Pyelonephritis Metrorrhagia after 12 weeks’ gestation
Effacement
Dilatation
Uterine irritability
5 Uterine anomaly Placenta previa
Second trimester abortion Hydramnios
DES exposure
10 Premature delivery Twins
Repeated second-trimester abortion Abdominal surgery
Table 4: Risk of Preterm Delivery (RPD) Creasy et al. (1980)

Table 5 shows the mapping we have developed of RPD factors to MFMU features.

RPD Factor MFMU Feature
2 children at home BPKIDS 2
Low socioeconomic status BPINCOME == 1 and SCHOOLYR == (13 or 14 )
Younger than 20 years AGEMOM and
Older than 40 years AGEMOM
Single parent BPMARITL_2 or BPMARITL_3
Very low socioeconomic status BPPHONE and BPCAR and BPINCOME
and BPWORK and SCHOOLYR
Shorter than 150 cm HEIGHT
Lighter than 45 kg WGTPRE
Younger than 18 years AGEMOM
1 abortion BPINDUCE
Less than 1 year since last birth LASTPREG
2 abortions BPINDUCE
3 abortions BPINDUCE
Pyelonephritis BPINFEC and PYELO
Uterine anomaly BPFIBR or BPLOWER_2
Second trimester abortion SECAB
DES exposure N/A
Premature delivery PRETERM
Repeated second-trimester abortion N/A
Work outside home BPJOB
More than 10 cigarettes per day BPSMOKE and CIGSPRE
Heavy work N/A
Long tiring trip N/A
Unusual fatigue BPSTAND or BPBREAK
or BPVIBES or BPHRS
Less than 13 kg gain by 32 weeks gestation WEIGHTV3 - WEIGHTV1
Albuminuria BPURINE
Hypertension BPHYPER
Bacteriuria BACTER
Breech at 32 weeks N/A
Weight loss of 2 kg WEIGHTV3 - WEIGHTV1
Head engaged N/A
Febrile illness HERPES or VHERPES or CYS
or VCYS
Metrorrhagia after 12 weeks’ gestation BPVAG2ND or PERBLD
Effacement N/A
Dilatation BPCRVLT
Uterine irritability N/A
Placenta previa N/A
Hydramnios OLIGO
Twins N/A
Abdominal surgery BPABD
Table 5: Mapping of RPD factors to MFMU dataset