Evaluating the effect of optimized cutoff values in the assessment of prognostic factors

Categorization of continuous covariates and complex regression models-friends or foes in intersectionality research

OBJECTIVES

To reduce health inequities, it is important to identify intersections in characteristics of individuals subject to privilege or disadvantage. Different proposals for that have recently been published. One approach (1) considers models specified with first- and all second-order effects and another (2) the stratification based on multiple covariates; both categorize continuous covariates. A simulation study was conducted in order to review both methods with regard to identification of intersections showing true differences, rate of false-positive results, and generalizability to independent data compared to an established approach (3) of backward variable elimination according to Bayesian information criterion (BE-BIC) combined with splines.

STUDY DESIGN AND SETTING

R software has been used to simulate the covariates age, sex, body mass index, education, and diabetes to examine their association with a continuous frailty score for osteoporosis using multiple linear regression. In setting 1, none of the covariates was associated with the frailty score, that is, only noise is present in the data. In setting 2, the covariates age, sex, and their interaction were associated with the frailty score, such that only females above 55 years formed an intersection associated with an increased frailty score. All approaches were compared under varying sample sizes (N = 200-3000) and signal-to-noise ratios (SNRs, 0.5-4) in 1000 replications. For model evaluation, bootstrap resampling was used. The models were fitted in internal learning data and then used to predict outcomes in the internal validation data. The mean squared error (MSE) was used for comparison and the frequency of false-positive findings calculated.

RESULTS

In setting 1, approaches 1 and 2 generated spurious effects in more than 90% of simulations across all sample sizes. In a smaller sample size, approach 3 (BE-BIC) selected 36.5% of the correct model, in larger sample size in 89.8% and always had a lower number of spurious effects. MSE in independent data was generally higher for approaches 1 and 2 when compared to 3. In setting 2, approach 1 selected most frequently the correct interaction but frequently showed spurious effects (>75%). Across all sample sizes and SNR, approach 3 generated least often spurious results and had lowest MSE in independent data.

CONCLUSION

Categorization of continuous covariates is detrimental to studies on intersectionality. Due to high and unrestricted model complexity, such approaches are prone to spurious effects and often lack interpretability. Approach 3 (BE-BIC) is considerably more robust against spurious findings, showed better generalizability to independent data, and can be used with most statistical software. For intersectionality research, we consider it most important to describe relevant differences between intersections and to avoid nonreproducible and spurious findings.

Depth of Radiographic Response and Time to Tumor Regrowth Predicts Overall Survival Following Anti-VEGF Therapy in Recurrent Glioblastoma

PURPOSE

Antiangiogenic therapies are known to cause high radiographic response rates due to reduction in vascular permeability resulting in a lower degree of contrast extravasation. In this study, we investigate the prognostic ability for model-derived parameters describing enhancing tumor volumetric dynamics to predict survival in recurrent glioblastoma treated with antiangiogenic therapy.

EXPERIMENTAL DESIGN

N = 276 patients in two phase II trials were used as training data, including bevacizumab ± irinotecan (NCT00345163) and cabozantinib (NCT00704288), and N = 74 patients in the bevacizumab arm of a phase III trial (NCT02511405) were used for validation. Enhancing volumes were estimated using T1 subtraction maps, and a biexponential model was used to estimate regrowth (g) and regression (d) rates, time to tumor regrowth (TTG), and the depth of response (DpR). Response characteristics were compared to diffusion MR phenotypes previously shown to predict survival.

RESULTS

Optimized thresholds occurred at g = 0.07 months-1 (phase II: HR = 0.2579, P = 5 × 10-20; phase III: HR = 0.2197, P = 5 × 10-5); d = 0.11 months-1 (HR = 0.3365, P < 0.0001; HR = 0.3675, P = 0.0113); TTG = 3.8 months (HR = 0.2702, P = 6 × 10-17; HR = 0.2061, P = 2 × 10-5); and DpR = 11.3% (HR = 0.6326, P = 0.0028; HR = 0.4785, P = 0.0206). Multivariable Cox regression controlling for age and baseline tumor volume confirmed these factors as significant predictors of survival. Patients with a favorable pretreatment diffusion MRI phenotype had a significantly longer TTG and slower regrowth.

CONCLUSIONS

Recurrent glioblastoma patients with a large, durable radiographic response to antiangiogenic agents have significantly longer survival. This information is useful for interpreting activity of antiangiogenic agents in recurrent glioblastoma.

A Computable Algorithm for Medication Optimization in Heart Failure With Reduced Ejection Fraction

Background

Guideline-directed medical therapy (GDMT) optimization can improve outcomes in heart failure with reduced ejection fraction.

Objectives

The objective of this study was to determine if a novel computable algorithm appropriately recommended GDMT.

Methods

Clinical trial data from the GUIDE-IT (Guiding Evidence-Based Therapy Using Biomarker Intensified Treatment in Heart Failure) and HF-ACTION (Heart Failure: A Controlled Trial Investigating Outcomes of Exercise Training) trials were evaluated with a computable medication optimization algorithm that outputs GDMT recommendations and a medication optimization score (MOS). Algorithm-based recommendations were compared to medication changes. A Cox proportional-hazards model was used to estimate the associations between MOS and the composite primary end point for both trials.

Results

The algorithm recommended initiation of angiotensin-converting enzyme inhibitor/angiotensin receptor blocker, beta-blockers, and mineralocorticoid receptor antagonists in 52.8%, 34.9%, and 68.1% of GUIDE-IT visits, respectively, when not prescribed the drug. Initiation only occurred in 20.8%, 56.9%, and 15.8% of subsequent visits. The algorithm also identified dose titration in 48.8% of visits for angiotensin-converting enzyme inhibitor/angiotensin receptor blockers and 39.4% of visits for beta-blockers. Those increases only occurred in 24.3% and 36.8% of subsequent visits. A higher baseline MOS was associated with a lower risk of cardiovascular death or heart failure hospitalization (HR: 0.41; 95% CI: 0.21-0.80; P = 0.009) in GUIDE-IT and all-cause death and hospitalization (HR: 0.61; 95% CI: 0.44-0.84; P = 0.003) in HF-ACTION.

Conclusions

The algorithm accurately identified patients for GDMT optimization. Even in a clinical trial with robust protocols, GDMT could have been further optimized in a meaningful number of visits. The algorithm-generated MOS was associated with a lower risk of clinical outcomes. Implementation into clinical care may identify and address suboptimal GDMT in patients with heart failure with reduced ejection fraction.

