In precision medicine, subgroup identification is crucial for designing personalized treatments. This research focuses on subgroup identification in longitudinal clinical trials by integrating the Interaction Tree (ITree) with the Mixed Model for Repeated Measures (MMRM). Our ITree-MMRM approach retains the flexibility of tree-based methods in capturing nonlinear treatment interactions for heterogeneous treatment effects, while adhering to Food and Drug Administration guidelines for assessing treatment effects at the conclusion of longitudinal studies using MMRM. Additionally, we explore various options for tuning parameters and employ bootstrap methods to prune trees, reducing the risk of overoptimism. We demonstrate that our method outperforms existing subgroup identification techniques in simulations. The ITree-MMRM model is applied to an Alzheimer's disease clinical trial to identify subgroups with long-term treatment responses.

In binary classification applications, conservative decision-making that allows for abstention can be advantageous. To this end, we introduce a novel approach that determines the optimal cutoff interval for risk scores, which can be directly available or derived from fitted models. Within this interval, the algorithm refrains from making decisions, while outside the interval, classification accuracy is maximized. Our approach is inspired by support vector machines (SVM), but differs in that it minimizes the classification margin rather than maximizing it. We provide the theoretical optimal solution to this problem, which holds important practical implications. Our proposed method not only supports conservative decision-making but also inherently results in a risk-coverage curve. Together with its associated area under the curve, this representation offers a comprehensive performance metric for evaluating and comparing classifiers, akin to the receiver operating characteristic (ROC). To investigate and illustrate our approach, we conduct both simulation studies and a real-world case study in the context of diagnosing prostate cancer. Supplemental materials are available online.

We introduce a new survival tree method for censored failure time data that incorporates three key advancements over traditional approaches. First, we develop a more computationally efficient splitting procedure that effectively mitigates the end-cut preference problem, and we propose an intersected validation strategy to reduce the variable selection bias inherent in greedy searches. Second, we present a novel framework for determining tree structures through fused regularization. In combination with conventional pruning, this approach enables the merging of non-adjacent terminal nodes, producing more parsimonious and interpretable models. Third, we address inference by constructing valid confidence intervals for median survival times within the subgroups identified by the final tree. To achieve this, we apply bootstrap-based bias correction to standard errors. The proposed method is assessed through extensive simulation studies and illustrated with data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) study.

BACKGROUND/OBJECTIVES:Prostate cancer (PCa) is the most common cancer among males. Approximately 20-40% of patients with clinically localized PCa will present with a biochemical recurrence after a radical prostatectomy (RP), while some will present with recurrent metastasis. Monitoring the disease post-treatment is crucial for detecting a potential cancer recurrence early. Urinary volatile organic compounds (VOCs) have shown potential to detect PCa. However, their application in disease monitoring remains unexplored. METHODS:A total of 165 urine samples were collected from male adults with biopsy-designated PCa-positive results before (n = 55) and after a RP (n = 55), and with biopsy-designated PCa-negative diagnosis (n = 55). The post-RP cohort was subdivided into three groups based on their health status after surgery as recovered healthy, biochemical recurrence, and recurrent metastasis. VOCs in the urine samples were extracted by stir bar sorptive extraction and analyzed using gas chromatography and mass spectrometry. We explored the use of metabolomics and a machine learning algorithm tool to investigate the potential of using VOCs for differentiating PCa diagnoses before and after the RP procedure with different outcomes. RESULTS:Over 100 potential VOCs were identified to differentiate PCa patients before and after a RP, and those with biochemical recurrence and recurrent metastasis. CONCLUSIONS:Urinary VOCs are promising biomarkers that could be used to differentiate PCa patients pre- and post-RP. The findings from this research provide preliminary insights and could aid future investigations in developing tools for PCa patients after treatment. The absence of a validation cohort limits the reproducibility and translational impact of these findings; therefore, the results should be considered exploratory and require confirmation in larger, independent cohorts.

