Fusing Data Mining, Machine Learning and
Traditional Statistics to Detect Biomarkers
Associated with Depression
Joanna F. Dipnall1,2*, Julie A. Pasco1,3,4,5, Michael Berk1,5,6,7,8, Lana J. Williams1,
Seetal Dodd1,5,6, Felice N. Jacka1,6,9,10, Denny Meyer2
1 IMPACT Strategic Research Centre, School of Medicine, Deakin University, Geelong, VIC, Australia,
2 Department of Statistics, Data Science and Epidemiology, Swinburne University of Technology,
Melbourne, VIC, Australia, 3 Department of Medicine, The University of Melbourne, St Albans, VIC,
Australia, 4 Department of Epidemiology and Preventive Medicine, Monash University, Melbourne, VIC,
Australia, 5 University Hospital Geelong, Barwon Health, Geelong, VIC, Australia, 6 Department of
Psychiatry, The University of Melbourne, Parkville, VIC, Australia, 7 Florey Institute of Neuroscience and
Mental Health, Parkville, VIC, Australia, 8 Orygen, the National Centre of Excellence in Youth Mental Health,
Parkville, VIC, Australia, 9 Centre for Adolescent Health, Murdoch Children’s Research Institute, Melbourne,
Australia, 10 Black Dog Institute, Sydney, Australia
These authors contributed equally to this work.
* jdipnall@deakin.edu.au
Abstract
Background
Atheoretical large-scale data mining techniques using machine learning algorithms have
promise in the analysis of large epidemiological datasets. This study illustrates the use of a
hybrid methodology for variable selection that took account of missing data and complex
survey design to identify key biomarkers associated with depression from a large epidemio-
logical study.
Methods
The study used a three-step methodology amalgamating multiple imputation, a machine
learning boosted regression algorithm and logistic regression, to identify key biomarkers
associated with depression in the National Health and Nutrition Examination Study (2009–
2010). Depression was measured using the Patient Health Questionnaire-9 and 67 bio-
markers were analysed. Covariates in this study included gender, age, race, smoking, food
security, Poverty Income Ratio, Body Mass Index, physical activity, alcohol use, medical
conditions and medications. The final imputed weighted multiple logistic regression model
included possible confounders and moderators.
Results
After the creation of 20 imputation data sets from multiple chained regression sequences,
machine learning boosted regression initially identified 21 biomarkers associated with
depression. Using traditional logistic regression methods, including controlling for possible
PLOS ONE | DOI:10.1371/journal.pone.0148195 February 5, 2016 1 / 23
OPEN ACCESS
Citation: Dipnall JF, Pasco JA, Berk M, Williams LJ,
Dodd S, Jacka FN, et al. (2016) Fusing Data Mining,
Machine Learning and Traditional Statistics to Detect
Biomarkers Associated with Depression. PLoS ONE
11(2): e0148195. doi:10.1371/journal.pone.0148195
Editor: Mansour Ebrahimi, Qom University, ISLAMIC
REPUBLIC OF IRAN
Received: September 30, 2015
Accepted: January 14, 2016
Published: February 5, 2016
Copyright: © 2016 Dipnall et al. This is an open
access article distributed under the terms of the
Creative Commons Attribution License, which permits
unrestricted use, distribution, and reproduction in any
medium, provided the original author and source are
credited.
Data Availability Statement: Original and cleaned
data for the NHANES data used in this study is open
access and located at the URL http://wwwn.cdc.gov/
Nchs/Nhanes/Search/nhanes09_10.aspx A Stata
syntax file containing a template for enabling those to
implement this methodology on other data files has
been provided as part of the Supplementary
information. This template also explains the NHANES
biomarker variables used for this study and
references key NHANES analytical information.
Funding: Michael Berk is supported by a NHMRC
Senior Principal Research Fellowship 1059660 and
Lana J Williams is supported by a NHMRC Career
confounders and moderators, a final set of three biomarkers were selected. The final three
biomarkers from the novel hybrid variable selection methodology were red cell distribution
width (OR 1.15; 95% CI 1.01, 1.30), serum glucose (OR 1.01; 95% CI 1.00, 1.01) and total
bilirubin (OR 0.12; 95% CI 0.05, 0.28). Significant interactions were found between total bili-
rubin with Mexican American/Hispanic group (p = 0.016), and current smokers (p<0.001).
Conclusion
The systematic use of a hybrid methodology for variable selection, fusing data mining tech-
niques using a machine learning algorithm with traditional statistical modelling, accounted
for missing data and complex survey sampling methodology and was demonstrated to be a
useful tool for detecting three biomarkers associated with depression for future hypothesis
generation: red cell distribution width, serum glucose and total bilirubin.
Background
Over the last two decades there has been a steady rise in the use of data mining techniques
across a number of disciplines. Data mining incorporates a path to knowledge discovery and is
a meaningful process for discovering patterns in data by exploring and modelling large quanti-
ties of data [1, 2]. The distinction between statistics and data mining has been attributed to the
nature of the analysis; statistics deals with primary analysis, whereas data mining deals with
secondary analysis [3] that learns from data [4]. Data mining incorporates machine-learning
algorithms to learn, extract and identify useful information and subsequent knowledge from
large databases [2].
For a number of years, data mining techniques incorporating machine learning algorithms
have been used for ‘big data’ analytics in both marketing and finance (i.e. cost saving, sales
opportunity) [5]. Supervised machine learning techniques have been successfully used in these
industries for feature or variable reduction to produce highly predictive models [6]. However,
it has only been over the last 10 years that data mining techniques have been used in medical
research, primarily in neuroscience and biomedicine [7, 8]. More recently, psychiatry has
begun to utilize the benefits of these techniques to gain further insight into the genetic makeup
of mental illness [9]. However, the implementation of data mining techniques in large epidemi-
ological studies has not been fully explored.
Epidemiological observational studies are based on a particular study population, often fol-
lowed over a period of time, and usually involving no intervention other than the administra-
tion of questionnaires and the carrying out of medical and laboratory or biomarker
examinations. These studies have been used to quantify prevalence and risk factors for diseases
within the population [10]. Sample sizes for these types of studies often comprise of some thou-
sands of individuals. Incorporating a methodology involving data mining techniques using a
machine learning algorithm with traditional statistics for variable selection in these studies
would augment the effective knowledge discovery processes of data mining and rigors of
machine learning algorithms with the well-established metrics of traditional statistics. A hybrid
methodology as such could take account of common analytical issues associated with these
types of studies, such as large numbers of variables, a complex survey design and missing data.
For these reasons, the aim of this study was to develop a systematic and sound hybrid
Data Mine & Machine Learn Biomarkers of Depression
PLOS ONE | DOI:10.1371/journal.pone.0148195 February 5, 2016 2 / 23
Development Fellowship 1064272. The funders had
no role in study design, data collection and analysis,
decision to publish, or preparation of the manuscript.