Prognostic role of the prognostic nutritional index in patients with pancreatic cancer who underwent curative resection without preoperative neoadjuvant treatment: A systematic review and meta-analysis

Background

The prognostic nutrition index (PNI), which has been evaluated in various kinds of cancers, offered a simple yet effective approach to predict the prognosis. The aim of this meta-analysis is to reveal the correlation between preoperative PNI and the prognosis of patients with pancreatic ductal adenocarcinoma (PDAC) who underwent curative resection.

Methods

We searched the PubMed, Embase, Web of Science and Cochrane Library databases, and extracted the hazard ratio (HR) with 95% confidential interval (CI) from eligible studies. The pooled HR with 95% CI was applied to evaluate the association between PNI and overall survival (OS), recurrence-free survival (RFS).

Results

A total of fourteen studies with 3,385 patients were included for meta-analysis. The results (the pooled HR: 1.664, 95% CI: 1.424–1.994, I² = 42.6%, p value = 0.046) indicated that low preoperative PNI was closely related to poor OS. In addition, the results suggested that PNI was negatively correlated with RFS (the pooled HR: 1.369, 95%CI: 1.080–1.734). The robustness of these pooled results was verified by our subgroup analysis and sensitivity analysis. Moreover, different cutoff values among studies are responsible for the heterogeneity of pooled HR of OS through meta-regression analysis (p value = 0.042). Funnel plots, Begg's test (p value = 0.228) and Egger’s test (p value = 0.702) indicated no significant publication bias in OS.

Conclusion

Preoperative PNI might be a promising marker to predict the prognosis of PDAC patients who underwent curative resection.

Design for a Multicentre Prospective Cohort for the Assessment of Platelet Function in Patients with Hepatitis-B-Virus-Related Acute-on-Chronic Liver Failure

Background

Acute-on-chronic liver failure (ACLF) has high short-term mortality and lacks sufficient medical therapy. Available algorithms are unable to precisely predict short-term outcomes or safely stratify patients with ACLF as emergent liver transplantation candidates. Therefore, a personalized prognostic tool is urgently needed.

Purpose

Platelet function and its clinical significance in ACLF patients with chronic hepatitis B virus (HBV) infection have not been investigated. This study aimed to assess changes in platelet function using thromboelastography (TEG) and platelet mapping (TEG-PM) in HBV-related ACLF patients.

Methods

Chronic liver disease patients with acute decompensation or acute hepatic injury were recruited. The derivation cohort enrolled HBV-related patients at Nanfang Hospital. HBV-related and non-HBV-related patients were both enrolled in internal and external validation cohorts at seven university hospitals. TEG and TEG-PM were performed at baseline in the derivation cohort and baseline, day 7, and day 14 in the validation cohorts. The primary outcome was all-cause 28-day mortality. Status check and new-onset complications were recorded during the 3-month follow-up, but status check will extend to 5 years.

Conclusion and Future Plans

In this study, 586 participants were enrolled, including 100 in derivation cohort, 133 in internal validation cohort, and 353 in external validation cohort. Biomaterials, including plasma, serum, urine, and some explanted liver tissues, were collected from these patients. A 3-month follow-up with survival status was completed. The baseline characteristics indicated that 51% of the patients had adenosine diphosphate (ADP)-hyporesponsive circulating platelets. The prognostic potential of platelet function will be explored in the derivation cohort (HBV-related ACLF patients) and further substantiated in the validation cohorts (HBV-related and non-HBV-related ACLF patients). Biosamples are currently used to explore the underlying mechanisms related to ADP-hyporesponsive platelets. The ongoing proteomic and metabolic analyses will provide new insights into the pathogenesis of extrahepatic organ failures in ACLF patients.

Tumor immune cell clustering and its association with survival in African American women with ovarian cancer

New technologies, such as multiplex immunofluorescence microscopy (mIF), are being developed and used for the assessment and visualization of the tumor immune microenvironment (TIME). These assays produce not only an estimate of the abundance of immune cells in the TIME, but also their spatial locations. However, there are currently few approaches to analyze the spatial context of the TIME. Therefore, we have developed a framework for the spatial analysis of the TIME using Ripley’s K, coupled with a permutation-based framework to estimate and measure the departure from complete spatial randomness (CSR) as a measure of the interactions between immune cells. This approach was then applied to epithelial ovarian cancer (EOC) using mIF collected on intra-tumoral regions of interest (ROIs) and tissue microarrays (TMAs) from 160 high-grade serous ovarian carcinoma patients in the African American Cancer Epidemiology Study (AACES) (94 subjects on TMAs resulting in 263 tissue cores; 93 subjects with 260 ROIs; 27 subjects with both TMA and ROI data). Cox proportional hazard models were constructed to determine the association of abundance and spatial clustering of tumor-infiltrating lymphocytes (CD3+), cytotoxic T-cells (CD8+CD3+), and regulatory T-cells (CD3+FoxP3+) with overall survival. Analysis was done on TMA and ROIs, treating the TMA data as validation of the findings from the ROIs. We found that EOC patients with high abundance and low spatial clustering of tumor-infiltrating lymphocytes and T-cell subsets in their tumors had the best overall survival. Additionally, patients with EOC tumors displaying high co-occurrence of cytotoxic T-cells and regulatory T-cells had the best overall survival. Grouping women with ovarian cancer based on both cell abundance and spatial contexture showed better discrimination for survival than grouping ovarian cancer cases only by cell abundance. These findings underscore the prognostic importance of evaluating not only immune cell abundance but also the spatial contexture of the immune cells in the TIME. In conclusion, the application of this spatial analysis framework to the study of the TIME could lead to the identification of immune content and spatial architecture that could aid in the determination of patients that are likely to respond to immunotherapies.

New technologies, such as multiplex immunofluorescence microscopy, are being developed and used for the assessment and visualization of the tumor immune microenvironment (TIME). These assays produce not only an estimate of the abundance of immune cells in the TIME, but also their spatial locations; however, there are currently few approaches to analyze the spatial context of the TIME. Thus, we have developed a framework for the spatial analysis of the TIME and applied this method to the analysis of T-cells collected from patients with high-grade serous ovarian carcinoma in the African American Cancer Epidemiology Study. We found that patients with high abundance and low spatial clustering of tumor-infiltrating lymphocytes and T-cell subsets in their tumors had the best overall survival. Additionally, best survival was observed for patients with tumors displaying high co-occurrence of cytotoxic T-cells and regulatory T-cells. These findings underscore the prognostic importance of evaluating not only immune cell abundance but also the spatial contexture of the immune cells in the ovarian TIME. The use of our framework for spatial analysis of the TIME and immune cell clustering may be applicable in other cancers and provide a novel approach to identification of biomarkers for predicting patient outcomes.