Prostate cancer (PCa) is the second leading cause of cancer-related death in American men after lung cancer. The current PCa diagnostic method, the serum prostate-specific antigen (PSA) test, is not specific, thus, alternatives are needed to avoid unnecessary biopsies and over-diagnosis of clinically insignificant PCa. To explore the application of metabolomics in such effort, urine samples were collected from 386 male adults aged 44-93 years, including 247 patients with biopsy-proven PCa and 139 with biopsy-proven negative results. The PCa-positive group was further subdivided into two groups: low-grade (ISUP Grade Group = 1; n = 139) and intermediate/high-grade (ISUP Grade Group ≥ 2; n = 108). Volatile organic compounds (VOCs) in urine were extracted by stir bar sorptive extraction (SBSE) and analyzed using thermal desorption with gas chromatography and mass spectrometry (GC-MS). We used machine learning tools to develop and evaluate models for PCa diagnosis and prognosis. In total, 22,538 VOCs were identified in the urine samples. With regularized logistic regression, our model for PCa diagnosis yielded an area under the curve (AUC) of 0.99 and 0.88 for the training and testing sets respectively. Furthermore, the model for differentiating between low-grade and intermediate/high-grade PCa yielded an average AUC of 0.78 based on a repeated test-sample approach for cross-validation. These novel methods using urinary VOCs and logistic regression were developed to fill gaps in PCa screening and assessment of PCa grades prior to biopsy. Our study findings provide a promising alternative or adjunct to current PCa screening and diagnostic methods to better target patients for biopsy and mitigate the challenges associated with over-diagnosis and over-treatment of PCa.

Greedy search (GS) or exhaustive search plays a crucial role in decision trees and their various extensions. We introduce an alternative splitting method called smooth sigmoid surrogate (SSS) in which the indicator threshold function used in GS is approximated by a smooth sigmoid function. This approach allows for parametric smoothing or regularization of the erratic and discrete GS process, making it more effective in identifying the true cutoff point, particularly in the presence of weak signals, as well as less prone to the inherent end-cut preference problem. Additionally, SSS provides a convenient means of evaluating the best split by referencing a parametric nonlinear model. Moreover, in many variants of recursive partitioning, SSS can be reformulated as a one-dimensional smooth optimization problem, rendering it computationally more efficient than GS. Extensive simulation studies and real data examples are provided to evaluate and demonstrate its effectiveness.

In randomized controlled trials, individual subjects experiencing recurrent events may display heterogeneous treatment effects. That is, certain subjects might experience beneficial effects, while others might observe negligible improvements or even encounter detrimental effects. To identify subgroups with heterogeneous treatment effects, an interaction survival tree approach is developed in this paper. The Classification and Regression Tree (CART) methodology (Breiman et al., 1984) is inherited to recursively partition the data into subsets that show the greatest interaction with the treatment. The heterogeneity of treatment effects is assessed through Cox’s proportional hazards model, with a frailty term to account for the correlation among recurrent events on each subject. A simulation study is conducted for evaluating the performance of the proposed method. Additionally, the method is applied to identify subgroups from a randomized, double-blind, placebo-controlled study for chronic granulomatous disease. R implementation code is publicly available on GitHub at the following URL: https://github.com/xgsu/IT-Frailty.

Early detection of prostate cancer is critical for successful treatment and survival. However, current diagnostic methods such as prostate-specific antigen (PSA) testing and digital rectal examination (DRE) have limitations in accuracy, specificity, and sensitivity. Recent research suggests that urinary volatile organic compounds (VOCs) could serve as potential biomarkers for prostate cancer diagnosis. In this study, urine samples from 337 PCa-positive and 233 PCa-negative patients were collected to develop a diagnosis model. The study involves a high dimensional (HD) classification problem due to the vast number of measured VOCs. Our findings reveal that regularized logistic regression outperforms numerous other classifiers when analyzing the collected data. In particular, we have selected a regularized logistic model with the SCAD (smoothly clipped absolute deviation) penalty as the final model, which attains an AUC (area under the ROC curve) of 0.748, in contrast to a PSA-based AUC of 0.540. These results underscore the potential of VOC-based diagnosis as a clinically feasible approach for PCa screening.

