A graph theory approach to analyze birth defect associations.

Birth defects are prenatal morphological or functional anomalies. Associations among them are studied to identify their etiopathogenesis. The graph theory methods allow analyzing relationships among a complete set of anomalies. A graph consists of nodes which represent the entities (birth defects in the present work), and edges that join nodes indicating the relationships among them. The aim of the present study was to validate the graph theory methods to study birth defect associations. All birth defects monitoring records from the Estudio Colaborativo Latino Americano de Malformaciones Congénitas gathered between 1967 and 2017 were used. From around 5 million live and stillborn infants, 170,430 had one or more birth defects. Volume-adjusted Chi-Square was used to determine the association strength between two birth defects and to weight the graph edges. The complete birth defect graph showed a Log-Normal degree distribution and its characteristics differed from random, scale-free and small-world graphs. The graph comprised 118 nodes and 550 edges. Birth defects with the highest centrality values were nonspecific codes such as Other upper limb anomalies. After partition, the graph yielded 12 groups; most of them were recognizable and included conditions such as VATER and OEIS associations, and Patau syndrome. Our findings validate the graph theory methods to study birth defect associations. This method may contribute to identify underlying etiopathogeneses as well as to improve coding systems.

Introduction

Birth defects (BD) are prenatal morphological or functional anomalies, classified as major or minor according to their clinical or biological significance. BD often exert a significant effect on the newborn's health as well as burden on treatment resources. The estimated BD prevalence, which has not substantially changed over time, is around 3% worldwide [1,2].

Since the thalidomide episode, BD surveillance has become a public health concern. BD registries have been created to identify new teratogens and studies, focusing on BD associations, have been carried out [3-7]. BD associations are defined as the unknown etiopathogenesis coexistence of two or more unrelated anomalies.

Mainly two approaches have been used to analyze associations between unrelated BD. One of them focuses on a specific defect and determines its association degree to other anomalies in combinations of two, three, or four. For this approach, observed versus expected ratios, and multivariate methods such as log-linear models have been used [8-10]. The second approach is based on clustering methods. This method codes each newborn BD using a binary rating system, and then newborns are clustered into groups. Discriminant analyses are performed to identify the anomalies significantly associated to each group [11,12].

Graph theory may be considered as another approach to analyze BD associations. A graph consists of nodes which represent the entities (BD in the present work), and edges that join nodes indicating the relationships among them [13]. For this approach, a vast amount of clustering algorithms have been designed [14], such as Infomap, which is based on the graph information flow [15]. Centrality measures have been designed to characterize each node according to its associations and those of its neighbors. For example, Degree represents the number of edges leading to a node, Betweenness evaluates the number of shortest paths that pass through a node, and Eigenvector considers the number of associations of a node, as well as those of the nodes it is connected to [13]. Thereby, the graph theory methods allow to focalize the whole set of BD, to characterize each BD according to its centrality value, and to identify groups.

The graph theory approach has been applied to social networks allowing to identifying influencers [16], and the propagation and impact of fake news [17]. Further networks have focused on protein interactions leading to identify the human interactome [18], genetic interactions defining the cell map of yeasts [19], and association between diseases with common genetic mutations [20], or common symptoms [21]. However, to our knowledge, the graph theory approach has not yet been applied to analyze BD associations. Although experimental as well as epidemiologic studies have been and are still being carried out to unravel pathogenic paths underlying BD associations, most of them have been unsuccessful [22].

The aim of the present study was to verify the ability of the graph theory methods to identify already known BD associations, and thereby to consider its inclusion as a further tool used in BD surveillance.

Material and methods

Ethical aspects

The study protocol was approved by the Ethics Committee “Centro de Educación Médica e Investigaciones Clínicas (CEMIC)” (DHHS-IRB #1745, IORG #1315). Written and signed informed consents are obtained from all subjects participating in the Estudio Colaborativo Latinoamericano de Malformaciones Congénitas (ECLAMC) program before data collection. Furthermore, ECLAMC pediatricians adequately explain the written informed consent content to the mother or legal guardian of the newborn. All data were fully anonymized prior to their utilization. All written consents are available in the ECLAMC coordination headquarters.