A Model-free Approach for Testing Association

The question of association between outcome and feature is generally framed in the context of a model based on functional and distributional forms. Our motivating application is that of identifying serum biomarkers of angiogenesis, energy metabolism, apoptosis, and inflammation, predictive of recurrence after lung resection in node-negative non-small cell lung cancer patients with tumor stage T2a or less. We propose an omnibus approach for testing association that is free of assumptions on functional forms and distributions and can be used as a general method. This proposed maximal permutation test is based on the idea of thresholding, is readily implementable and is computationally efficient. We demonstrate that the proposed omnibus tests maintain their levels and have strong power for detecting linear, nonlinear and quantile-based associations, even with outlier-prone and heavy-tailed error distributions and under nonparametric setting. We additionally illustrate the use of this approach in model-free feature screening and further examine the level and power of these tests for binary outcome. We compare the performance of the proposed omnibus tests with comparator methods in our motivating application to identify preoperative serum biomarkers associated with non-small cell lung cancer recurrence in early stage patients.

Clinical conditions and treatment requirements for long-term survival among hepatitis B-related hepatocellular carcinoma initially treated with chemoembolization

OBJECTIVE

Transarterial chemoembolization (TACE) is recommended to treat intermediate/advanced stage of hepatocellular carcinoma (HCC). However, the overall survival among initially TACE-treated patients varies significantly. The clinical characterization of long-term survival following TACE remains uncertain. We sought to identify clinical parameters and treatment requirements for long-term survival among patients with hepatitis B-related HCC who were initially treated with TACE.

MATERIALS AND METHODS

The included patients with HCC were admitted to our cancer center between December 2009 and May 2015. Patients who survived for >3 years were compared with those who died within 3 years. The clinical and laboratory findings that were associated with the survival were also analyzed.

RESULTS

One in six (17.9%) patients with HCC in this cohort survived for > 3 years after TACE. Body mass index (BMI) ≥ 23kg/m² , aspartate aminotransferase levels ≤ 40 U/L, an activated partial thromboplastin time ≤ 34 seconds, α-fetoprotein (AFP) levels ≤ 25 ng/mL, antiviral therapy, tumor size ≤ 8 cm, solitary nodule, and the absence of vascular invasion were independently favorably associated with a 3-year survival. An absence of vascular invasion was the only independent factor associated with 3-year survival in patients who received resection and/or ablation after TACE.

CONCLUSION

In this cohort, a 3-year survival was associated with BMI, antivirus treatment, tumor status, hepatic function, and AFP level. Distant metastasis did not negatively impact the long-term survival among patients with hepatitis B-related HCC initially treated with TACE. Vascular invasion was the single impediment to long-term survival in patients who received add-on resection and/or ablation after TACE.

Assessing the Optimal Cutpoint for Tumor Size in Patients with Lung Cancer Based on Linear Rank Statistics in a Competing Risks Framework

PURPOSE

In clinical studies, patients may experience several types of events during follow up under the competing risks (CR) framework. Patients are often classified into low- and high-risk groups based on prognostic factors. We propose a method to determine an optimal cutpoint value for prognostic factors on censored outcomes in the presence of CR.

MATERIALS AND METHODS

We applied our method to data collected in a study of lung cancer patients. From September 1, 1991 to December 31, 2005, 758 lung cancer patients received tumor removal surgery at Samsung Medical Center in Korea. The proposed statistic converges in distribution to that of the supremum of a standardized Brownian bridge. To overcome the conservativeness of the test based on an approximation of the asymptotic distribution, we also propose a permutation test based on permuted samples.

RESULTS

Most cases considered in our simulation studies showed that the permutation-based test satisfied a significance level of 0.05, while the approximation-based test was very conservative: the powers of the former were larger than those of the latter. The optimal cutpoint value for tumor size (unit: cm) prior to surgery for classifying patients into two groups (low and high risks for relapse) was found to be 1.8, with decent significance reflected as p values less than 0.001.

CONCLUSION

The cutpoint estimator based on the maximally selected linear rank statistic was reasonable in terms of bias and standard deviation in the CR framework. The permutation-based test well satisfied type I error probability and provided higher power than the approximation-based test.

Biostatistical Methods for the Validation of Alternative Methods for In Vitro Toxicity Testing

Statistical methods for the validation of toxicological in vitro test assays are developed and applied. Validation is performed either in comparison with in vivo assays or in comparison with other in vitro assays of established validity. Biostatistical methods are presented which are of potential use and benefit for the validation of alternative methods for the risk assessment of chemicals, providing at least an equivalent level of protection through in vitro toxicity testing to that obtained through the use of current in vivo methods. Characteristic indices are developed and determined. Qualitative outcomes are characterised by the rates of false-positive and false-negative predictions, sensitivity and specificity, and predictive values. Quantitative outcomes are characterised by regression coefficients derived from predictive models. The receiver operating characteristics (ROC) technique, applicable when a continuum of cut-off values is considered, is discussed in detail, in relation to its use for statistical modelling and statistical inference. The methods presented are examined for their use for the proof of safety and for toxicity detection and testing. We emphasise that the final validation of toxicity testing is human toxicity, and that the in vivo test itself is only a predictor with an inherent uncertainty. Therefore, the validation of the in vitro test has to account for the vagueness and uncertainty of the "gold standard" in vivo test. We address model selection and model validation, and a four-step scheme is proposed for the conduct of validation studies. Gaps and research needs are formulated to improve the validation of alternative methods for in vitro toxicity testing.

A Smooth Nonparametric Approach to Determining Cut-Points of A Continuous Scale

The problem of determining cut-points of a continuous scale according to an establish categorical scale is often encountered in practice for the purposes such as making diagnosis or treatment recommendation, determining study eligibility, or facilitating interpretations. A general analytic framework was recently proposed for assessing optimal cut-points defined based on some pre-specified criteria. However, the implementation of the existing nonparametric estimators under this framework and the associated inferences can be computationally intensive when more than a few cut-points need to be determined. To address this important issue, a smoothing-based modification of the current method is proposed and is found to substantially improve the computational speed as well as the asymptotic convergence rate. Moreover, a plug-in type variance estimation procedure is developed to further facilitate the computation. Extensive simulation studies confirm the theoretical results and demonstrate the computational benefits of the proposed method. The practical utility of the new approach is illustrated by an application to a mental health study.