The lack of accuracy in the current prostate specific antigen (PSA) test for prostate cancer (PCa) screening causes around 60-75% of unnecessary prostate biopsies. Therefore, alternative diagnostic methods that have better accuracy and can prevent over-diagnosis of PCa are needed. Researchers have examined various potential biomarkers for PCa, and of those fatty acids (FAs) markers have received special attention due to their role in cancer metabolomics. It has been noted that PCa metabolism prefers FAs over glucose substrates for continued rapid proliferation. Hence, we proposed using a urinary FAs based model as a non-invasive alternative for PCa detection. Urine samples collected from 334 biopsy-designated PCa positive and 232 biopsy-designated PCa negative subjects were analyzed for FAs and lipid related compounds by stir bar sorptive extraction coupled with gas chromatography/mass spectrometry (SBSE-GC/MS). The dataset was split into the training (70%) and testing (30%) sets to develop and validate logit models and repeated for 100 runs of random data partitioning. Over the 100 runs, we confirmed the stability of the models and obtained optimal tuning parameters for developing the final FA based model. A PSA model using the values of the patients' PSA test results was constructed with the same cohort for the purpose of comparing the performances of the FA model against PSA test. The FA final model selected 20 FAs and rendered an AUC of 0.71 (95% CI = 0.67-0.75, sensitivity = 0.48, and specificity = 0.83). In comparison, the PSA model performed with an AUC of 0.51 (95% CI = 0.46-0.66, sensitivity = 0.44, and specificity = 0.71). The study supports the potential use of urinary FAs as a stable and non-invasive alternative test for PCa diagnosis.

We propose a novel regression tree method named "TreeFuL," an abbreviation for 'Tree with Fused Leaves.' TreeFuL innovatively combines recursive partitioning with fused regularization, offering a distinct approach to the conventional pruning method. One of TreeFuL's noteworthy advantages is its capacity for cross-validated amalgamation of non-neighboring terminal nodes. This is facilitated by a leaf coloring scheme that supports tree shearing and node amalgamation. As a result, TreeFuL facilitates the development of more parsimonious tree models without compromising predictive accuracy. The refined model offers enhanced interpretability, making it particularly well-suited for biomedical applications of decision trees, such as disease diagnosis and prognosis. We demonstrate the practical advantages of our proposed method through simulation studies and an analysis of data collected in an obesity study.

Background: Clear cell renal cell carcinoma (ccRCC) comprises the majority, approximately 70–80%, of renal cancer cases and often remains asymptomatic until incidentally detected during unrelated abdominal imaging or at advanced stages. Currently, standardized screening tests for renal cancer are lacking, which presents challenges in disease management and improving patient outcomes. This study aimed to identify ccRCC-specific volatile organic compounds (VOCs) in the urine of ccRCC-positive patients and develop a urinary VOC-based diagnostic model. Methods: This study involved 233 pretreatment ccRCC patients and 43 healthy individuals. VOC analysis utilized stir-bar sorptive extraction coupled with thermal desorption gas chromatography/mass spectrometry (SBSE-TD-GC/MS). A ccRCC diagnostic model was established via logistic regression, trained on 163 ccRCC cases versus 31 controls, and validated with 70 ccRCC cases versus 12 controls, resulting in a ccRCC diagnostic model involving 24 VOC markers. Results: The findings demonstrated promising diagnostic efficacy, with an Area Under the Curve (AUC) of 0.94, 86% sensitivity, and 92% specificity. Conclusions: This study highlights the feasibility of using urine as a reliable biospecimen for identifying VOC biomarkers in ccRCC. While further validation in larger cohorts is necessary, this study’s capability to differentiate between ccRCC and control groups, despite sample size limitations, holds significant promise.