Competing Interests: JFD has no conflicts of
interest. JAP has recently received grant/research
support from the National Health and Medical
Research Council (NHMRC), BUPA Foundation,
Amgen, GlaxoSmithKline, Osteoporosis Australia,
Barwon Health and Deakin University. MB has
received Grant/Research Support from the NIH,
Cooperative Research Centre, Simons Autism
Foundation, Cancer Council of Victoria, Stanley
Medical Research Foundation, MBF, NHMRC,
Beyond Blue, Rotary Health, Geelong Medical
Research Foundation, Bristol Myers Squibb, Eli Lilly,
Glaxo SmithKline, Meat and Livestock Board,
Organon, Novartis, Mayne Pharma, Servier and
Woolworths, has been a speaker for Astra Zeneca,
Bristol Myers Squibb, Eli Lilly, Glaxo SmithKline,
Janssen Cilag, Lundbeck, Merck, Pfizer, Sanofi
Synthelabo, Servier, Solvay and Wyeth, and served
as a consultant to Astra Zeneca, Bioadvantex, Bristol
Myers Squibb, Eli Lilly, Glaxo SmithKline, Janssen
Cilag, Lundbeck Merck and Servier. Drs Copolov, MB
and Bush are co-inventors of provisional patent
02799377.3-2107-AU02 “Modulation of physiological
process and agents useful for same”. MB and Laupu
are co-authors of provisional patent 2014900627
“Modulation of diseases of the central nervous
system and related disorders”. MB is supported by a
NHMRC Senior Principal Research Fellowship
1059660. LJW is supported by a NHMRC Career
Development Fellowship 1064272. SD has received
grants/research support from the Stanley Medical
Research Institute, NHMRC, Beyond Blue, ARHRF,
Simons Foundation, Geelong Medical Research
Foundation, Fondation FondaMental, Eli Lilly, Glaxo
SmithKline, Organon, Mayne Pharma and Servier,
speaker’s fees from Eli Lilly, advisory board fees from
Eli Lilly and Novartis, and conference travel support
from Servier. FNJ has received Grant/Research
support from the Brain and Behaviour Research
Institute, the National Health and Medical Research
Council (NHMRC), Australian Rotary Health, the
Geelong Medical Research Foundation, the Ian
Potter Foundation, Eli Lilly, the Meat and Livestock
Board and The University of Melbourne and has
received speakers honoraria from Sanofi-Synthelabo,
Janssen Cilag, Servier, Pfizer, Health Ed, Network
Nutrition, Angelini Farmaceutica, and Eli Lilly. This
does not alter the authors’ adherence to all the PLOS
ONE policies on sharing data and materials, as
detailed online in the guide for authors. DM has
recently received grant/research support from the
Australian research Council (ARC), Mental Illness
Research Fund (MIRF), Victorian Department of
methodology involving these elements to perform variable selection that would be appropriate
for use in large epidemiological studies.
To test the proposed hybrid methodology, data from a large cross section population based
U.S. epidemiology study was utilised to identify key biomarkers for depression. Depression is a
serious medical illness, with the World Health Organization estimating that 350 million people
worldwide are affected by depression, with depressive disorders ranking second in terms of
global disability burden and depression expected to be the number one health concern in both
developed and developing nations by 2020 [11–13].
Biomarkers are used in medicine as indicators of risk, diagnosis or trait, disease state or acu-
ity, stage of illness, treatment response and prognosis [14]. Identifying diagnostic biomarkers
of depression may help in its detection and furthermore, circumvent the onset. Despite inten-
sive approaches into the investigation of biomarkers in psychiatry, limitations of sensitivity
and specificity of single biomarkers have made it impractical to assess an individual’s clinical
situation and make determinations regarding diagnosis and prognosis on the basis of biomark-
ers. Thus, establishing key informative biomarkers would be of benefit to psychiatry [15]. The
nature of this type of data is such that missing data often needs to be accommodated using
multiple imputation and the complex survey sampling methodology taken into account. To
date, conventional variable selection methods do not deal with both these issues associated
with this type of data.
The proposed novel hybrid methodology involved a three-step approach, combining data
mining techniques using the machine learning algorithm of boosted regression and bagging,
with traditional statistical techniques. To take into account missing data and complex survey
sampling methodologies, this new three-step approach to variable selection was developed.
This methodology was effectively used to identify key biomarkers for depression in a large
cross-sectional population-based U.S. epidemiological study.
Methods
Study design and participants
Data from the National Health and Nutrition Examination Survey (NHANES) (2009–2010)
[16] were utilised. Relevant NHANES data files were downloaded from the website and inte-
grated using the Data Integration Protocol In Ten-Steps (DIPIT) [17]. NHANES is a cross-sec-
tional, population-based study of approximately 10,000 non-institutionalised U.S. civilians
aged 18 to 80 years, conducted in two-year blocks. A four-stage sampling methodology was
applied: counties; segments within counties; households within segments; and finally, individu-
als within households. Data were collected from 15 different locations across 50 states of Amer-
ica and the District of Columbia. In addition, oversampling of subgroups of the population of
particular public health interest was performed to increase the reliability and precision of pop-
ulation estimates [16]. Finally, subsamples for the mental health and laboratory components of
the survey were chosen, at random, with a sampling frame especially designed to reduce
respondent fatigue and help scheduling in the biomarker collection [16, 18].
Over 250 biomarkers were available for 5,546 participants. Duplicate biomarkers (n = 75),
biomarkers with a high missing count predominantly due to the sampling protocol (n = 94)
and low incidence (n = 26) were excluded from the analysis. The final set consisted of 67 bio-
markers for inclusion. Of the 5,546 participants, 5.6% were excluded from the analysis due to
having six or more missing data values across the 67 biomarkers, and a further six outlier cases
were removed to enable the multiple imputation to converge. The final sample size included in
this research study was 5,227.
Data Mine & Machine Learn Biomarkers of Depression
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Justice, Beyond Blue, Swinburne University of
Technology.
Abbreviations: BMI, Body Mass Index; DIPIT, Data
Integration Protocol In Ten-Steps; DSM-IV, Diagnostic
and Statistical Manual of Mental Disorder Fourth
Edition; FSSM, Food Security Survey Module; MDD,
Major Depressive Disorder; MEC, Mobile
Examination Center; MART, Multiple Additive
Regression Trees; NCHS, National Center for Health
Statistics; NHANES, National Health and Nutrition
Examination Survey; PHQ-9, Patient Health
Questonnaire-9; WHO, World Health Organization
(WHO) World Health Organization.
NHANES received approval from the National Center for Health Statistics (NCHS)
research ethics review board and informed consent was obtained for all participants. Use of
data from the NHANES 2009–2010 is approved by the National Center for Health Statistics
(NCHS) Research Ethics Review Board (ERB) Approval for NHANES 2009–2010 (Continua-
tion of Protocol #2005–06).
Study Measurements
The Patient Health Questonnaire-9 (PHQ-9) [19] was used to assess depressive symptoms
(depression). The PHQ-9 is a well-validated, self-report tool for detecting and monitoring
depression, with good concordance with a clinical diagnosis of major depressive disorder
(MDD) [20]. Items assess the presence of nine Diagnostic and Statistical Manual of Mental
Disorder Fourth Edition (DSM-IV) depression symptoms over the past two weeks, and are
scored on a four-point scale indicating the degree of severity from 0 (not at all) to 3 (nearly
every day). Items were then summed to form a total severity score ranging from 0 to 27 where
those with a total score of 10 or more were considered depressed (i.e. moderately to severely
depressed) [21].
Health report status was measured as an ordinal five-point rating scale (excellent, very
good, good, fair, poor) and incorporated as predictor in the multiple imputation models as an
indicator of general health.
Blood and urine samples were collected in the Mobile Examination Center (MEC) and
shipped weekly for laboratory analyses. Specific laboratory techniques for each test are avail-
able from the NHANES Laboratory Procedures Manual [22].
Demographic variables were self-reported and included: age, gender, and race (collapsed
into four groups: Mexican American and other Hispanic, Non-Hispanic White, Non-Hispanic
Black, and other).
Current and past smoking status was determined from self-reported questions from the
smoking cigarette use component from NHANES. Smoking status was categorized into those
who were never, former or current smokers. Physical activity was grouped into active (low to
high activity) and not active from the physical activity component from NHANES. Alcohol
regularity per month was calculated from the self-report question regarding how often alcohol
was drunk over the past 12 months, calculated from the weekly, monthly and yearly figures.