Integrated tumor identification and automated scoring minimizes pathologist involvement and provides new insights to key biomarkers in breast cancer

Digital image analysis (DIA) is becoming central to the quantitative evaluation of tissue biomarkers for discovery, diagnosis and therapeutic selection for the delivery of precision medicine. In this study, automated DIA using a new purpose-built software platform (QuPath) is applied to a cohort of 293 breast cancer patients to score five biomarkers in tissue microarrays (TMAs): ER, PR, HER2, Ki67 and p53. This software is able to measure IHC expression following fully automated tumor recognition in the same immunohistochemical (IHC)-stained tissue section, as part of a rapid workflow to ensure objectivity and accelerate biomarker analysis. The digital scores produced by QuPath were compared with manual scores by a pathologist and shown to have a good level of concordance in all cases (Cohen's κ>0.6), and almost perfect agreement for the clinically relevant biomarkers ER, PR and HER2 (κ>0.86). To assess prognostic value, cutoff thresholds could be applied to both manual and automated scores using the QuPath software, and survival analysis performed for 5-year overall survival. DIA was shown to be capable of replicating the statistically significant stratification of patients achieved using manual scoring across all biomarkers (P<0.01, log-rank test). Furthermore, the image analysis scores were shown to consistently lead to statistical significance across a wide range of potential cutoff thresholds, indicating the robustness of the method, and identify sub-populations of cases exhibiting different expression patterns within the p53 and Ki67 data sets that warrant further investigation. These findings have demonstrated QuPath's suitability for fast, reproducible, high-throughput TMA analysis across a range of important biomarkers. This was achieved using our tumor recognition algorithms for IHC-stained sections, trained interactively without the need for any additional tumor recognition markers, for example, cytokeratin, to obtain greater insight into the relationship between biomarker expression and clinical outcome applicable to a range of cancer types.

Time to positivity of blood cultures in patients with bloodstream infections: A useful prognostic tool

OBJECTIVE

The time to positivity (TTP) of blood cultures in patients with bloodstream infections (BSIs) has been considered to be a possible prognostic tool for some bacterial species. However, notable differences have been found between sampling designs and statistical methods in published studies to date, which makes it difficult to compare results or to derive reliable conclusions. Our objective was to evaluate the clinical and microbiological implications of TTP among patients with BSI caused by the most common pathogens.

METHODS

A total of 361 episodes of BSI were reported for 332 patients. The survival of the entire cohort was measured from the time of blood culture sampling. In order to compare our results with those of previous studies, TTP was divided in three different groups based on log rank (short TTP <12h; medium TTP ≥12h to ≤27h, and long TTP >27h). Cox proportional hazard models were used to calculate crude and adjusted hazard ratios (HR).

RESULTS

The Cox proportional hazard model revealed that TTP is an independent predictor of mortality (HR=1.00, p=0.031) in patients with BSIs. A higher mortality was found in the group of patients with the shortest TTP (<12h) (HR=2.100, p=0.047), as well as those with longest TTP (>27h) (HR=3.277, p=0.031).

CONCLUSIONS

It seems that TTP may provide a useful prognostic tool associated with a higher risk of mortality, not only in patients with shorter TTP, but also in those with longer TTP.

Predicting the occurrence of major adverse cardiac events within 30 days of a vascular surgery: an empirical comparison of the minimum p value method and ROC curve approach using individual patient data meta-analysis

We aimed to compare the minimum p value method and the area under the receiver operating characteristics (ROC) curve approach to categorize continuous biomarkers for the prediction of postoperative 30-day major adverse cardiac events in noncardiac vascular surgery patients. Individual-patient data from six cohorts reporting B-type natriuretic peptide (BNP) or N-terminal pro-B-type natriuretic peptide (NTproBNP) were obtained. These biomarkers were dichotomized using the minimum p value method and compared with previously reported ROC curve-derived thresholds using logistic regression analysis. A final prediction model was developed, internally validated, and assessed for its sensitivity to clustering effects. Finally, a preoperative risk score system was proposed. Thresholds identified by the minimum p value method and ROC curve approach were 115.57 pg/ml (p < 0.001) and 116 pg/ml for BNP, and 241.7 pg/ml (p = 0.001) and 277.5 pg/ml for NTproBNP, respectively. The minimum p value thresholds were slightly stronger predictors based on our logistic regression analysis. The final model included a composite predictor of the minimum p value method’s BNP and NTproBNP thresholds [odds ratio (OR) = 8.5, p < 0.001], surgery type (OR = 2.5, p = 0.002), and diabetes (OR = 2.1, p = 0.015). Preoperative risks using the scoring system ranged from 2 to 49 %. The minimum p value method and ROC curve approach identify similar optimal thresholds. We propose to replace the revised cardiac risk index with our risk score system for individual-specific preoperative risk stratification after noncardiac nonvascular surgery.

Older Age and Leg Pain Are Good Predictors of Pain and Disability Outcomes in 2710 Patients Who Receive Lumbar Fusion

BACKGROUND

Identifying appropriate candidates for lumbar spine fusion is a challenging and controversial topic. The purpose of this study was to identify baseline characteristics related to poor/favorable outcomes at 1 year for a patient who received lumbar spine fusion.

QUESTIONS/PURPOSES

The aims of this study were to describe baseline characteristics of those who received lumbar surgery and to identify baseline characteristics from a spine repository that were related to poor and favorable pain and disability outcomes for patient who received lumbar fusion (with or without decompression), who were followed up for 1 full year and discriminate predictor variables that were either or in contrast to prognostic variables reported in the literature.

METHODS

This study analyzed data from 2710 patients who underwent lumbar spine fusion. All patient data was part of a multicenter, multi-national spine repository. Ten relatively commonly captured data variables were used as predictors for the study. Univariate/multivariate logistic regression analyses were run against outcome variables of pain/disability.

RESULTS

Multiple univariate findings were associated with pain/disability outcomes at 1 year including age, previous surgical history, baseline disability, baseline pain, baseline quality of life scores, and leg pain greater than back pain. Notably significant multivariate findings for both pain and disability include older age, previous surgical history, and baseline mental summary scores, disability, and pain.