Although vibration training has been applied in older adults, it remains unclear if it can reduce falls. This pilot randomized-controlled trial aimed to test the effects of an 8-week vibration training program on reducing falls among community-dwelling adults. Forty-eight older adults were randomized to two groups: training and control. The training group received three weekly training sessions over eight weeks while the control group maintained their normal lifestyle over the 8-week period. Immediately before (or baseline), following (post-training), and three months after (retest) the 8-week training course, a group of fall risk factors were assessed for all participants. Each participant was also exposed to an unexpected gait-slip on a treadmill during post-training and retest sessions. Their daily-living fall incidence was collected for 12 months after the baseline test. The slip fall was the primary outcome, prospective all-cause falls were the secondary outcome, and fall risk factors acted as the tertiary ones. The vibration training program significantly reduced the risk of slip-falls and improved all fall risk factors immediately after the training course. The training effect may be carried over for three months. The 8-week training program could also lower the number of falls between the baseline test and retest and reduce the recurrent faller rate across the 12 months after the baseline test. This study indicates that vibration training might have some effects on fall-related measures in older adults. An 8-week vibration training program could be effective to reduce falls in older adults. NCT02694666.

Moderation analysis for evaluating differential treatment effects serves as the bedrock of precision medicine, which is of growing interest in many fields. In the analysis of data with binary outcomes, we observe an interesting symmetry property concerning the ratio of odds ratios, which suggests that heterogeneous treatment effects could be equivalently estimated via a role exchange between the outcome and treatment variable in logistic regression models. We then obtain refined inference on moderating effects by rearranging data and combining two models into one via a generalized estimating equation approach. The improved efficiency is helpful in addressing the lack-of-power problem that is common in the search for important moderators. We investigate the proposed method by simulation and provide an illustration with data from a randomized trial on wart treatment.

Moderation analysis is an integral part of precision medicine research. Concerning moderation analysis with categorical outcomes, we start with an interesting observation, which shows that heterogeneous treatment effects could be equivalently estimated via a role exchange between the outcome and the treatment variable in logistic regression models. Hence two estimators of moderating effects can be obtained. We then established the joint asymptotic normality for the two estimators, on which basis refined inference can be made for moderation analysis. The improved precision is helpful in addressing the lack-of-power problem that is common in search of moderators. The above-mentioned results hold for both experimental and observational data. We investigate the proposed method by simulation and provide an illustration with data from a randomized trial on wart treatment.

Background: Cancer detection presents challenges regarding invasiveness, cost, and reliability. As a result, exploring alternative diagnostic methods holds significant clinical importance. Urinary metabolomic profiling has emerged as a promising avenue; however, its application for cancer diagnosis may be influenced by sample preparation or storage conditions. Objective: This study aimed to assess the impact of sample storage and processing conditions on urinary volatile organic compounds (VOCs) profiles and establish a robust standard operating procedure (SOP) for such diagnostic applications. Methods: Five key variables were investigated: storage temperatures, durations, freeze-thaw cycles, sample collection conditions, and sample amounts. The analysis of VOCs involved stir bar sorptive extraction coupled with thermal desorption-gas chromatography/mass spectrometry (SBSE-TD-GC-MS), with compound identification facilitated by the National Institute of Standards and Technology Library (NIST). Extensive statistical analysis, including combined scatterplot and response surface (CSRS) plots, partial least squares-discriminant analysis (PLS-DA), and probability density function plots (PDFs), were employed to study the effects of the factors. Results: Our findings revealed that urine storage duration, sample amount, temperature, and fasting/non-fasting sample collection did not significantly impact urinary metabolite profiles. This suggests flexibility in urine sample collection conditions, enabling individuals to contribute samples under varying circumstances. However, the influence of freeze-thaw cycles was evident, as VOC profiles exhibited distinct clustering patterns based on the number of cycles. This emphasizes the effect of freeze-thaw cycles on the integrity of urinary profiles. Conclusions: The developed SOP integrating SBSE-TD-GC-MS and statistical analyses can serve as a valuable tool for analyzing urinary organic compounds with minimal preparation and sensitive detection. The findings also support that urinary VOCs for cancer screening and diagnosis could be a feasible alternative offering a robust, non-invasive, and sensitive approach for cancer screening.