Food insecurity, a measure relating to the limited or uncertain access to food due to inade-
quate financial resources, was determined from the 10-item Food Security Survey Module
(FSSM) [23] and categorized into two groups: full food security (no affirmative response in any
of the 10 items); and food insecurity (at least one affirmative responses).
Body measurements were collected in the MEC by trained health technicians. Weight and
height were measured and body mass index (BMI) calculated as weight/height2 (kg/m2
). BMI
was categorised as underweight (BMI < 18.5 kg/m2
), normal (BMI between 18.5 to under 25
kg/m2
), overweight (between 25 to under 30 kg/m2
) and obese (BMI 30kg/m2
) [24].
Participants were identified as having Type 2 diabetes if they (i) reported that either a doctor
or health professional had told them they had diabetes or sugar diabetes (other than during
pregnancy); (ii) reported the use of hyperglycaemic agents, with the medication bottle seen by
the interviewer [25]; and/or (iii) diabetes based on their fasting blood glucose >126 mg/dL (7.0
mmol/L) [26–29] and glycated haemoglobin level of >6.5% [30–32].
Participants were identified as having cardiovascular disease using the self-report questions
regarding past history of heart conditions (i.e. congestive heart failure, coronary heart disease,
angina/angina pectoris, heart attack, stroke) which have been shown to have high concordance
with laboratory measures for cardiovascular disease [33, 34].
Data Mine & Machine Learn Biomarkers of Depression
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Participants were also identified as having the inflammatory conditions of arthritis and can-
cer or malignancy using the self-report questions.
Participants were asked to bring currently used medications to the assessment. The Lexicon
Plus1 proprietary comprehensive database of Cerner Multum, Inc. was used to assist with data
collection, data editing and release of the NHANES medication data. All prescription and some
non-prescription drug products available in the U.S. were coded using the Lexicon Plus medi-
cation database. For the current analyses, Lexicon Plus medication categories with higher than
2% incidence were included: anti-infective, cardiovascular agents, central nervous system
agents, coagulation modifiers, gastrointestinal agents, hormones/hormone modifiers, meta-
bolic agents, nutritional products, psychotherapeutic agents, respiratory agents, and topical
agents.
Methodology
The proposed hybrid methodology was applied to this study to select key biomarkers associ-
ated with depression from the NHANES data set (Fig 1).
STEP 1: Multiple Imputation (MI) for Missing Data
In many ‘big data’ situations, missing data are not an issue due to the large volume of observa-
tions and variables or features available. In contrast, missing data in studies with small sample
sizes can influence the results greatly [35, 36]. There have been a number of missing data pro-
cedures suggested in the literature over the last decades: listwise deletion; pairwise deletion;
mean substitution; regression imputation; Maximum Likelihood (ML) estimation [37, 38].
However, most of these methods can only be used when there is no pattern for the missing
data. The choice of method used for dealing with missing data is often less important when the
proportion of missing data is less than 5% [39]. However, it is not unusual for the proportion
of missing data in large epidemiological studies to exceed this percentage, thereby potentially
reducing statistical power, producing biased parameters and increasing the risk of a Type I
error [35]. All these issues could be detrimental to traditional statistical multivariate regression
models.
Multiple imputation is a useful flexible strategy for addressing the missing value problem.
Multiple imputation is considered when the missingness is not totally random, depending on
observed or unobserved values. However, this method is applicable even when the pattern of
missing data is not random. Multiple imputation using chained sequences of equations is a
flexible imputation method with the ability to handle different variable types, as an imputation
model is generated for each variable with missing data [40]. This method is also referred to as
fully conditional specification [41] and sequential regression multivariate imputation [42]. A
selected imputation model generates ‘mi’ complete imputed sets of data. Analysis is then per-
formed and results are pooled. The number of ‘mi’ sets depends on the amount of missing
data, nature of the data and analysis model used. More than 50 imputed sets may be required
to obtain stable results [43], but between 5 to 20 has been considered appropriate to reduce the
imputation sampling error when fractions of missing data are low [44].
Prior to imputing the missing data, missing values are often tested for Missing At Random
(MAR) or Missing Completely At Random (MCAR) [38, 45]. MAR occurs when the probabil-
ity of being missing is dependent on the variables measured in the study, but independent of
those not measured in the study. To test MAR, logistic regression is often performed with a
missing data indicator created for each potential predictor (i.e. 1 for missing, 0 for non-miss-
ing). No significant relationship between the missingness indicators and the outcome of inter-
est suggests MAR. MCAR occurs when the probability of being missing is independent of all
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the variables in the study (those measured and not measured) The assumption that the data are
missing completely at random (MCAR) can be assessed using Little's MCAR chi-squared test,
which can be applied to a large set of variables [46, 47], including all the predictors simulta-
neously. A significant result rejects the null hypothesis that the data is MCAR. Rejection of
MAR or MCAR confirms the need for multiple imputation for the missing values in the data.
As the highest missing data percentage for this study data set was above 5% and the assump-
tions of MAR and MCAR were rejected, multiple imputation was required. The multiple impu-
tation framework of inference was developed by Rubin [38] and implemented in Stata.
Multiple imputation was performed, with chained sequences of equations [40, 48] using all bio-
markers, age, race, and a measure of self-report health status, but run separately for males and
females due to possible differences in biomarker importance between the sexes [49]. A mix of
binary logistic and linear regression, using chained equations, was used, contingent on the
nature of the biomarker imputed. This study involved 20 chained sequences with the primary
data set of 5,227 observations. Thus, the combined original and imputed data sets contained
Fig 1. Hybrid Methodology Steps.
doi:10.1371/journal.pone.0148195.g001
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109,767 observations. Convergence for each of the chained equations was achieved within an
acceptable 20 imputed data sets [44].
STEP 2: Technique for Initial Selection of Predictors (Boosted
Regression)
There are many potential statistical and machine learning algorithms available for variable
selection [2], but boosted regression is recognised as being particularly effective [50]. This tech-
nique has often been thought of as a ‘bucket’ or ensemble method (a method that averages over
multiple classifiers), and has gained popularity amongst mainstream statisticians due to its pre-
dictive accuracy and ease of interpretation [51, 52]. Boosted regression has been used in studies
involving animal ecology [53], for example to build predictive models for fish and coral metrics
[54], and to identify factors predicting the reproductive success of dominant pairs of clown
anemonefish [55]. It has also been used in the development of the Chicago Adolescent Depres-
sion Risk Assessment (CADRA) index from an array of baseline social and cognitive vulnera-
bility and mood risk factors [56].
Boosting was invented by Freund and Schapire for regression trees [57] and translated to
the logistic regression model by Hastie, Tibshirani, and Friedman [54]. One of the advantages
with boosted regression is that the algorithm can accommodate any type of variable (continu-
ous, categorical, censored), any type of likelihood loss function (Gaussian, Binomial, Poisson,
and robust), and can deal with highly correlated predictors [58]. In addition it can automati-
cally accommodate non-linearity and interaction effects between predictor variables. The
boosting regression algorithm fits a sequence of simple trees based on a set of data splitting
rules to provide a more accurate estimate of the outcome with over-fitting avoided using a vali-
dation data set and shrinkage. Each tree consists of a series of yes/no questions which is applied
to each observation in the training data. Predictions are obtained using the average of the out-
comes for the observations found in each terminal node. Residuals are computed as the differ-
ence between the true and outcome values. Each successive tree is built for the prediction of the
residuals of the preceding tree. Essentially the technique successively gives larger weights to
observations that are repeatedly misclassified.
The final classifier consists of a weighted average of previous classifiers, with lower weights
(shrinkage) for later trees in order to avoid over-fitting. Shrinkage is accomplished by adding a
parameter λ to the last regression tree of residuals, where λ = 1 corresponds to no shrinkage.