Data collection

For the present work, ECLAMC BD database was used. ECLAMC is a hospital-based BD monitoring system that has been operating in twelve Latin American countries since 1967 [23]. It records all major and minor anomalies diagnosed at birth or before the infant's hospital discharge. Between 1967 and 2017, around 5 million live and stillborn infants have been examined; 170,430 cases (around 3%) had one or more BD.

Written and signed informed consents are obtained from all subjects participating in the ECLAMC program before data collection. Furthermore, ECLAMC pediatricians adequately explain the written informed consent content to the mother or legal guardian of the newborn.

The ECLAMC BD classification system combines ICD8 and specific ECLAMC codes for major and minor anomalies, as well as for some chromosome anomaly syndromes.

For the present work, codes recorded in the whole ECLAMC BD set of live and stillborn infants were used.

Representation of BD associations as a graph

To study BD associations using the graph theory, anomalies were represented as nodes and their associations as undirected weighted edges. Edges were weighted using the association strength volume-adjusted Chi-Square (VA-Chi2) (S1 Appendix). VA-Chi2 can be interpreted as a distance from independence; a value close to zero indicates that events are independent [24].

The number of edges in the BD graph (BDG) was defined based on a minimum number of cases with two defects (I parameter = 18), and considering the edges with the strongest association (VA-Chi2) (A parameter = 550). Parameters I and A were selected based on the average codeword length described in S1 and S2 Figs.

Graph partition

Graph partition was performed with the Infomap method (version 0.19.21) [15]. Nodes could only belong to one group of the obtained in the partition (Infomap default setting). The Infomap algorithm is based on the information flow tendency within well connected groups. Groups composing a network are identified by the definition of an optimally compressed description of the way information flows in the network. The Huffman code [25] is used to describe the information flow through an infinite random walk, considering it as a proxy of the flow in the network.

Two measures were used to evaluate the graph partition quality:

Modularity

It reflects the concentration of edges within groups compared to a random distribution of edges; its values range between -1 and 1. The closer to 1, the higher is the partition quality [26].

Average codeword length

It is an information-theoretical approach that uses a measure based on the Huffman code length of a random walker whose values are greater than zero. The lower the value, the higher is the partition quality [15].

Network characteristics

The following metrics were analyzed [27]:

Density (D)

Density of a graph indicates the number of associations between nodes. It is calculated as the number of observed associations over the number of all possible associations:

D = edge number x 2/nodes x (nodes-1)

D values range between 0 and 1.

Degree assortativity (DA)

It represents the Pearson correlation coefficient of degree between pairs of linked nodes. Its values range between -1 and 1 [28]. Nodes with values closer to 1 tend to associate to nodes with similar degree values; those with low values tend to associate to nodes with different numbers of associations.

Clustering coefficient (CC)

It measures the connection degree among neighbors of a node. In a graph, it is calculated as the number of triplets of fully connected nodes over all possible triplets. It ranges between 0 and 1, where 1 indicates a fully connected graph.

Average short path length (ASPL)

It indicates the average of the minimum number of steps (edges) among all node pairs.

Small-World index

Small-World is a kind of graph. Telesford et al. (2011) designed an index to measure the belonging of a graph to the Small-Word kind [29]. The index compares network clustering to an equivalent lattice network, and path length to a random network. Its values range from -1 to 1, where -1 indicates that the graph has features of a lattice graph, zero means that it has characteristics of a Small-World graph, and 1 that it has appearances of a random graph.

To characterize BD, based on their position in the graph, three centrality indexes were used:

Degree

Number of edges of a node.

Strength

Sum of edge weights of a node.

Eigenvector (EV)

Its values arise from a reciprocal process where the centrality of each node is proportional to the sum of centralities of the nodes it is connected to. Algebraically, the EV centrality refers to the values of the first EV of the graph weighted with the adjacency matrix. A normalized EV value between 0 and 1 was used. Nodes with values close to 1 indicate a high number of associated nodes as well as its connection to nodes with a high number of associations.

Validation of the results was based on clinical evaluation and interpretation of BD groups obtained in the partitioned graph.

