Optimal Cutpoint Estimation With Censored Data

Tumor-associated mononuclear cells in the tumor bed of triple-negative breast cancer associate with clinical outcomes in the post-neoadjuvant chemotherapy setting

PURPOSE

To evaluate the clinical role of tumor-associated macrophages, including foamy (FM) and hemosiderin-laden macrophages (HLM) in the tumor bed (TB) of triple-negative breast cancer (TNBC) post-neoadjuvant chemotherapy (NACT).

METHODS

We conducted a pathologic review of 129 women, diagnosed with TNBC between 2002 and 2016 at our institute. The residual cancer burden (RCB) was calculated. We estimated the percentage of tumor-infiltrating lymphocytes (TILs) in the core needle biopsy (CNB), and FM, HLM, and TILs (in TB) [the combined cells are designated as tumor-associated mononuclear cells (TAMNC)]. The information on patient demographics, chemotherapy regimen, recurrence-free survival (RFS), and overall survival (OS) was extracted from the medical records.

RESULTS

Pathologic complete response (pCR) was achieved in 34.1% of the women. TILs (10% increment in CNB) only were associated with pCR in the multivariable analysis [odds ratio 1.04 (1.02, 1.06) (p = 0.0003)]. Immune cells associated with better OS included TAMNC (≤ 30%) [hazard ratio (HR) 4.32 (1.93, 9.66) (p = 0.0004)], and FM (0%) [HR 2.30 (1.06, 4.98) (p = 0.036)]. While increased HLM (10% increment) was statistically significant with HR 0.93 and 95% CI (0.88 to 0.98) (p = 0.0061), using a cutoff of 0%, HLM (0%: negative vs. ≥ 1%: positive) achieved only borderline significance with HR 2.05 (0.98, 4.31) (p = 0.058). Similarly, these immune cells were also associated with better RFS: TAMNC (≤ 30%) [HR 4.57 (2.04, 10.21) (p = 0.0002)], FM (0%) [HR 2.80 (1.23, 6.35) (p = 0.014)], and HLM (0%) [HR 2.34 (1.07, 5.11) (p = 0.03)]. TILs (in TB) were not associated with any clinical outcomes.

CONCLUSIONS

Although TILs may play a role in the response to NACT, they may not be critical to the prognosis after NACT. Instead, FM and HLM may assume this role. More studies are warranted.

Time-dependent ROC curve estimation for interval-censored data

The receiver-operating characteristic (ROC) curve is the most popular graphical method for evaluating the classification accuracy of a diagnostic marker. In time-to-event studies, the subject's event status is time-dependent, and hence, time-dependent extensions of ROC curve have been proposed. However, in practice, the calculation of this curve is not straightforward due to the presence of censoring that may be of different types. Existing methods focus on the more standard and simple case of right-censoring and neglect the general case of mixed interval-censored data that may involve left-, right-, and interval-censored observations. In this context, we propose and study a new time-dependent ROC curve estimator. We also consider some summary measures (area under the ROC curve and Youden index) traditionally associated with ROC as well as the Youden-based cutoff estimation method. The proposed method uses available data very efficiently. To this end, the unknown status (positive or negative) of censored subjects are estimated from the data via the estimation of the conditional survival function given the marker. For that, we investigate both model-based and nonparametric approaches. We also provide variance estimates and confidence intervals using Bootstrap. A simulation study is conducted to investigate the finite sample behavior of the proposed methods and to compare their performance with a competitor. Globally, we observed better finite sample performances for the proposed estimators. Finally, we illustrate the methods using two data sets one from a hypobaric decompression sickness study and the other from an oral health study. The proposed methods are implemented in the R package cenROC.

The association between walking speed from short- and standard-distance tests with the risk of all-cause mortality among adults with radiographic knee osteoarthritis: data from three large United States cohort studies

OBJECTIVE

Adults with radiographic knee OA (rKOA) are at increased risk of mortality and walking difficulty may modify this relation. Little is known about specific aspects of walking difficulty that increase mortality risk. We investigated the association of walking speed (objective measure of walking difficulty) with mortality and examined the threshold that best discriminated this risk in adults with rKOA.

METHODS

Participants with rKOA from the Johnston County Osteoarthritis Project (JoCoOA, longitudinal population-based cohort), Osteoarthritis Initiative and Multicenter Osteoarthritis Study (OAI and MOST, cohorts of individuals with or at high risk of knee OA) were included. Baseline speed was measured via 2.4-meter (m) walk test (short-distance) in JoCoOA and 20-m walk test (standard-distance) in OAI and MOST. To examine the association of walking speed with mortality risk over 9 years, hazard ratios (HR) and 95% confidence intervals (CI) were calculated from Cox regression models adjusted for potential confounders. A Maximal Likelihood Ratio Chi-square Approach was utilized to identify an optimal threshold of walking speed predictive of mortality.