Typically λ is 0.1 or smaller, with λ = 0.01 or λ = 0.001 common. Smaller shrinkage values
require larger number of iterations which can be computationally demanding.
The steps in the boosted regression technique incorporating the shrinkage parameter:
• An initial guess for the predicted outcomes is created. Compute the residuals based on the
current model.
• For each regression tree:
• Fit a regression tree to the residuals
• Compute the predicted outcome of the residuals for each terminal node
• Use the regression tree to predict the new set of residuals
• Update the boosting regression model to reflect the current regression tree, applying the
shrinkage parameter to the last regression tree of residuals
• This model is applied to the validation data and if there is an improvement in predictive
accuracy over the results for the previous iteration the next iteration commences. If not,
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then training stops and no more iterations are executed and no more residual trees are
developed.
In order to improve the robustness of the final model without introducing bias ‘bagging’ was
used [59]. Bagging is sometimes referred to as bootstrap aggregating and was originally devel-
oped by Breiman as a method for creating multiple versions of a predictor to form an aggregated
predictor [60]. Combining this method with boosting, bagging randomly selects a proportion of
the residuals at each iteration to build a new tree. While not all observations are used in each
iteration, all observations are eventually used across all iterations. Thus, the tree analysis is run
on multiple similar datasets, and the aggregate results are used to construct the final model and
relevant statistics. Friedman recommends bagging with 50% of the database [59].
The final boosted regression tree model tends to be more robust than a single regression
tree model, enabling complex functions and interactions to be modelled without assumptions
[53]. Since no probability values (p-value) are produced from the boosted regression algorithm,
the relative importance of variables has been used to pick likely predictors [59]. Each variable is
assigned a relative importance percentage or contribution, where the sum of the standardized
values of all variable importances add to 100%. The importance is calculated from the number
of times a variable is selected for splitting, weighted by the squared improvement to the model
fit achieved from each such split, averaged over all trees. Higher values of importance indicate
stronger contributions to outcomes values. With a binary outcome measure the importance
represents the percentage of the log likelihood explained by each variable. For the proposed
methodology, the importance percentage for each predictor will be of particular interest for the
variable selection process.
The analysis approach for selecting the preliminary subset of predictors for the proposed
methodology is one of inclusion rather than exclusion. A potential predictor was selected based
on the relative importance percentage in the original data set and the average importance per-
centage statistics across the 20 imputed data sets. The cut-off relative importance percentage is
therefore relatively inclusive, ensuring that a reasonable percentage of the total log likelihood is
retained.
For the NHANES study, depression was a binary indicator. The boosted regression method
used the Multiple Additive Regression Trees (MART) boosting algorithm [54, 59] imple-
mented by Schonlau [61]. This method was performed on the original data set of 5,227 obser-
vations with missing data, then for each of the 20 imputed data sets. For each run, validation
was performed by randomly splitting each data set into 60% training and 40% validation ensur-
ing that additional boosting iterations were employed only when improved prediction accuracy
was achieved with the validation data set. After some initial testing, the final shrinkage parame-
ter used was 0.001 with the recommended 50% of the residuals used to fit each individual tree
(50% bagging) [59]. The maximum number of boosting interactions (i.e. number of terminal
nodes plus 1) allowed was 6, being marginally higher than the default (i.e. 5) and within the
recommended range by Hastie, Tibshirani and Friedman [54]. Finally, a random-number seed
was used to generate the same sequence of random numbers for bagging, ensuring that the
results could be reproduced. Biomarkers with the greatest relative importance for the predic-
tion of depression were identified.
To ensure the inclusion criterion was implemented and a reasonable proportion of the total
relative importance was retained, cut-off percentages of 4%, 3% and 2% were tested. It was
decided to use 2% to ensure more than 50% of the total relative importance was included in this
stage of variable selection. Thus, a biomarker was included in the initial biomarker selection if
its relative importance percentage in the original data set was higher than 2%, or its average
importance percentage statistics across the 20 imputed data sets yielded average of at least 2%.
Data Mine & Machine Learn Biomarkers of Depression
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STEP 3: Traditional statistical regression
At the heart of data mining is the concept of data splitting to address overfitting the data from
the machine learning techniques used. Data are randomly split into two groups: a training set
and a validation set. Thus, the imputed data set was split into training and validation data sets.
For the NHANES study, the imputed data set was split into approximately 50% training and
50% validation data for the traditional statistical analysis. Each set maintained the balance in
regard to depression levels and imputation sets.
The standard approach of univariate regressions for each of the potential predictors selected
from step two were then performed, with the variable of interest as the outcome variable. Pre-
dictors with the strongest relationship with the outcome for both these data sets were chosen
based on traditional statistical 95% confidence (i.e. p<0.05). As required for the NHANES
data, the study’s complex survey sampling methodology was taken into account using univari-
ate weighted logistic regressions. These regressions, were conducted for each selected bio-
marker from the machine learning boosted regression algorithm with depression as the
outcome. Biomarkers having a significant relationship with depression were chosen (i.e.
p<0.05) at the final variable selection stage.
Using the selected biomarkers from the univariate analysis, a traditional statistical multivariate
regression model was then estimated for both the training and validation data sets. Multicollinear-
ity and mediation relationships were tested and predictors removed accordingly. For the NHANES
data, it was important that this step took account of the complex four-staged survey design.
Finally, demographic and medical covariates and significant interactions were included in
this multivariate model to control for any confounders and account for any moderation effect
with models fitted using both the training and validation imputed data sets. The final model
was also fitted using the original set of observations (with missing values) to obtain an indica-
tive measure for goodness of fit and to ensure consistent direction and significance for the
important biomarkers identified using the primary data set and the combined data set with
imputation for missing values.
All statistical procedures were performed using Stata V14 software (StataCorp., 2014). A
Stata plugin was used for the boosted regression component of the analysis [61].
Results
Estimated statistics for each of the covariates and the significance of the relationship with
depression for each covariate is presented in Table 1. The complex survey design of NHANES
is taken into account in these estimates.
STEP 1: Multiple Imputation results
The impact of missing data across the 67 laboratory data was quantified [17]. The results from
the imputed weighted logistic regression with the missing data indicator for each biomarker as
the outcome and depression as the predictor are reported in the last column in Table 1. Signifi-
cant results for several biomarkers indicated that missing biomarker data affected the depres-
sion status (i.e. p<0.05), confirming that the data was not MAR. Little's test also provided
evidence against the assumption that all laboratory data were MCAR (p<0.001). The missing
data were therefore imputed using multiple imputation.
STEP 2: Machine Learning boosted regression results
Multiple imputation produced 20 separate data sets with distinct imputed missing values for
the boosted regression step. The relative importance statistics are reported in Table 2 for the
Data Mine & Machine Learn Biomarkers of Depression
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Table 1. Estimated covariate statistics.