Results

The complete BDG comprised 118 nodes and 550 edges (S1 and S2 Tables). Its edge density was 0.08, and its degree and EV centralities were 0.28 and 0.78, respectively. This BDG differed from the three models taken as reference (Table 1). The median BDG values (CC, DA, and ASPL) were not within the 95% confidence interval of the random graphs generated with Erdos & Renyi (ER) [30], and Barabási & Albert (BA) [31] models, nor within random graphs generated with the same degree and weight distributions (SDD); meanwhile, the Telesford et al. (2011) small-world index for the BDG was -0.30. BDG degree distribution was closer to a Log-Normal distribution (Kolmogorov-Smirnov distance: 0.05, P-Value: 0.23) than to other distributions such as Power and Poisson (S4 Table).

Table 1

Comparison between the birth defects graph and three graph models.

Erdos & Renyi, Barabási & Albert, and Same Degree Distribution data correspond to the median of 1000 graphs. The models were created with the same number of nodes, edges, and weight distribution as the birth defects graph.

Features	Birth Defect Graph	Erdos & Renyi	Barabási & Albert	Same Degree Distribution
Clustering Coefficient	0.41	0.08	0.21	0.30
Degree Assortativity	-0.05	-0.02	-0.29	-0.12
Average shortest path length	2.72	2.36	2.31	2.50
Modularity	0.32	0.19	0.06	0.07
Average codeword length	5.28	6.31	6.04	6.03

BDG partition yielded 12 groups (Fig 1, S3 Table). Ten groups represented known BD associations, syndromes, or clinically consistent complexes, while two of them (groups 9 and 10) did not.

Fig 1

Birth defects graph.

Each node represents a birth defect code. S2 Table depicts code names. Color of nodes and edges indicates the partition group to which they belong. Edges between groups are gray and dotted.

Nodes that showed the highest degree, EV and strength values were Other upper limb anomalies and Microretrognathia (S5 Table). The three strongest associations were Localized edema with Turner syndrome, Proboscis with Cyclopia, and Liver and bile duct defects with Other spleen defects (S1 Table).

Minor BD presented a median EV centrality of 0.10, greater than the observed for major BD (0.03) (Wilcoxon p-value 0.0004). Minor BD also presented greater degree (7.50 vs. 5.00) and strength (0.60 vs. 0.44) values but their significance was lower than major BD values (Wilcoxon p-value 0.0559 and 0.0396, respectively).

Group 1 showed the highest number of nodes (35), 62% were minor BD; it included syndromes such as Edwards and Other autosomal chromosome anomalies (Fig 1).

Following, Groups 2, 3, and 5 are described as examples.

Group 2, shown in Fig 2, comprised 16 nodes and 50 edges; its density, degree, EV, and CC centrality values were 0.41, 0.45, 0.50, and 0.59, respectively. Nodes with the highest degree and EV values were Ambiguous genitalia, Anus atresia, and Spinal anomalies (S3 Table). The three strongest associations were Ambiguous genitalia with Anus atresia, Epispadias with Exstrophy of urinary bladder, and Other abdominal wall defect with Umbilical cord anomaly (S1 Table). The following subgroups could be identified: VATER and OEIS associations, Sirenomelia complex, Abdominal wall defect (which included the Limb-body wall-complex and Short cord), and Congenital adrenal hyperplasia.

Fig 2

Subgroups and associated anomalies identified in Group 2.

Group 3, shown in Fig 3A, comprised 16 nodes and 40 edges; its density, degree, EV and CC centrality values were 0.33, 0.53, 0.57, and 0.51, respectively. Nodes with the highest degree values were An/Microphthalmia and Holoprosencephaly; those with the highest EV values were Patau Syndrome and An/Microphthalmia (S3 Table). The three strongest associations were Proboscis with Cyclopia, Aplasia cutis vertex with Patau syndrome, and An/Microphthalmia with Patau syndrome (S1 Table). The following subgroups could be recognized in Group 3: Patau syndrome, Craniofacial disruption, Holoprosencephaly complex, and Microcephaly+Cataract. When a graph was created excluding the Patau syndrome code (with parameters I = 18 and A = 350), most of the previously found BD still appeared while others, such as Truncal heart anomalies, Encephalocele, Microcephaly, Cataract, and Cleft lip without cleft palate, did not (Fig 3B).