CONCLUSION

Leg pain greater than back pain and older age may yield promising value when predicting positive outcomes. Other significant findings may yield less value since these findings are similar to those that are considered to be prognostic regardless of intervention type.

A new approach to categorising continuous variables in prediction models: Proposal and validation

When developing prediction models for application in clinical practice, health practitioners usually categorise clinical variables that are continuous in nature. Although categorisation is not regarded as advisable from a statistical point of view, due to loss of information and power, it is a common practice in medical research. Consequently, providing researchers with a useful and valid categorisation method could be a relevant issue when developing prediction models. Without recommending categorisation of continuous predictors, our aim is to propose a valid way to do it whenever it is considered necessary by clinical researchers. This paper focuses on categorising a continuous predictor within a logistic regression model, in such a way that the best discriminative ability is obtained in terms of the highest area under the receiver operating characteristic curve (AUC). The proposed methodology is validated when the optimal cut points’ location is known in theory or in practice. In addition, the proposed method is applied to a real data-set of patients with an exacerbation of chronic obstructive pulmonary disease, in the context of the IRYSS-COPD study where a clinical prediction rule for severe evolution was being developed. The clinical variable PCO2 was categorised in a univariable and a multivariable setting.

Prediction of the 10-year probability of gastric cancer occurrence in the Japanese population: the JPHC study cohort II

Gastric cancer is a particularly important issue in Japan, where incidence rates are among the highest observed. In this work, we provide a risk prediction model allowing the estimation of the 10-year cumulative probability of gastric cancer occurrence. The study population consisted of 19,028 individuals from the Japanese Public Health Center cohort II who were followed-up from 1993 to 2009. A parametric survival model was used to assess the impact on the probability of gastric cancer of clinical and lifestyle-related risk factors in combination with serum anti-Helicobacter pylori antibody titres and pepsinogen I and pepsinogen II levels. Based on the resulting model, cumulative probability estimates were calculated and a simple risk scoring system was developed. A total of 412 cases of gastric cancer occurred during 270,854 person-years of follow-up. The final model included (besides the biological markers) age, gender, smoking status, family history of gastric cancer and consumption of highly salted food. The developed prediction model showed good predictive performance in terms of discrimination (optimism-corrected c-index: 0.768) and calibration (Nam and d'Agostino's χ(2) test: 14.78; p values = 0.06). Estimates of the 10-year probability of gastric cancer occurrence ranged from 0.04% (0.02, 0.1) to 14.87% (8.96, 24.14) for men and from 0.03% (0.02, 0.07) to 4.91% (2.71, 8.81) for women. In conclusion, we developed a risk prediction model for gastric cancer that combines clinical and biological markers. It might prompt individuals to modify their lifestyle habits, attend regular check-up visits or participate in screening programmes.

Predictors of pain and disability outcomes in one thousand, one hundred and eight patients who underwent lumbar discectomy surgery

BACKGROUND

A key component toward improving surgical outcomes is proper patient selection. Improved selection can occur through exploration of prognostic studies that identify variables which are associated with good or poorer outcomes with a specific intervention, such as lumbar discectomy. To date there are no guidelines identifying key prognostic variables that assist surgeons in proper patient selection for lumbar discectomy. The purpose of this study was to identify baseline characteristics that were related to poor or favourable outcomes for patients who undergo lumbar discectomy. In particular, we were interested in prognostic factors that were unique to those commonly reported in the musculoskeletal literature, regardless of intervention type.

METHODS

This retrospective study analysed data from 1,108 patients who underwent lumbar discectomy and had one year outcomes for pain and disability. All patient data was part of a multicentre, multi-national spine repository. Ten relatively commonly captured data variables were used as predictors for the study: (1) age, (2) body mass index, (3) gender, (4) previous back surgery history, (5) baseline disability, unique baseline scores for pain for both (6) low back and (7) leg pain, (8) baseline SF-12 Physical Component Summary (PCS) scores, (9) baseline SF-12 Mental Component Summary (MCS) scores, and (10) leg pain greater than back pain. Univariate and multivariate logistic regression analyses were run against one year outcome variables of pain and disability.

RESULTS

For the multivariate analyses associated with the outcome of pain, older patients, those with higher baseline back pain, those with lesser reported disability and higher SF-12 MCS quality of life scores were associated with improved outcomes. For the multivariate analyses associated with the outcome of disability, presence of leg pain greater than back pain and no previous surgery suggested a better outcome.

CONCLUSIONS

For this study, several predictive variables were either unique or conflicted with those advocated in general prognostic literature, suggesting they may have value for clinical decision making for lumbar discectomy surgery. In particular, leg pain greater than back pain and older age may yield promising value. Other significant findings such as quality of life scores and prior surgery may yield less value since these findings are similar to those that are considered to be prognostic regardless of intervention type.

Senescence-associated-gene signature identifies genes linked to age, prognosis, and progression of human gliomas

BACKGROUND

Senescence-associated genes (SAGs) are responsible for the senescence-associated secretory phenotype, linked in turn to cellular aging, the aging brain, and the pathogenesis of cancer.

OBJECTIVE

We hypothesized that senescence-associated genes are overexpressed in older patients, in higher grades of glioma, and portend a poor prognosis.

METHODS

Forty-seven gliomas were arrayed on a custom version of the Affymetrix HG-U133+2.0 GeneChip, for expression of fourteen senescence-associated genes: CCL2, CCL7, CDKN1A, COPG, CSF2RB, CXCL1, ICAM-1, IGFBP-3, IL-6, IL-8, SAA4, TNFRSF-11B, TNFSF-11 and TP53. A combined "senescence score" was generated using principal component analysis to measure the combined effect of the senescence-associated gene signature.

RESULTS

An elevated senescence score correlated with older age (r=0.37; P=.01) as well as a higher degree of malignancy, as determined by WHO, histological grade (r=0.49; P<.001). There was a mild association with poor prognosis (P=.06). Gliosarcomas showed the highest scores. Six genes independently correlated with either age (IL-6, TNFRSF-11B, IGFBP-3, SAA4, and COPG), prognosis (IL-6, SAA4), or the grade of the glioma (IL-6, IL-8, ICAM-1, IGFBP-3, and COPG).

CONCLUSION

We report: 1) a novel molecular signature in human gliomas, based on cellular senescence, translating the concept of SAG to human cancer; 2) the senescence signature is composed of genes central to the pathogenesis of gliomas, defining a novel, aggressive subtype of glioma; and 3) these genes provide prognostic biomarkers, as well as targets, for drug discovery and immunotherapy.