: Observational studies of relatively large data can have potentially hidden heterogeneity with respect to causal effects and propensity scores–patterns of a putative cause being exposed to study subjects. This underlying heterogeneity can be crucial in causal inference for any observational studies because it is systematically generated and structured by covariates which influence the cause and/or its related outcomes. Addressing the causal inference problem in view of data structure, machine learning techniques such as tree analysis can be naturally necessitated. Kang, Su, Hitsman, Liu and Lloyd-Jones (2012) proposed Marginal Tree (MT) procedure to explore both the confounding and interacting effects of the covariates on causal inference. In this paper, we extend the MT method to the case of binary responses along with a clear exposition of its relationship with established causal odds ratio. We assess the causal effect of dieting on emotional distress using both a real data set from the Lalonde’s National Supported Work Demonstration Analysis (NSW) and a simulated data set from the National Longitudinal Study of Adolescent Health (Add Health).

AbstractIn this article, we present the random forest algorithm by Breiman in 2001, discuss a few of the most popular random forest extensions, and present random forest of interaction trees for both randomized trials and observational data. In particular, extremely randomized trees, acceptance‐rejection trees, and conditional random forest are detailed and compared in terms of algorithm differences, prediction accuracy for classification and regression problems, computation time, and variable selection bias. We also briefly highlight additional random forest‐related methods and algorithms, while providing references of relevant articles in the literature and, if available, R packages. Random forest of interaction trees (RFIT) is described within the context of precision medicine for randomized clinical trials as well as RFIT incorporating propensity score appropriate for data from observational studies. A simulation study demonstrates that this RFIT approach can improve prediction accuracy of the individualized treatment effect (ITE) for observational study data. The RFIT method is applied to a study of headache treatments, providing individualized treatment effect for all patients, variable importance rankings, and the effects of the most important variables on the ITE via partial dependence plots.

In the multiple linear regression setting, we propose a general framework, termed weighted orthogonal components regression (WOCR), which encompasses many known methods as special cases, including ridge regression and principal components regression. WOCR makes use of the monotonicity inherent in orthogonal components to parameterize the weight function. The formulation allows for efficient determination of tuning parameters and hence is computationally advantageous. Moreover, WOCR offers insights for deriving new better variants. Specifically, we advocate weighting components based on their correlations with the response, which leads to enhanced predictive performance. Both simulated studies and real data examples are provided to assess and illustrate the advantages of the proposed methods.

In this article, we present the random forest algorithm by Breiman in 2001, discuss a few of the most popular random forest extensions, and present random forest of interaction trees for both randomized trials and observational data. In particular, extremely randomized trees, acceptance-rejection trees, and conditional random forest are detailed and compared in terms of algorithm differences, prediction accuracy for classification and regression problems, computation time, and variable selection bias. We also briefly highlight additional random forest-related methods and algorithms, while providing references of relevant articles in the literature and, if available, R packages. Random forest of interaction trees (RFIT) is described within the context of precision medicine for randomized clinical trials as well as RFIT incorporating propensity score appropriate for data from observational studies. A simulation study demonstrates that this RFIT approach can improve prediction accuracy of the individualized treatment effect (ITE) for observational study data. The RFIT method is applied to a study of headache treatments, providing individualized treatment effect for all patients, variable importance rankings, and the effects of the most important variables on the ITE via partial dependence plots.

In clinical studies, the treatment effect may be heterogeneous among patients. It is of interest to identify subpopulations which benefit most from the treatment, regardless of the treatment's overall performance. In this study, we are interested in subgroup identification in longitudinal studies when nonlinear trajectory patterns are present. Under such a situation, evaluation of the treatment effect entails comparing longitudinal trajectories while subgroup identification requires a further evaluation of differential treatment effects among subgroups induced by moderators. To this end, we propose a tree-structured subgroup identification method, termed "interaction tree for longitudinal trajectories", which combines mixed effects models with regression splines to model the nonlinear progression patterns among repeated measures. Extensive simulation studies are conducted to evaluate its performance and an application to an alcohol addiction pharmacogenetic trial is presented.