Fig 3

Subgroups and associated anomalies identified in Group 3.

(A) With Patau syndrome code. (B) Without Patau syndrome code.

Group 5, shown in Fig 4, comprised 12 nodes and 15 edges; its density, degree, EV and CC centrality were 0.23, 0.68, 0.70, and 0.20, respectively. The node with the highest degree value was Syndactyly, while those with the highest EV values were Constriction band scar, and Amputation (S3 Table). The three strongest associations were Constriction band scar with Amputation, Limb hypoplasia with Pectoralis muscle defect, and Limb hypoplasia with Syndactyly (S1 Table). Two subgroups (Poland and Amniotic band complexes) could be identified. Syndactyly also independently associated to each one of a number of Limb reduction defects and Polydactylies.

Fig 4

Subgroups and associated anomalies identified in Group 5.

Discussion

The usual way to characterize a graph is by comparing it with other networks and models to identify specific features of the phenomenon under study [32].

In the present work, one of the compared features was degree distribution. The BDG showed a better adjustment to a Log-Normal distribution, which is in accordance with Broido & Clauset (2019) who observed this distribution in most empirical networks [33]. However, the BDG differed from ER graphs widely used as the backbone of null models [34], and whose degree distribution follows a Poisson law [30]. This difference with ER graphs suggests that the association probability between two BD is not constant. Furthermore, the BDG Log-Normal distribution also determined its difference from scale-free graphs whose distribution follows a Power law. Scale-free graphs are characterized by the presence of few nodes with a degree that greatly exceeds the average (i.e. World Wide Web network) [35]. Finally, small-world graphs present a high clustering coefficient and a small characteristic path length implying the presence of sub networks and a global reachability property [36]. Many real networks meet these characteristics [37-39], while the BDG has differed.

That the BDG did not adjust to any of these models is an indicator of its singularity which would require further studies of the BD registry characteristics.

The graph partition showed a modularity greater than zero and greater than the observed in ER and SDD graphs, as well as a lower code length. These characteristics suggest a modular structure where each group (or module) could associate to different clinical conditions. That several related conditions were detected within each group is in accordance with this observation.

In group 2, at least five overlapping conditions could be recognized, with Anus atresia acting as the link among them. Although Ambiguous genitalia also showed high centrality values, some of its associated BD, such as a Persistent cloaca or Congenital adrenal hyperplasia, are pathogenetically related and therefore redundant.

In Group 3, the highest centrality values for An/Microphthalmia point to this defect as the most common one to the observed overlapping conditions (meaning the strongest link among them), and probably to other outlying groups as well. It was followed by Holoprosencephaly, which appeared as the link between BD related to the Holoprosencephaly complex (Single nostril, Absent nose, Proboscis, and Cyclopia) and Patau syndrome.

In group 5, two overlapping conditions (Poland and Amniotic band complexes) could be recognized linked by Syndactyly. The observed association between Syndactyly and Craniosynostosis probably represents a group of syndromes known as Acrocephalopolysyndactylies.

The congruence between obtained BDG groups and clinical conditions demonstrates the ability of the graph theory approach to identify known associations. This ability is further highlighted by the fact that even after excluding the Patau syndrome code in Group 3, the obtained defects still suggested this diagnosis. The differences between groups with and without the Patau syndrome code may have a biological meaning; however, they could also be due to operational factors. For example, when justifying the diagnosis of a Patau syndrome, the operator should be very exhaustive and describe redundant BD such as Microcephaly, which otherwise, he/she would not. This, in turn, would lead to the appearance of defects these redundant anomalies are associated to, such as Encephalocele or Cataracts.

The application of the graph theory methods to so far undefined case registries with multiple BD could help establish new associations.

Minor anomalies

While an association is defined as the coexistence of two or more mainly major independent BD (i.e. VATER, OEIS, etc.), a syndrome refers to a known or suspected condition, with or without major anomalies, whose recognition often mainly relies on minor BD (i.e. Down or Edwards syndromes).

The group with the highest number of nodes was the one including syndromes such as Edwards and other autosomal chromosome anomalies and, as expected, 62% of them were minor BD.

Minor anomalies often present alone as well as in association with a number of different conditions [40]. That in our sample minor anomalies showed the highest EV values could indicate a preferential reporting of such BD when they occur in association to others.