Measurement of lens density using Scheimpflug imaging system as a screening test in the field of health examination for age-related cataract

PURPOSE

To assess Pentacam (Oculus, Wetzlar, Germany) Scheimpflug quantitative images in evaluating lens density and providing objective measurements to suggest optimal time of cataract surgery in the field of health examination.

METHODS

Two hundred and twenty-nine eyes with age-related cataract were enrolled. Lens density was measured using Pentacam. All Pentacam images were exported to ImageJ (NIH, Bethesda, Maryland, USA) for quantitative analysis. Average lens density (ALD) and nuclear lens density (NLD) were calculated. Lens density was also evaluated by built-in Pentacam Nucleus Staging (PNS) software. Slit-lamp microscopy was performed for cataract grading according to Lens Opacification Classification System III (LOCS III). The best-corrected visual acuity (BCVA) was measured. All measurements were compared between the cataract surgery and non-cataract surgery groups.

RESULTS

The measurements of Pentacam images significantly correlated with LOCS III for nuclear opalescence (NO) and nuclear colour (NC) grading (p<0.01). Pentacam ImageJ showed higher correlation than PNS. The mean NLD was most highly correlated with NO (r=0.8833) and NC (r=0.6815). The maximum ALD was most highly correlated with cortical opacity (r=0.5381). All Pentacam measurements of lens density and BCVA were significantly different between the cataract surgery and non-surgery groups (p<0.01). The optimised cut-off values to perform cataract surgery for mean NLD and maximum ALD were 26 and 74, respectively (p<0.01).

CONCLUSIONS

The Pentacam ImageJ method provided objective measurements to evaluate cataracts needing surgery. The method has the potential to be generally applied in the field of health examination and is effective in screening patients with cataract.

Arthroscopic débridement for primary osteoarthritis of the elbow: analysis of preoperative factors affecting outcome

BACKGROUND

The purposes of this study were to evaluate the clinical results of arthroscopic débridement and to identify preoperative factors that influence the outcome.

METHODS

Forty-three elbows with primary osteoarthritis in 43 patients treated with arthroscopic débridement were retrospectively evaluated. At a mean follow-up of 38 months (range, 18-77 months), the visual analog scale (VAS) score for pain, the arc of elbow motion, and the Mayo Elbow Performance Index (MEPI) score were assessed. The relationships between postoperative MEPI score and postoperative motion arc and preoperative factors including age, sex, involvement of the dominant arm, duration of symptoms, demand of elbow activity, VAS score, previous history of failed surgery, and arc of elbow motion were statistically evaluated.

RESULTS

The mean VAS score for pain, the mean arc of flexion-extension, and the mean MEPI score significantly improved after the operation (all P values < .001). Multivariate regression analysis revealed that among preoperative variables, arc of motion was found to be the only independent prognostic factor that affected both postoperative elbow function (P = .024) and final arc of motion (P < .001). The cutoff value of preoperative arc of motion for the final arc of motion was determined to be 80° (P < .001). Involvement of the dominant arm was found to be another independent factor that affected postoperative MEPI scores (P = .016).

CONCLUSIONS

Arthroscopic débridement for elbow osteoarthritis provides satisfactory pain relief, improvement of elbow motion, and good functional outcome. Based on the fact that preoperative motion arc is the independent factor that can predict clinical outcome, arthroscopic treatment is highly recommended for patients who have a motion arc of 80° or more as it yields reliable results.

Identifying cut points for biomarker defined subset effects in clinical trials with survival endpoints

The advancements in biotechnology and genetics lead to an increasing research interest in personalized medicine, where a patient's genetic profile or biological traits contribute to choosing the most effective treatment for the patient. The process starts with finding a specific biomarker among all possible candidates that can best predict the treatment effect. After a biomarker is chosen, identifying a cut point of the biomarker value that splits the patients into treatment effective and non-effective subgroups becomes an important scientific problem. Numerous methods have been proposed to validate the predictive marker and select the appropriate cut points either prospectively or retrospectively using clinical trial data. In trials with survival outcomes, the current practice applies an interaction testing procedure and chooses the cut point that minimizes the p-values for the tests. Such method assumes independence between the baseline hazard and biomarker value. In reality, however, this assumption is often violated, as the chosen biomarker might also be prognostic in addition to its predictive nature for treatment effect. In this paper we propose a block-wise estimation and a sequential testing approach to identify the cut point in biomarkers that can group the patients into subsets based on their distinct treatment outcomes without assuming independence between the biomarker and baseline hazard. Numerical results based on simulated survival data show that the proposed method could pinpoint accurately the cut points in biomarker values that separate the patient subpopulations into subgroups with distinctive treatment outcomes.

Age- and health-related quality of life after total hip replacement: decreasing gains in patients above 70 years of age

BACKGROUND

While age is a common confounder, its impact on health-related quality of life (HRQoL) after total hip replacement is uncertain. This could be due to improper statistical modeling of age in previous studies, such as treating age as a linear variable or by using age categories. We hypothesized that there is a non-linear association between age and HRQoL.

METHODS

We selected a nationwide cohort from the Swedish Hip Arthroplasty Register of patients operated with total hip replacements due to primary osteoarthritis between 2008 and 2010. For estimating HRQoL, we used the generic health outcome questionnaire EQ-5D of the EuroQol group that consits or 2 parts: the EQ-5D index and the EQ VAS estimates. Using linear regression, we modeled the EQ-5D index and the EQ VAS against age 1 year after surgery. Instead of using a straight line for age, we applied a method called restricted cubic splines that allows the line to bend in a controlled manner. Confounding was controlled by adjusting for preoperative HRQoL, sex, previous contralateral hip surgery, pain, and Charnley classification.

RESULTS

Complete data on 27,245 patients were available for analysis. Both the EQ-5D index and EQ VAS showed a non-linear relationship with age. They were fairly unaffected by age until the patients were in their late sixties, after which age had a negative effect.

INTERPRETATION

There is a non-linear relationship between age and HRQoL, with improvement decreasing in the elderly.

Surgical treatment of elbow stiffness caused by post-traumatic heterotopic ossification

BACKGROUND

Heterotopic ossification (HO) is considered as a common extrinsic cause of elbow stiffness. The purpose of this study was to show the results of surgical treatment for post-traumatic elbow stiffness caused by HO in a large, consecutive series of patients in a single unit.