RESULTS

Deaths after 9 years of follow-up occurred in 23.3% (290/1244) of JoCoOA and 5.9% (249/4215) of OAI + MOST. Walking 0.2 m/s slower during short- and standard-distance walk tests was associated with 23% (aHR [95%CI]; 1.23 [1.10, 1.39]) and 25% (1.25 [1.09, 1.43]) higher mortality risk, respectively. Walking <0.5 m/s on short-distance and <1.2 m/s standard-distance walk tests, best discriminated those with and without mortality risk.

CONCLUSION

Slower walking speed measured via short- and standard-distance walk tests was associated with increased mortality risk in adults with rKOA.

Smoothed time-dependent receiver operating characteristic curve for right censored survival data

The prediction reliability is of primary concern in many clinical studies when the objective is to develop new predictive models or improve existing risk scores. In fact, before using a model in any clinical decision making, it is very important to check its ability to discriminate between subjects who are at risk of, for example, developing certain disease in a near future from those who will not. To that end, the time-dependent receiver operating characteristic (ROC) curve is the most commonly used method in practice. Several approaches have been proposed in the literature to estimate the ROC nonparametrically in the context of survival data. But, except one recent approach, all the existing methods provide a nonsmooth ROC estimator whereas, by definition, the ROC curve is smooth. In this article we propose and study a new nonparametric smooth ROC estimator based on a weighted kernel smoother. More precisely, our approach relies on a well-known kernel method used to estimate cumulative distribution functions of random variables with bounded supports. We derived some asymptotic properties for the proposed estimator. As bandwidth is the main parameter to be set, we present and study different methods to appropriately select one. A simulation study is conducted, under different scenarios, to prove the consistency of the proposed method and to compare its finite sample performance with a competitor. The results show that the proposed method performs better and appear to be quite robust to bandwidth choice. As for inference purposes, our results also reveal the good performances of a proposed nonparametric bootstrap procedure. Furthermore, we illustrate the method using a real data example.

Median-based incremental cost-effectiveness ratios with censored data

Cost-effectiveness is an essential part of treatment evaluation, in addition to effectiveness. In the cost-effectiveness analysis, a measure called the incremental cost-effectiveness ratio (ICER) is widely utilized, and the mean cost and the mean (quality-adjusted) life years have served as norms to summarize cost and effectiveness for a study population. Recently, the median-based ICER was proposed for complementary or sensitivity analysis purposes. In this article, we extend this method when some data are censored.

Optimal cut-point definition in biomarkers: the case of censored failure time outcome

BACKGROUND

Cut-point finding is a crucial step for clinical decision making when dealing with diagnostic (or prognostic) biomarkers. The extension of ROC-based cut-point finding methods to the case of censored failure time outcome is of interest when we are in the presence of a biomarker, measured at baseline, used to identify whether there will be the development, or not, of some disease condition within a given time point τ of clinical interest.

METHODS

Three widely used cut-point finding methods, namely the Youden index, the concordance probability and the point closest to-(0,1) corner in the ROC plane, are extended to the case of censored failure time outcome resorting to non-parametric estimators of the sensitivity and specificity that account for censoring. The performance of these methods in finding the optimal cut-point is compared under Normal and Gamma distributions of the biomarker (in subjects developing or not the disease condition). Normality ensures that estimators point theoretically to the same cut-point. Two motivating examples are provided in the paper.

RESULTS

The point closest-to-(0,1) corner approach has the best performance from simulations in terms of mean square error and relative bias.

CONCLUSIONS

We discuss the use of the Youden index or concordance probability associated to the cut-point identified through the closest-to-(0,1) corner approach to ease interpretability of the classification performance of the dichotomized biomarker. In addition, the achieved performance of the dichotomized biomarker classification associated to the estimated cut-point can be represented through a confidence interval of the point on the ROC curve.

Optimal survival time-related cut-point with censored data

In biomedical research and practice, continuous biomarkers are often used for diagnosis and prognosis, with a cut-point being established on the measurement to aid binary classification. When survival time is examined for the purposes of disease prognostication and is found to be related to the baseline measure of a biomarker, employing a single cut-point on the biomarker may not be very informative. Using survival time-dependent sensitivity and specificity, we extend a concordance probability-based objective function to select survival time-related cut-points. To estimate the objective function with censored survival data, we adopt a non-parametric procedure for time-dependent receiver operational characteristics curves, which uses nearest neighbor estimation techniques. In a simulation study, the proposed method, when used to select a cut-point to optimally predict survival at a given time within a specified range, yields satisfactory results. We apply the procedure to estimate survival time-dependent cut-point on the prognostic biomarker of serum bilirubin among patients with primary biliary cirrhosis.