Unspecified defects

Some ill-defined BD such as Other upper limb anomalies or Neck anomalies, which often associate to other conditions, were also among those with the highest EV values. That the EV values of some equally unspecific BD, such as Liver and bile duct anomalies or Other adrenal defects were low could be due to the low overall prevalence (or low detection rate) of such BD in recognized associations.

Therefore, indexes such as EV could be used to improve coding systems by detecting codes whose low specification level might interfere when interpreting the network.

Limitations

The present results were mainly determined by the established significance thresholds (I and A parameters), which were selected after evaluating the graph partition quality, as well as by the recognition of known associations. The latter was prioritized, given the exploratory nature of this work; therefore, lax thresholds were selected. However, even when using tighter thresholds, known clinical conditions could still be identified.

Conclusions

The findings of this work suggest the graph theory as a new approach to study BD associations, as well as a tool to evaluate and improve coding systems. Its main advantage is the ability to analyze relationships among defect complexes and associations which may lead to the identification of common pathways and, eventually, to their etiopathogeneses. With this aim, a number of studies are being planned which could identify associations that have not yet been described, and may add information to those already known.

Median average codeword length by minimum number of cases with both birth defects.

The median average codeword length corresponds to the partition of weighted graphs generated with the VA-Chi2 function and different threshold values: I) minimum number of cases with both defects between 10 and 30, with a step of 1; A) number of edges (with greater strength of association) included in the graph, between 50 and 800 with a step of 25. The blue dot was the threshold selected in this work.

(TIF)

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Variation of average codeword length (ACL) by number of edges.

The average codeword length corresponds to the partition of weighted graphs generated with the VA-Chi2 function, a minimum number of cases with both defects of 18, and number of edges (A) (with greater strength of association) included in the graph, between 50 and 800 with a step of 25. The variation of ACL for each value of A was calculated with respect to the previous value of A (ordered from highest to lowest). A positive variation indicates a decrease in the ACL. The blue dot was the threshold selected in this work.

(TIF)

Click here for additional data file.

Edges included in the birth defects graph.

Chi2: Chi-Square independence test. VA-Chi2: volume-adjusted Chi-Square independence test. Group: Partition group, edge between groups has empty value.

(XLSX)

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Description of birth defects codes.

(XLSX)

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Nodes of each partition group and their centrality indices with respect to their group.

(XLSX)

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Function adjustment to the degree distribution of the graph.

KS Dist: Kolmogorov-Smirnov distance. X min: Initial grade where adjustment begins.

(XLSX)

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Node centrality indices with respect to complete graph.

(XLSX)

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Methodological details.

(DOCX)

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25 Feb 2020

PONE-D-19-35846

The Graph Theory: A new approach to analyze birth defect associations

PLOS ONE

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Reviewer #1: In this manuscript the authors apply graph theoretic methods to the analysis of patterns of birth defects diagnoses in a large collaborative birth defects surveillance database. The paper holds some interest, but should be framed in a broader context and substantially revised. Some specific comments appear below.

First, the title and throughout refers to 'The Graph Theory'. Actually what the authors do is to apply graph-theoretic methods to analysis of birth defects diagnoses. There are other approaches under exploration that take a similar approach, using machine learning methods. The authors should discuss their approach within this context, and describe how it differs and what advantages if any it offers. All of these approaches are agnostic in that they don't take into account things we might know about diagnoses, so the value-add from the approach outlined here should be interpreted in context as well.

Second, throughout the text there are poorly constructed sentences, mis-spelling, statements that are not as well referenced as they might be. Taking just the abstract and first page of the body of the manuscript as examples:

In the abstract, all acronyms should be spelled out, and the actual acronym used only if referenced more than once. Saying the findings 'seems to validate' the proposed method is a bit weak.