Covariate Proportion Std Error 95% CI Low 95% CI High p-value
Depressed
Not Depressed 0.923 0.005 0.913 0.934
Depressed 0.077 0.005 0.066 0.087
Gender
Male 0.496 0.006 0.483 0.509 Reference
Female 0.504 0.006 0.491 0.517 <0.001
Age Group
18–34 years 0.329 0.009 0.309 0.348 Reference
35–44 years 0.210 0.008 0.193 0.226 0.457
45–54 years 0.223 0.007 0.207 0.238 0.117
55–64 years 0.176 0.006 0.162 0.189 0.272
65+ years 0.063 0.004 0.056 0.071 0.006
Race
Mexican American/Hispanic 0.147 0.031 0.082 0.213 0.010
Non-Hispanic White 0.678 0.035 0.602 0.753 Reference
Non-Hispanic Black 0.110 0.009 0.089 0.130 <0.001
Other 0.065 0.009 0.046 0.084 0.542
Smoking
Current Smoker 0.219 0.008 0.201 0.237 <0.001
Former Smoker 0.226 0.014 0.195 0.257 0.800
Never Smoked 0.555 0.019 0.515 0.595 Reference
Food Security
Full food security 0.782 0.013 0.755 0.809 <0.001
Food insecurity 0.218 0.013 0.191 0.245 Reference
BMI Category
Underweight 0.018 0.003 0.012 0.024 0.396
Normal 0.295 0.014 0.266 0.324 Reference
Overweight 0.331 0.011 0.307 0.355 0.358
Obese 0.356 0.011 0.333 0.379 0.035
Physical Activity
Low to high activity 0.451 0.018 0.411 0.490 Reference
No low to high activity 0.549 0.018 0.510 0.589 0.882
Diabetes Status
No Diabetes 0.910 0.005 0.900 0.920 Reference
Diabetes 0.090 0.005 0.080 0.100 0.001
Cardiovascular Disease Status
No Cardiovascular Disease 0.924 0.007 0.910 0.938 Reference
Cardiovascular Disease 0.076 0.007 0.062 0.090 0.009
Arthritis Status
No Arthritis 0.928 0.005 0.918 0.938 Reference
Arthritis 0.072 0.005 0.062 0.082 <0.001
Cancer or malignancy
No Cancer or malignancy 0.901 0.008 0.884 0.919 Reference
Cancer or malignancy 0.099 0.008 0.081 0.116 0.925
Use Central Nervous System
No 0.854 0.008 0.836 0.871 Reference
Medication(s)
(Continued)
Data Mine & Machine Learn Biomarkers of Depression
PLOS ONE | DOI:10.1371/journal.pone.0148195 February 5, 2016 10 / 23
Table 1. (Continued)
Yes 0.146 0.008 0.129 0.164 <0.001
Use Psychotherapeutic Agents
No 0.915 0.006 0.902 0.928 Reference
Yes 0.085 0.006 0.072 0.098 <0.001
Mean Std Error 95% CI Low 95% CI High p-value
Family Poverty Income Ratio (PIR) 3.013 0.044 2.918 3.108 <0.001
Number of times drink alcohol pm 6.235 0.290 5.615 6.856 0.005
Note: Multiple-imputation, survey estimation. Based on 20 imputations, primary N = 5,227. P-value indicates the significance of biomarker with depression.
doi:10.1371/journal.pone.0148195.t001
Table 2. Boosted regression statistics.
Biomarker Original data set Imputation sets 1 to 20
Mean Std Dev Min Max
T.gondii antibodies (IU/ml) 0.220 0.562 0.444 0.326 2.388
Blood lead (ug/dL) 1.482 1.658 0.066 1.537 1.753
Mercury, total (ug/L) 1.958 1.847 0.110 1.628 2.049
Mercury, inorganic (ug/L) 0.290 1.668 0.116 1.358 1.788
White blood cell count (1000 cells/uL) 1.243 1.126 0.065 1.000 1.277
Lymphocyte percent (%) 1.331 0.978 0.078 0.780 1.176
Monocyte percent (%) 1.996 1.595 0.172 1.371 1.904
Segmented neutrophils percent (%) 1.240 1.004 0.082 0.856 1.121
Eosinophils percent (%) 1.770 0.971 0.126 0.819 1.406
Basophils percent (%) 0.565 0.585 0.051 0.503 0.690
Lymphocyte number (1000 cells/uL) 0.754 0.912 0.171 0.691 1.559
Monocyte number (1000 cells/uL) 0.835 0.492 0.043 0.392 0.552
Segmented neutrophils num (1000 cell/uL) 1.138 1.103 0.075 0.950 1.282
Eosinophils number (1000 cells/uL) 0.229 0.129 0.026 0.052 0.157
Basophils number (1000 cells/uL) 0.069 0.084 0.012 0.056 0.100
Red blood cell count (million cells/uL) 0.829 1.083 0.148 0.898 1.595
Hemoglobin (g/dL) 1.717 2.942 0.152 2.667 3.210
Hematocrit (%) 0.847 2.798 0.148 2.533 3.103
Mean cell volume (fL) 0.494 0.943 0.082 0.853 1.154
Mean cell hemoglobin (pg) 0.848 1.307 0.045 1.251 1.432
Mean Cell hemoglobin concentration (MCHC) (g/dL) 5.139 3.380 0.105 3.195 3.610
Red cell distribution width (%) 3.423 1.918 0.105 1.685 2.058
Platelet count (1000 cells/uL) 2.395 2.632 0.112 2.443 2.842
Mean platelet volume (fL) 1.257 1.348 0.095 1.214 1.519
Blood cadmium (nmol/L) 5.306 4.159 0.136 3.908 4.447
Glycohemoglobin (%) 1.526 1.830 0.107 1.604 1.986
C-reactive protein(mg/dL) 1.877 2.264 0.107 2.024 2.405
Direct HDL-Cholesterol (mg/dL) 1.097 1.149 0.104 0.946 1.328
RBC folate (ng/mL) 0.536 0.779 0.097 0.588 1.021
Serum folate (ng/mL) 1.955 1.840 0.163 1.486 2.087
Cotinine (ng/mL) 2.011 1.982 0.277 1.542 2.739
Urinary Total NNAL (ng/mL) 3.226 5.579 0.496 4.544 6.459
(Continued)
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original data set and across the 20 imputed data sets. Based on the selection criterion explained
above, 21 biomarkers were selected for the next stage of the analysis. The selected biomarkers
consistently explained more that 50% of the total relative importance for both the original data
set (53.85%) and for the mean values computed across the 20 imputed data sets (53.33%).
Table 2. (Continued)
Biomarker Original data set Imputation sets 1 to 20
Mean Std Dev Min Max
Albumin (g/dL) 0.914 0.543 0.050 0.459 0.662
Alanine aminotransferase ALT (U/L) 0.843 0.836 0.033 0.791 0.889
Aspartate aminotransferase AST (U/L) 0.727 0.577 0.053 0.462 0.694
Alkaline phosphotase (U/L) 2.992 1.966 0.086 1.825 2.184
Blood urea nitrogen (mg/dL) 0.840 0.875 0.088 0.718 1.061
Total calcium (mg/dL) 0.671 0.610 0.053 0.528 0.753
Cholesterol (mg/dL) 0.373 0.793 0.086 0.680 1.076
Bicarbonate (mmol/L) 3.769 1.840 0.089 1.661 2.035
Creatinine (mg/dL) 3.286 3.041 0.189 2.491 3.370
Gamma glutamyl transferase (U/L) 1.023 0.689 0.045 0.628 0.823
Glucose, serum (mg/dL) 4.911 2.487 0.168 2.140 2.742
Iron, refigerated (ug/dL) 1.752 1.443 0.088 1.288 1.559
Lactate dehydrogenase (U/L) 1.050 1.102 0.066 0.973 1.202
Phosphorus (mg/dL) 0.556 0.587 0.040 0.514 0.668
Total bilirubin (mg/dL) 3.366 2.555 0.291 1.841 2.853
Total protein (g/dL) 0.639 0.930 0.064 0.820 1.055
Triglycerides (mg/dL) 0.987 1.285 0.170 1.126 1.867
Uric acid (mg/dL) 2.598 2.401 0.116 2.232 2.675
Sodium (mmol/L) 0.957 0.299 0.034 0.242 0.366
Potassium (mmol/L) 0.654 0.664 0.059 0.559 0.778
Chloride (mmol/L) 2.810 1.629 0.065 1.460 1.726
Osmolality (mmol/Kg) 0.749 1.165 0.061 1.019 1.263
Globulin (g/dL) 0.501 0.679 0.062 0.529 0.778
Total Cholesterol (mg/dL) 0.457 0.609 0.058 0.488 0.714
Albumin, urine (ug/mL) 1.247 1.459 0.085 1.326 1.680
Creatinine, urine (umol/L) 0.963 0.992 0.108 0.769 1.193
First albumin creatinine ratio (mg/g) 0.723 0.787 0.118 0.636 1.110
Second albumin (ug/mL) 0.975 2.314 1.184 1.071 5.309
Second creatinine (mg/dL) 1.768 2.056 0.525 1.459 3.329
Second albumin creatinine ratio (mg/g) 1.176 3.321 0.825 1.783 5.326
The volume of urine collection #1 1.485 2.082 0.092 1.948 2.336
Urine #1 Flow Rate 3.262 2.921 0.720 1.743 4.456
Urine osmolality (mOsm/kg) 1.308 1.675 0.179 1.352 2.242
Hepatitis A Antibody 0.031 0.089 0.028 0.046 0.151
Hepatitis B surface antibody 0.034 0.051 0.018 0.023 0.082
Note: Highlighted indicate biomarker selected for univariate logistic regression. Validation on original plus each imputed data set. Random splitting of
60:40 training:validation, λ = 0.001, 50% bagging, 6 maximum number of boosting interactions. Original pseudo-R2 = 0.032, imputed data set pseudo-R2
ranged from 0.044 to 0.052. Variables selected at this step accounted for more than 50% of the total relative importance: original data was 53.85%; mean
of 20 imputation sets was 53.33%.
