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 integrated using the Data Integration Protocol In Ten-Steps (DIPIT) [17]. NHANES is a cross-sectional, 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, individuals within households. Data were collected from 15 different locations across 50 states of America 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 population 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 biomarkers 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.

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 (Continuation 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 available 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 inadequate 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].

Participants were also identified as having the inflammatory conditions of arthritis and cancer or malignancy using the self-report questions.

Participants were asked to bring currently used medications to the assessment. The Lexicon Plus^® 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 medication 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, metabolic agents, nutritional products, psychotherapeutic agents, respiratory agents, and topical agents.

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 observations 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 procedures 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 performed 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 probability 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-missing). No significant relationship between the missingness indicators and the outcome of interest suggests MAR. MCAR occurs when the probability of being missing is independent of all 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 simultaneously. 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 assumptions of MAR and MCAR were rejected, multiple imputation was required. The multiple imputation 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 biomarkers, 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 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 technique 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 predictive 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 Depression Risk Assessment (CADRA) index from an array of baseline social and cognitive vulnerability 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 (continuous, 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 automatically 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 validation 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 outcomes for the observations found in each terminal node. Residuals are computed as the difference 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, 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 developed 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 percentage 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] implemented by Schonlau [61]. This method was performed on the original data set of 5,227 observations 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 ensuring 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 parameter 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 prediction 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%.

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. Predictors 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 univariate weighted logistic regressions. These regressions, were conducted for each selected biomarker 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. Multicollinearity 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 indicative 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].

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. Significant results for several biomarkers indicated that missing biomarker data affected the depression 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 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%).

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Table 2. Boosted regression statistics.

https://doi.org/10.1371/journal.pone.0148195.t002

STEP 3: Traditional statistical regression results

The training data yielded five biomarkers with significant univariate relationship with depression: 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 biomarkers 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.

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Table 3. Univariate Logistic Regression statistics.

https://doi.org/10.1371/journal.pone.0148195.t003

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. Consistent results were obtained for the multiple logistic regression model in the training and validation data (Table 4).

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Table 4. Final Four biomarkers from boosted regression.

https://doi.org/10.1371/journal.pone.0148195.t004

The final model controlling for potential confounders and including significant interactions are reported in Table 5.

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Table 5. Final Multivariate Logistic Regression.

https://doi.org/10.1371/journal.pone.0148195.t005

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 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) indicating 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, significant 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.

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 effectiveness 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 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 estimation instability and structural misspecification [62]. In contrast, the boosted regression downgraded 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 regression algorithm was employed in the R statistical software using the glmnet package [65]. Consistent 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 regression validated the results of the boosted regression analysis but provided a much less parsimonious 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.

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Table 6. Top 15 biomarkers selected from lasso regression.

https://doi.org/10.1371/journal.pone.0148195.t006

Running a multiple regression directly on the 21 variables selected from the boosted regression on the training and validation data sets, without first using univariate regressions to reduce the number of variables further, produced some unstable results across the training and validation 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 multiple 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 erythrocytes 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 prediabetes and to monitor for hyperglycaemia or hypoglycaemia. Diabetes is often comorbid with major depression [78, 79], but has a complex bidirectional relationship [75]. An association 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 interaction found between bilirubin and smoking status is consistent with previous research indicating 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 continuously 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.

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 reasonable 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 algorithm 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 regression 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-sectional study that contains both missing data and utilises a complex four-stage sampling methodology. 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 depression, 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].