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ESTROGEN RECEPTOR EXPRESSION ON BREAST CANCER PATIENTS’ SURVIVAL UNDER SHAPE RESTRICTED COX REGRESSION MODEL

ABSTRACT: For certain subtypes of breast cancer, study findings show that their level of estrogen receptor expression is associated with their risk of cancer death, and also suggests a non-linear effect on the hazard of death. A flexible form of the proportional hazards model, λ(t∣x, z) = λ(t) exp(zTβ)q(x), is desirable to facilitate a rich class of covariate effect on a survival outcome to provide meaningful insight, where the functional form of q(x) is not specified except for its shape. Prior biologic knowledge on the shape of the underlying distribution of the covariate effect in regression models can be used to enhance statistical inference. Despite recent progress, major challenges remain for the semiparametric shape-restricted inference due to lack of practical and efficient computational algorithms to accomplish non-convex optimization. We propose an alternative algorithm to maximize the full log-likelihood with two sets of parameters iteratively under monotone constraints. The first set consists of the non-parametric estimation of the monotone-restricted function q(x), while the second set includes estimating the baseline hazard function and other covariate coefficients. The iterative algorithm in conjunction with the pool-adjacent-violators algorithm makes the computation efficient and practical. The Jackknife resampling effectively reduces the estimator bias, when sample size is small. Simulations show that the proposed method can accurately capture the underlying shape of q(x), and outperforms the estimators when q(x) in the Cox model is mis-specified. We apply the method to model the effect of estrogen receptor on breast cancer patients’ survival.

SUBMITTER: Qin J

PROVIDER: S-EPMC8570133 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Project description:Early-stage estrogen receptor-positive (ER+) breast cancer (BCa) is the most common type of BCa in the United States. One critical question with these tumors is identifying which patients will receive added benefit from adjuvant chemotherapy. Nuclear pleomorphism (variance in nuclear shape and morphology) is an important constituent of breast grading schemes, and in ER+ cases, the grade is highly correlated with disease outcome. This study aimed to investigate whether quantitative computer-extracted image features of nuclear shape and orientation on digitized images of hematoxylin-stained and eosin-stained tissue of lymph node-negative (LN-), ER+ BCa could help stratify patients into discrete (<10 years short-term vs. >10 years long-term survival) outcome groups independent of standard clinical and pathological parameters. We considered a tissue microarray (TMA) cohort of 276 ER+, LN- patients comprising 150 patients with long-term and 126 patients with short-term overall survival, wherein 177 randomly chosen cases formed the modeling set, and 99 remaining cases the test set. Segmentation of individual nuclei was performed using multiresolution watershed; subsequently, 615 features relating to nuclear shape/texture and orientation disorder were extracted from each TMA spot. The Wilcoxon's rank-sum test identified the 15 most prognostic quantitative histomorphometric features within the modeling set. These features were then subsequently combined via a linear discriminant analysis classifier and evaluated on the test set to assign a probability of long-term vs. short-term disease-specific survival. In univariate survival analysis, patients identified by the image classifier as high risk had significantly poorer survival outcome: hazard ratio (95% confident interval) = 2.91(1.23-6.92), p = 0.02786. Multivariate analysis controlling for T-stage, histology grade, and nuclear grade showed the classifier to be independently predictive of poorer survival: hazard ratio (95% confident interval) = 3.17(0.33-30.46), p = 0.01039. Our results suggest that quantitative histomorphometric features of nuclear shape and orientation are strongly and independently predictive of patient survival in ER+, LN- BCa.

Dataset Information

ESTROGEN RECEPTOR EXPRESSION ON BREAST CANCER PATIENTS’ SURVIVAL UNDER SHAPE RESTRICTED COX REGRESSION MODEL

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