doi:10.1371/journal.pone.0148195.t002
Data Mine & Machine Learn Biomarkers of Depression
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STEP 3: Traditional statistical regression results
The training data yielded five biomarkers with significant univariate relationship with depres-
sion: hemoglobin (g/dL), Red cell distribution width (%), blood cadmium (nmol/L), cotinine
(ng/mL), and total bilirubin (mg/dL) (Table 3). The validation data confirmed the five bio-
markers from the training data with the addition of glucose, serum (mg/dL) (Table 3). Since
the p-value from the training data was 0.05 for this sixth biomarker it was decided to include
this variable in the final model.
A multiple logistic regression with these predictors suggested that the effect of hemoglobin
was fully mediated by total bilirubin and that cotinine was fully mediated by blood cadmium.
Both haemoglobin and cotinine were therefore excluded from the final model, leaving four key
biomarkers: red cell distribution width, blood cadmium, serum glucose and total bilirubin.
The direction and significance of the four biomarkers were tested with the combined
imputed data sets, allowing for a 50:50 random split between training and validation data. Con-
sistent results were obtained for the multiple logistic regression model in the training and vali-
dation data (Table 4).
The final model controlling for potential confounders and including significant interactions
are reported in Table 5.
Only Central nervous system medications and / or psychotherapeutic agents and diabetes
were included in the final multivariate model. The final validated model, using the original
Table 3. Univariate Logistic Regression statistics.
TRAINING VALIDATION
Biomarker Odds Ratio Std. Err. p-value CI Low CI High Odds Ratio Std. Err. p-value CI Low CI High
Hemoglobin (g/dL) 0.85 0.057 0.042 0.73 0.99 0.85 0.059 0.048 0.72 1.00
Hematocrit (%) 0.95 0.024 0.084 0.90 1.01 0.95 0.025 0.077 0.89 1.01
MCHC (g/dL) 0.85 0.115 0.261 0.63 1.15 0.89 0.131 0.454 0.65 1.23
Red cell distribution width (%) 1.20 0.080 0.024 1.03 1.40 1.20 0.079 0.023 1.03 1.40
Platelet count (1000 cells/uL) 1.00 0.002 0.058 1.00 1.01 1.00 0.002 0.083 1.00 1.01
Blood cadmium (nmol/L) 1.07 0.018 0.014 1.02 1.11 1.07 0.018 0.012 1.02 1.11
C-reactive protein(mg/dL) 1.18 0.106 0.091 0.97 1.44 1.15 0.098 0.141 0.95 1.38
Cotinine (ng/mL) 1.00 0.001 0.011 1.00 1.00 1.00 0.001 0.009 1.00 1.00
Urinary Total NNAL (ng/mL) 1.07 0.092 0.444 0.87 1.32 1.10 0.117 0.390 0.85 1.44
Alkaline phosphotase (U/L) 1.00 0.004 0.197 1.00 1.01 1.00 0.004 0.262 1.00 1.01
Bicarbonate (mmol/L) 0.93 0.045 0.156 0.83 1.03 0.92 0.044 0.133 0.83 1.03
Creatinine (mg/dL) 0.87 0.409 0.770 0.30 2.48 0.87 0.430 0.778 0.28 2.67
Glucose, serum (mg/dL) 1.00 0.002 0.050 1.00 1.01 1.01 0.002 0.039 1.00 1.01
Total bilirubin (mg/dL) 0.19 0.093 0.009 0.06 0.58 0.24 0.112 0.016 0.08 0.71
Uric acid (mg/dL) 0.97 0.069 0.655 0.83 1.13 0.94 0.062 0.345 0.81 1.08
Chloride (mmol/L) 0.98 0.039 0.700 0.90 1.08 0.98 0.038 0.624 0.90 1.07
Second albumin (ug/mL) 1.00 0.001 0.477 1.00 1.00 1.00 0.001 0.290 1.00 1.00
Second creatinine (mg/dL) 1.00 0.002 0.438 1.00 1.00 1.00 0.001 0.479 1.00 1.00
Second albumin creatinine ratio (mg/g) 1.00 0.000 0.516 1.00 1.00 1.00 0.000 0.315 1.00 1.00
The volume of urine collection #1 1.00 0.001 0.813 1.00 1.00 1.00 0.001 0.651 1.00 1.00
Urine #1 Flow Rate 0.89 0.125 0.438 0.65 1.23 0.86 0.136 0.382 0.60 1.24
Note: Bold Biomarker indicates selection. Multiple imputation logistic regression used taking account of the survey design of NHANES with 15 strata, 31
Primary Sampling Units (PSU).
doi:10.1371/journal.pone.0148195.t003
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data set of observations including missing values, took account of the complex survey data of
NHANES and the test for goodness of fit was not significant (F(9,8) = 2.05, p = 0.163) indicat-
ing that the model provided a good fit to the data (76). In addition, the odds ratios and p-values
were consistent with the final model in Table 5.
In Table 5, three of the four biomarkers remained significant predictors of depression at the
95% level (p<0.05) after controlling for the potential confounders: red cell distribution width,
serum glucose and total bilirubin. Significant interactions were found between bilirubin and
the Mexican American / Hispanic group compared to the Non-Hispanic White group, and
those who were current smokers compared to those who have never smoked.
Blood cadmium was not found to be significant in the final model (p = 0.180). However, sig-
nificant interactions (p<0.05) were found between blood cadmium and the 45–54 age group
when compared to the younger 18–34 age group, and the diabetic group when compared to the
non-diabetic group.
Discussion
The novel proposed hybrid methodology of fusing data mining techniques using a boosted
regression machine learning algorithm with traditional statistical techniques offers an inte-
grated approach to variable selection from a large number of features for large epidemiological
studies. The methodology uses a systematic stepped approach that can be applied to large epi-
demiological population-based studies using complex survey designs.
The methodology ensures that missing data are quantified and addressed using multiple
imputation techniques which are appropriate even when the data is not missing at random;
however, should multiple imputation not be required, then the methodology is still appropriate
using only the original data set. The boosted regression ensures that variable importance is reli-
ably measured taking into account observations that are difficult to predict while at the same
time shrinking the effects of these difficult observations in order to avoid over-fitting. This
method ensures that multicollinearity does not obscure the influence of important predictors,
giving all variables a chance to shine, while taking into account any non-linearity or interaction
effects.