METHODS

We retrospectively reviewed 77 surgically treated patients with post-traumatic elbow stiffness caused by HO. Final motion arc and Mayo Elbow Performance Index (MEPI) were assessed as final results. Univariable and multivariable analyses were done to determine which factors had an effect on the final motion arc.

RESULTS

The average arc of elbow motion increased from 45° preoperatively to 112°, with an improvement of 67° at the final follow-up evaluation. The mean MEPI score was 91.9. At the final evaluation, 65 patients (84.4%) obtained a total motion arc of ≥100°. Recurrent HO was observed in 16 patients postoperatively, and 6 underwent repeated surgical release. The time from the initial injury to surgical release with a cutoff value of 19 months was the only independent factor affecting the final range of motion (ROM) in multivariable median regression analysis. With the numbers studied, no significant association was found between the final ROM and other clinical variables except for the recurrence of HO (93° vs 117°).

CONCLUSIONS

From the results of our study, we can support the surgical treatment of elbow stiffness caused by post-traumatic HO regardless of preoperative ROM. However, recurrence of heterotopic bone and delay in surgery of more than 19 months are associated with less favorable results.

A systematic selection method for the development of cancer staging systems

The tumor-node-metastasis (TNM) staging system has been the anchor of cancer diagnosis, treatment, and prognosis for many years. For meaningful clinical use, an orderly, progressive condensation of the T and N categories into an overall staging system needs to be defined, usually with respect to a time-to-event outcome. This can be considered as a cutpoint selection problem for a censored response partitioned with respect to two ordered categorical covariates and their interaction. The aim is to select the best grouping of the TN categories. A novel bootstrap cutpoint/model selection method is proposed for this task by maximizing bootstrap estimates of the chosen statistical criteria. The criteria are based on prognostic ability including a landmark measure of the explained variation, the area under the receiver operating characteristic (ROC) curve, and a concordance probability generalized from Harrell's c-index. We illustrate the utility of our method by applying it to the staging of colorectal cancer.

An industry statistician's perspective on PHC drug development

In the past decade, the cost of drug development has increased significantly. The estimates vary widely but frequently quoted numbers are staggering-it takes 10-15 years and billions of dollars to bring a drug to patients. To a large extent this is due to many long, expensive and ultimately unsuccessful drug trials. While one approach to combat the low yield on investment could be to continue searching for new blockbusters, an alternative method would lead us to focus on testing new targeted treatments that have a strong underlying scientific rationale and are more likely to provide enhanced clinical benefit in population subsets defined by molecular diagnostics. Development of these new treatments, however, cannot follow the usual established path; new strategies and approaches are required for the co-development of novel therapeutics and the diagnostic. In this paper we will review, from the point of view of industry, the approaches to, and challenges of drug development strategies incorporating predictive biomarkers into clinical programs. We will outline the basic concepts behind co-development with predictive biomarkers and summarize the current regulatory paradigm. We will present guiding principles of personalized health care (PHC) development and review the statistical, strategic, regulatory and operational challenges that statisticians regularly encounter on development programs with a PHC component. Some practical recommendations for team statisticians involved in PHC drug development are included. The majority of the examples and recommendations are drawn from oncology but broader concepts apply across all therapeutic areas.

A maximally selected test of symmetry about zero

The problem of testing symmetry about zero has a long and rich history in the statistical literature. We introduce a new test that sequentially discards observations whose absolute value is below increasing thresholds defined by the data. McNemar's statistic is obtained at each threshold and the largest is used as the test statistic. We obtain the exact distribution of this maximally selected McNemar and provide tables of critical values and a program for computing p-values. Power is compared with the t-test, the Wilcoxon Signed Rank Test and the Sign Test. The new test, MM, is slightly less powerful than the t-test and Wilcoxon Signed Rank Test for symmetric normal distributions with nonzero medians and substantially more powerful than all three tests for asymmetric mixtures of normal random variables with or without zero medians. The motivation for this test derives from the need to appraise the safety profile of new medications. If pre and post safety measures are obtained, then under the null hypothesis, the variables are exchangeable and the distribution of their difference is symmetric about a zero median. Large pre-post differences are the major concern of a safety assessment. The discarded small observations are not particularly relevant to safety and can reduce power to detect important asymmetry. The new test was utilized on data from an on-road driving study performed to determine if a hypnotic, a drug used to promote sleep, has next day residual effects.

Semiparametric smoothing of discrete failure time data

An estimator of the hazard rate function from discrete failure time data is obtained by semiparametric smoothing of the (nonsmooth) maximum likelihood estimator, which is achieved by repeated multiplication of a Markov chain transition-type matrix. This matrix is constructed so as to have a given standard discrete parametric hazard rate model, termed the vehicle model, as its stationary hazard rate. As with the discrete density estimation case, the proposed estimator gives improved performance when the vehicle model is a good one and otherwise provides a nonparametric method comparable to the only purely nonparametric smoother discussed in the literature. The proposed semiparametric smoothing approach is then extended to hazard models with covariates and is illustrated by applications to simulated and real data sets.

Accuracy and cut-off point selection in three-class classification problems using a generalization of the Youden index

We study properties of the index J(3), defined as the accuracy, or the maximum correct classification, for a given three-class classification problem. Specifically, using J(3) one can assess the discrimination between the three distributions and obtain an optimal pair of cut-off points c(1)<c(2) in the sense that the sum of the correct classification proportions will be maximized. It also serves as the generalization of the Youden index in three-class problems. Parametric and non-parametric approaches for estimation and testing are considered and methods are applied to data from an MRS study on human immunodeficiency virus (HIV) patients.

MIBG scintigraphy for differentiating Parkinson's disease with autonomic dysfunction from Parkinsonism-predominant multiple system atrophy

Parkinson's disease (PD) with autonomic dysfunction is difficult to differentiate from Parkinsonism-predominant multiple system atrophy (MSA-p). This study aimed to analyze the validity of MIBG scintigraphy for PD with autonomic dysfunction and MSA-p. Thirty-nine patients (PD: 27 patients, MSA-p type: 12) and 12 age-matched controls were prospectively enrolled and underwent MIBG scintigraphy and autonomic function test (AFT). We separately calculated early and delayed heart-to-mediastinal (H/M) ratio and washout rates (WRs). AFT was composed of sympathetic skin reflex and parasympathetic tests based on heart rate variability. Abnormal AFT was observed in 17 (63%) of PD and 10 (83%) of MSA-p. On comparing PD with abnormal AFT with MSA-p, either the early or delayed H/M ratio in PD was not different from that in MSA-p (P > 0.05). Only the WR could differentiate PD with abnormal AFT from MSA-p (47.07 +/- 57.48 vs. 31.39 +/- 31.52, respectively) (P = 0.026). According to the results, WR may be more useful than the early and delayed H/M ratio to distinguish MSA-p from PD with abnormal AFT. Furthermore, the MIBG uptake did not reflect the disease duration or severity.