On p 3, line 54, one of these references is from 1983?

line 55 - what is meant by thalidomide and rubella 'episodes'? Thalidomide has been strongly linked with the development of birth defects surveillance, and there is a literature to support this (none cited), but this is less true for congenital exposure to Rubella, which came to attention decades before any substantial activity in birth defects surveillance ensued.

line 59, would read better as 'Most studies have used one of two approaches to analyze associations between unrelated birth defects.' Then, 'One approach focuses . . .'

lines 60-62, this sentence seems to over-generalize

line 62, you mean 'multivariable' rather than 'multivariate'

line 73, should use 'have' rather than 'has' to refer to 'vast amount'

The above comments refer to a single page in the manuscript. This reviewer could make similar recommendations throughout, and suggests that the entire manuscript be copyedited by a scientist familiar with birth defects surveillance who has English as a first language.

Additional comments:

p 4 line 91-94: it doesn't necessarily follow that, if the graph-theoretic approach works well to identify known associations it will therefore be able to identity novel associations.

p 5, line 103 - so the available data is continually coded in ICD8, even to the present?

line 112, 117 and elsehwere. What is the volume-adjusted Chi-square test? A little more detail would be helpful to readers.

line 123 what about associations requiring more than two birth defects - how does this method aggregate?

The section on methods contains a great deal of detail, more than is needed in the body of the manuscript. Consider placing some of this material in an appendix, and referring only to the terms and methods needed to describe the results in the methods section.

Table 1, p 8-9, the first two rows are repetitive across all columns. Place in the title or in a note at bottom of table instead.

p 9 - lots of VA-Chi2 values in text. What's required for one to be significant? 3.84??

Some of the material in the discussion belongs in results, for example lines 270-272 on p 11. The discussion is not the place to introduce findings not previously mentioned elsewhere.

This reviewer did not comment in detail on the discussion. But its hard to know whether these results 'seem to validate' the approach (p 14 line 336). To do this, it would be better to directly compare this method with other methods such as machine learning, discriminant or clustering analyses, etc, and show that it is similar or superior to those approaches.

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Reviewer #1: Yes: Russell S. Kirby

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7 Apr 2020

We have incorporated your recommendations into the revised version of the manuscript. Thank you for your help.

Submitted filename: Response to Reviewers.docx

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14 Apr 2020

PONE-D-19-35846R1

The Graph Theory: A new approach to analyze birth defect associations

PLOS ONE

Dear Dr López-Camelo,

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Reviewer #1: (No Response)

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Reviewer #1: Partly

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3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

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Reviewer #1: Yes

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Reviewer #1: Yes

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6. Review Comments to the Author

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Reviewer #1: The authors have revised the manuscript and addressed most major concerns. This reviewer still takes issue with the title - there is no 'the graph theory', but rather, a variety of graph-theoretic methods have been developed and used in a wide array of disciplines.

I strongly recommend that the title be changed to something like 'A Graph-Theoretic Approach to Analysis of Birth Defects Associations'.

Throughout the text, the authors should review how graph theory is described, for example in the next to last sentence of the abstract where it is also referred to as 'the graph theory'. Better to say '... validate graph-theoretic methods as ...'

It would also be important to consider how this method identifies potential unrecognized associations, considering study power (sample size), as well as inclusion and exclusion criteria.

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Reviewer #1: Yes: Russell S. Kirby

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23 Apr 2020

Suggestions from the reviewer have been addressed in the revised version of the manuscript

7 May 2020

A graph theory approach to analyze birth defect associations

PONE-D-19-35846R2

Dear Dr. López-Camelo,

We are pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it complies with all outstanding technical requirements.

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Academic Editor

PLOS ONE

Additional Editor Comments (optional):

The authors should have this manuscript copyedited by someone familiar with scientific writing with English as a first language to improve the quality of the paper.

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

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Reviewer #1: All comments have been addressed

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2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

**********

3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

**********

4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

**********

5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

**********

6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: (No Response)

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Reviewer #1: Yes: Russell S. Kirby

12 May 2020

PONE-D-19-35846R2

A graph theory approach to analyze birth defect associations

Dear Dr. Lopez Camelo:

I am pleased to inform you that your manuscript has been deemed suitable for publication in PLOS ONE. Congratulations! Your manuscript is now with our production department.

If your institution or institutions have a press office, please notify them about your upcoming paper at this point, to enable them to help maximize its impact. If they will be preparing press materials for this manuscript, please inform our press team within the next 48 hours. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information please contact onepress@plos.org.

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on behalf of

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Academic Editor

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