An inclusive choice of cut-off values ensures that the regression boosting only reduces the
number of predictors from 67 to 21. However, this is enough to remove the multicollinearity
problem and to allow a conventional logistic regression analysis that takes account of the com-
plex survey sampling design to be employed in order to further reduce the number of
Table 4. Final Four biomarkers from boosted regression.
Biomarker Training Validation
Odds
Ratio
Std.
Err.
p-
value
95% CI
Low
95% CI
High
Odds
Ratio
Std.
Err.
p-
value
95% CI
Low
95% CI
High
Red cell distribution
width
1.159 0.079 0.057 0.995 1.350 1.161 0.080 0.063 0.990 1.362
Blood cadmium (nmol/
L)
1.060 0.017 0.020 1.015 1.107 1.060 0.017 0.017 1.016 1.106
Glucose, serum (mg/dL) 1.005 0.002 0.066 1.000 1.009 1.005 0.002 0.051 1.000 1.010
Total bilirubin (mg/dL) 0.241 0.112 0.016 0.082 0.703 0.315 0.143 0.034 0.111 0.895
Constant 0.017 0.014 0.001 0.002 0.116 0.012 0.011 0.001 0.002 0.094
Note: Multiple imputation logistic regression using subpopulation based on a random split of approximately 50:50 train:validation (n = 2,590 train:
n = 2,637 validation).
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Table 5. Final Multivariate Logistic Regression.
Odds Ratio Std. Err. p-value 95% CI Low 95% CI High
Biomarkers
Red cell distribution width 1.145 0.067 0.037 1.009 1.298
Blood cadmium (nmol/L) 1.024 0.018 0.182 0.987 1.063
Glucose, serum (mg/dL) 1.005 0.002 0.009 1.001 1.008
Total bilirubin (mg/dL) 0.116 0.049 <0.001 0.047 0.284
Gender
Male (Reference) 1.000
Female 1.610 0.312 0.027 1.064 2.439
Age group (years)
18–34 (Reference) 1.000
35–44 1.287 0.346 0.364 0.724 2.288
45–54 1.993 0.419 0.005 1.271 3.124
55–64 1.475 0.398 0.171 0.828 2.627
65+ 0.660 0.421 0.525 0.169 2.585
Race
Non-Hispanic White (Reference) 1.000
Mexican Amer/Hispanic 0.409 0.150 0.029 0.186 0.898
Non-Hispanic Black 0.842 0.391 0.718 0.312 2.278
Other 1.552 1.527 0.662 0.189 12.743
Smoking
Never smoked (Reference) 1.000
Current smoker 0.382 0.162 0.039 0.154 0.946
Former smoker 0.506 0.326 0.308 0.127 2.013
Food Security
Food insecurity (Reference) 1.000
Full food security 0.492 0.093 0.002 0.328 0.737
Poverty Income Ratio (PIR) 0.787 0.058 0.006 0.671 0.923
BMI Category
Normal (Reference) 1.000
Underweight 2.497 1.630 0.182 0.617 10.101
Overweight 0.864 0.177 0.486 0.557 1.339
Obese 1.007 0.194 0.973 0.666 1.521
Inactivity
Active (Reference) 1.000
Inactive 1.104 0.135 0.431 0.850 1.433
Alcohol consumption per month 1.008 0.014 0.601 0.978 1.038
Diabetes
No (Reference) 1.000
Yes 0.798 0.210 0.407 0.454 1.403
Central Nervous System Meds
No (Reference) 1.000
Yes 2.279 0.292 <0.001 1.732 2.999
Psychotherapeutic Agents
No (Reference) 1.000
Yes 2.912 0.433 <0.001 2.118 4.002
Interactions:
Age Group by Blood cadmium
(Continued)
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predictors from 21 to 4. Interestingly no biomarker interaction or polynomial terms were
found to be significant in the final multivariate logistic regression model making this a particu-
larly simple model which was also found to be robust in relation to important possible con-
founder variables. Three of the four important biomarkers remained significant to the 95%
level despite the inclusion of several confounder covariates and several important biomarker
interaction effects with these covariates.
The flexibility of the methodology is exemplified by its ability to take account of any sam-
pling methodology used for an epidemiological study (i.e. simple random samples through to
multi-staged complex survey sampling). This was demonstrated using the well-known
NHANES data set which used a complex four-staged sampling design encompassing clustered,
stratified and weighted data. There are currently no available stepwise or regularized regression
procedures which can be applied with complex sample designs making variable selection
impossible when there are initially 67 often highly correlated predictors. The boosted regres-
sion overcomes this problem by reducing the number of predictors to 21 and ensuring that
these predictors are not highly correlated, allowing the complex survey based logistic regression
model to be used to manually select the final three predictor variables.
Validation
There are a number of approaches for assessing models in data mining. This methodology
employs the criteria of validity, reliability, parsimony and usefulness to evaluate the effective-
ness of the proposed method.
A simulation was initially used to evaluate the effectiveness of the boosted regression and
importance percentage metric over a traditional backward stepwise variable selection method
to test the impact of a highly correlated predictor in the model such as the case with the
Table 5. (Continued)
Odds Ratio Std. Err. p-value 95% CI Low 95% CI High
18–34 (Reference) 1.000
35–44 0.974 0.024 0.308 0.924 1.027
45–54 0.950 0.019 0.025 0.910 0.993
55–64 0.946 0.029 0.088 0.887 1.009
65+ 0.966 0.062 0.606 0.842 1.110
Diabetes by Blood cadmium
No (Reference) 1.000
Yes 1.115 0.049 0.025 1.016 1.225
Race by Bilirubin
Non-Hispanic White (Reference) 1.000
Mexican Amer/Hispanic 3.946 1.988 0.016 1.342 11.603
Non-Hispanic Black 1.715 1.333 0.499 0.325 9.050
Other 0.484 0.628 0.585 0.030 7.777
Smoking by Bilirubin
Never smoked (Reference) 1.000
Current smoker 9.131 4.193 <0.001 3.418 24.398
Former smoker 2.676 2.396 0.290 0.394 18.187
Constant 0.040 0.030 0.001 0.008 0.200
Note: Multiple imputation logistic regression taking account of the complex survey design of NHANES with 15 strata, 31 PSUs. (n = 3,326).
doi:10.1371/journal.pone.0148195.t005
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biomarker data in this study. A simple random sample of the same size as the original
NHANES data was generated (n = 5,227) for six potential predictors. The correlation for two
predictors was set to 0.8 to indicate multicollinearity, with the remaining correlations emulated
correlations found in the NHANES biomarker data. Two simulations were generated: one with
the same betas for all predictors; the other with varying betas. In both simulations the stepwise
regression failed to drop one of the two highly correlated predictors, indicating possible estima-
tion instability and structural misspecification [62]. In contrast, the boosted regression down-
graded the importance of one of the two highly collinear predictors and produced importance
rankings that reflected the beta values used for the other variables. This validates the use of
boosted regression for variable selection over stepwise regression.
To further assess the validity of using boosted regression, a lasso regression was used as a
comparative machine learning technique for variable selection [63, 64]. This method is similar
to boosted regression in terms of its ability to handle a large number of predictors. Using a
L1-norm penalty for shrinkage in order to prevent the problem of overfitting, the lasso regres-
sion algorithm was employed in the R statistical software using the glmnet package [65]. Con-
sistent with the boosted regression step, the algorithm was performed on the original data and
20 imputed data sets and included cross-validation on 60:40 train:test data. The lasso regres-
sion validated the results of the boosted regression analysis but provided a much less parsimo-
nious solution and it was more difficult to combine the variable selection results across the
imputed data sets. Results from the lasso analysis contained non-zero coefficients only for the
selected variables, making the number of selections a suitable variable importance measure for
each variable. Two of the final three biomarkers from the proposed methodology were chosen
by the lasso regression in at least 20 of the 21 data sets, and the other was in 16 of the 21 data
sets (Table 6). However, for the lasso regression the number of selected variables varied
between 18 and 34 for these 21 data sets, with an average of 25 variables selected, making the
lasso regression much less parsimonious than the boosted regression method.