Correlation of arthroscopic repairability of large to massive rotator cuff tears with preoperative magnetic resonance imaging scans

PURPOSE

The purpose of this study was to determine whether there are preoperative magnetic resonance imaging (MRI) variables that could predict the repairability of large to massive rotator cuff tears (RCTs), especially in terms of distinguishing between complete repair and incomplete repair.

METHODS

Fifty-one consecutive patients who had large to massive RCTs were treated by arthroscopic repair with suture anchors. The primary repair was subclassified into 4 types. Types I and II were complete repairs with coverage of the lateral end of the greater tuberosity footprint (type I) or to the medial one half or less of the footprint (type II). Types III and IV were incomplete repairs with either small exposure of the humeral head (<10 mm) (type III) or moderate exposure of the head with repair of the force couple of the rotator cuff (type IV). Six preoperative MRI measurements (fatty degeneration index [FDI] in all planes, occupational grade, tangent sign, coronal oblique tear distance [COTD], sagittal oblique tear distance [SOTD], and coronal oblique thickness) that were reported in the previous literature were examined. These measurements were correlated with our classification of repair.

RESULTS

There were 28 large and 23 massive tears. Interobserver reproducibility was good to excellent. When we compared the completely and incompletely repaired groups, the FDI values for sagittal oblique sections of the supraspinatus and the infraspinatus and the FDI values for COTD and SOTD showed statistically significant differences. The cutoff values for SOTD and COTD were 32 mm and 31 mm, respectively. Regarding FDI, values greater than 3 on sagittal oblique sections of the supraspinatus and greater than 2 on sagittal oblique sections of the infraspinatus can be discouraging findings for complete repair.

CONCLUSIONS

On preoperative MRI of RCTs, FDI values of greater than 3 on sagittal oblique sections of the supraspinatus and greater than 2 on sagittal oblique sections of the infraspinatus with greater than 31 mm in COTD and 32 mm in SOTD can imply incomplete arthroscopic repair of the torn tendon or type III/IV repair.

LEVEL OF EVIDENCE

Level II, development of diagnostic criteria based on consecutive patients with universally applied gold standard.

Prolonged cold ischemic time is a risk factor for biliary strictures in duct-to-duct biliary reconstruction in living donor liver transplantation

BACKGROUND

Duct-to-duct (DD) anastomosis is an accepted procedure for biliary reconstruction in living donor liver transplantation (LDLT). However, biliary complication rates in LDLT recipients have been reported to be as high as 20% to 30% or more. In this study, we examined various potential risk factors for biliary stricture (BS) that occurs in the context of DD reconstruction in a single-active transplant center.

METHODS

Enrolled in this study were adults who underwent their first LDLT with DD reconstruction between August 2002 and May 2007 (n=283). BSs were defined as anastomotic strictures that required interventions or operative procedures to be corrected. We reviewed retrospectively the medical records of recipients, including medical history, surgical procedures, and progress, and analyzed risk factors of BS with the Kaplan-Meier method.

RESULTS

BS occurred in 58 of the 283 recipients (20.5%). The mean follow-up period was 24.4 months posttransplant (SD=16.5). The univariate analysis revealed that recipient age (P=0.032), bile duct size (P=0.003), biliary reconstruction surgeon (P=0.023), perfusion solution (P=0.001), cold ischemic time (CIT) (P<0.001), and biliary leakage history (P<0.001) were significant risk factors. In the multivariable analysis, CIT (P=0.001), biliary leakage history (P=0.002), bile duct size (P=0.021), and recipient age (P=0.036) were significant risk factors for BS. And, a CIT cutoff value of 71 min was calculated using the minimum P value approach with correction by the Miller and Siegmund method (P=0.0186).

CONCLUSIONS

In this study, prolonged CIT is identified as a risk factor for BS in DD biliary reconstruction in LDLT.

Polychotomization of continuous variables in regression models based on the overall C index

BACKGROUND

When developing multivariable regression models for diagnosis or prognosis, continuous independent variables can be categorized to make a prediction table instead of a prediction formula. Although many methods have been proposed to dichotomize prognostic variables, to date there has been no integrated method for polychotomization. The latter is necessary when dichotomization results in too much loss of information or when central values refer to normal states and more dispersed values refer to less preferable states, a situation that is not unusual in medical settings (e.g. body temperature, blood pressure). The goal of our study was to develop a theoretical and practical method for polychotomization.

METHODS

We used the overall discrimination index C, introduced by Harrel, as a measure of the predictive ability of an independent regressor variable and derived a method for polychotomization mathematically. Since the naïve application of our method, like some existing methods, gives rise to positive bias, we developed a parametric method that minimizes this bias and assessed its performance by the use of Monte Carlo simulation.

RESULTS

The overall C is closely related to the area under the ROC curve and the produced di(poly)chotomized variable's predictive performance is comparable to the original continuous variable. The simulation shows that the parametric method is essentially unbiased for both the estimates of performance and the cutoff points. Application of our method to the predictor variables of a previous study on rhabdomyolysis shows that it can be used to make probability profile tables that are applicable to the diagnosis or prognosis of individual patient status.

CONCLUSION

We propose a polychotomization (including dichotomization) method for independent continuous variables in regression models based on the overall discrimination index C and clarified its meaning mathematically. To avoid positive bias in application, we have proposed and evaluated a parametric method. The proposed method for polychotomizing continuous regressor variables performed well and can be used to create probability profile tables.

Maximally Selected Chi-Square Statistics and Binary Splits of Nominal Variables

We address the problem of maximally selected chi-square statistics in the case of a binary Y variable and a nominal X variable with several categories. The distribution of the maximally selected chi-square statistic has already been derived when the best cutpoint is chosen from a continuous or an ordinal X, but not when the best split is chosen from a nominal X. In this paper, we derive the exact distribution of the maximally selected chi-square statistic in this case using a combinatorial approach. Applications of the derived distribution to variable selection and hypothesis testing are discussed based on simulations. As an illustration, our method is applied to a birth data set.