Running a multiple regression directly on the 21 variables selected from the boosted regres-
sion on the training and validation data sets, without first using univariate regressions to reduce
Table 6. Top 15 biomarkers selected from lasso regression.
Biomarker Frequency
Blood cadmium (nmol/L) 21
Blood urea nitrogen (mg/dL) 21
Glucose, serum (mg/dL) 21
Blood lead (ug/dL) 20
Cotinine (ng/mL) 20
Total bilirubin (mg/dL) 20
Mercury, total (ug/L) 20
Platelet count (1000 cells/uL) 19
Mercury, inorganic (ug/L) 18
Globulin (g/dL) 18
Red blood cell count (million cells/uL) 17
Red cell distribution width (%) 16
Albumin (g/dL) 16
Phosphorus (mg/dL) 16
Direct HDL-Cholesterol (mg/dL) 15
Note: Bold represents the final 3 biomarkers selected from proposed methodology.
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the number of variables further, produced some unstable results across the training and valida-
tion data sets. The odds ratio for Haemoglobin differed drastically between the two models
which was consistent with haemoglobin having singularity with haematocrit (r = 0.968) [66]. In
addition, predictor significance was inconsistent: total bilirubin was the only significant predictor
in the training model and no predictors were significant in the validation model. Finally, the mul-
tiple regression models did not highlight mediation effects as significant univariate relationships
with the outcome were hidden when all predictors were included in the multivariate models.
Results are considered reliable if the same variables are selected regardless of the data supplied.
At step 3 this methodology employs the robust data mining technique of randomly splitting the
data into testing and validation data sets at multiple stages of the traditional statistical regression
to ensure the variables selected and significance are reliable. In addition, at step 2, validation was
performed for each run during the boosted regression by randomly splitting each data set into
training and validation sets to make sure that boosting iterations were employed only when
improved prediction accuracy was achieved with the validation data set. Usefulness relates to
evaluating if the model provides useful information. This hybrid methodology identified three
biomarkers associated with depression from an initial set of 67 in the NHANES data set: red cell
distribution width, serum glucose, and total bilirubin. The direction of the relationship between
depression and the final three biomarkers are broadly concordant with current literature.
Red cell distribution width is a marker of the variability in size of red blood cells or erythro-
cytes and used for differential diagnosis of anaemia, especially iron deficiency anaemia. This
biomarker has been found as a predictor of mortality in the general population [67] and other
conditions such as cardiovascular complications [68], Alzheimer’s disease [69] and diabetes
[70]. In addition, this biomarker has been investigated as a substitute marker for inflammatory
conditions such as inflammatory cancers [71, 72]. Many previous studies have reported the
association between inflammatory markers and depression [73, 74], with depression found to
be comorbid with both diabetes [25, 75] and cardiovascular diseases [76, 77].
Fasting plasma or serum glucose tests are used to screen for and diagnose diabetes and pre-
diabetes and to monitor for hyperglycaemia or hypoglycaemia. Diabetes is often comorbid
with major depression [78, 79], but has a complex bidirectional relationship [75]. An associa-
tion between depression and glucose utilisation dysfunction has been documented [80].
Bilirubin has been reported to be an antioxidant [81, 82]. Depression has been found to be
associated with oxidative stress [83] and mild to moderately elevated serum bilirubin levels are
associated with better outcome in diseases involving oxidative stress [82]. The significant inter-
action found between bilirubin and smoking status is consistent with previous research indicat-
ing that smoking is associated with decreased serum bilirubin concentrations [84, 85].
Hemoglobin was found to be fully mediated by total bilirubin. Red blood cells are continu-
ously being broken down, with hemoglobin splitting into globin (protein), iron and heme. The
heme initially breaks apart into biliverdin which is reduced to bilirubin. Cotinine was found to
be fully mediated by blood cadmium.
Strengths and Limitations
The strength of this hybrid methodology over other variable selection methods is the potential
to adequately handle missing data and complex survey samples using a sound and systematic
multi-stepped approach to variable selection. The application of the data mining knowledge
discovery process to large epidemiological studies allows researchers to include a large array of
data (i.e. variables and observations) to be investigated to generate hypotheses that may have
been otherwise overlooked. This is probably true for this NHANES study, particularly in regard
to the total bilirubin finding.
Data Mine & Machine Learn Biomarkers of Depression
PLOS ONE | DOI:10.1371/journal.pone.0148195 February 5, 2016 18 / 23
The data mining method of splitting data files into training and validation minimises issues
of overfitting that is often problematic in traditional statistical techniques with a large number
of predictors. The boosted machine learning technique can accommodate different types of
variables and has been found to have high predictive accuracy, with shrinkage also used to
avoid over-fitting. The iterative learning nature of the algorithm provides researchers with rea-
sonable confidence in the results with its boosted handling of residuals at each iteration. The
relative importance measure produced by this technique has been demonstrated to be more
effective than the traditional coefficient measures produced by lasso regularized regression and
stepwise regression.
A limitation of the methodology is the potential computing power required to perform the
machine learning techniques when implementing a small shrinkage parameter. In addition,
this study implemented the recommended bagging and number of iterations for the machine
learning boosted regression algorithm, but it may be appropriate in the future to run the algo-
rithm on a number of different bagging percentages and number of iterations.
A limitation of this methodology is the complexity of the implementing a multi-stepped
variable selection approach compared to a simpler single-stepped variable selection approach.
However, unlike simpler single-stepped variable selection procedures such as stepwise regres-
sion and regularized regression this multi-stepped method can accommodate missing data
using multiple imputation combined with complex survey designs.
The NHANES study used in the example for this hybrid methodology is a large cross-sec-
tional study that contains both missing data and utilises a complex four-stage sampling meth-
odology. The limitations of this type of data restrict the ability to infer the direction of the
relationship between the key biomarkers and depression. The self-report instrument of depres-
sion, the PHQ-9, may have missed less severe cases of depression [19, 21]. It is also recognised
that the imbalance of depressive symptoms in the data set may have resulted in a prediction
bias towards the major classes [86].
Conclusion
An amalgamation of data mining techniques using a machine learning algorithm with tradi-
tional statistical techniques provided an effective systematic approach to variable selection in a
large epidemiological study, detecting three biomarkers associated with depression for future
hypothesis generation: red cell distribution width, serum glucose and total bilirubin. The use of
this novel methodology yielded results concordant with previous research, taking account of
the missing data and complex survey design of NHANES. This methodology highlights the
effectiveness of implementing a hybrid of big data and small sample techniques for variable
and potential hypothesis generation.
Supporting Information
S1 Stata Syntax File. Hybrid Methodology Template.
(TXT)
Acknowledgments
MB is supported by a NHMRC Senior Principal Research Fellowship 1059660 and LJW is sup-
ported by a NHMRC Career Development Fellowship 1064272.
The authors would like to thank the referees and editors of this issue for their valuable and
insightful comments and suggestions that have improved this paper.
Data Mine & Machine Learn Biomarkers of Depression
PLOS ONE | DOI:10.1371/journal.pone.0148195 February 5, 2016 19 / 23
Author Contributions
Analyzed the data: JFD. Wrote the paper: JFD JAP MB LJW SD FNJ DM. Designed and per-
formed the statistical methodology and analysis: JFD.
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