Prognostic factors and survival in metastatic breast cancer: A single institution experience

Background

The current retrospective study aims to identify some determinants of survival in metastatic breast cancer.

Methods

The study concerned 332 patients with synchronous (SM) or metachronous (MM) metastatic breast cancer treated between January 2000 and December 2007. Statistical comparison between subgroups of patients concerning survival was carried out employing log-rank test for the invariable analysis and Cox model for the multivariable analysis. Factors included: age group (≤50 years vs. >50; ≤70 years vs. >70; ≤35 years vs. >35), menopausal status, presentation of metastatic disease (SM vs. MM), disease free interval (DFI) (≤24 months vs. >24 months; ≤60 months vs. >60 months), performance status at diagnosis of metastatic disease (PS) (0–1 vs. >1), hormone receptors (HR), number of metastatic sites (1 site vs. >1), nature of the metastatic site (visceral vs. non visceral), first line therapy, surgery of the primary tumor (SPT), locoregional radiotherapy (LRRT) and use or not of bisphosphonates.

Results

Overall survival at 5 years was 12%. Positive prognostic factors in univariate analysis were: age ≤ 70 years, hormono-dependence of the tumor, good PS (PS 0–1), less than two metastatic sites, no visceral metastases, DFI ≥ 24 months, SPT or LRRT. In multivariate analysis, favorable independent prognostic factors included: good PS (PS 0–1), absence of visceral metastases (liver, lung, brain) and age ≤ 70 years.

Conclusion

Many of the prognostic factors in metastatic breast cancer found in our study are known in the literature but some of them, like the application of locoregional treatment (radiotherapy or surgery) and the use of bisphosphonates, need to be further investigated in randomized clinical trials.     

Confidence scores for prediction models

In medical statistics, many alternative strategies are available for building a prediction model based on training data. Prediction models are routinely compared by means of their prediction performance in independent validation data. If only one data set is available for training and validation, then rival strategies can still be compared based on repeated bootstraps of the same data. Often, however, the overall performance of rival strategies is similar and it is thus difficult to decide for one model. Here, we investigate the variability of the prediction models that results when the same modelling strategy is applied to different training sets. For each modelling strategy we estimate a confidence score based on the same repeated bootstraps. A new decomposition of the expected Brier score is obtained, as well as the estimates of population average confidence scores. The latter can be used to distinguish rival prediction models with similar prediction performances. Furthermore, on the subject level a confidence score may provide useful supplementary information for new patients who want to base a medical decision on predicted risk. The ideas are illustrated and discussed using data from cancer studies, also with high-dimensional predictor space.     

Reduced rank proportional hazards model for competing risks

Competing events concerning individual subjects are of interest in many medical studies. For example, leukemia-free patients surviving a bone marrow transplant are at risk of developing acute or chronic graft-versus-host disease, or they might develop infections. In this situation, competing risks models provide a natural framework to describe the disease. When incorporating covariates influencing the transition intensities, an obvious approach is to use Cox's proportional hazards model for each of the transitions separately. A practical problem then is how to deal with the abundance of regression parameters. Our objective is to describe the competing risks model in fewer parameters, both in order to avoid imprecise estimation in transitions with rare events and in order to facilitate interpretation of these estimates. Suppose that the regression parameters are gathered into a p x K matrix B, with p and K as the number of covariates and transitions, respectively. We propose the use of reduced rank models, where B is required to be of lower rank R, smaller than both p and K. One way to achieve this is to write B = AGamma(intercal) with A and Gamma matrices of dimensions p x R and K x R, respectively. We shall outline an algorithm to obtain estimates and their standard errors in a reduced rank proportional hazards model for competing risks and illustrate the approach on a competing risks model applied to 8966 leukemia patients from the European Group for Blood and Marrow Transplantation.     

89例喉鳞癌患者术后生存的cox模型多因素分析

目的：探讨影响喉癌手术后生存的相关危险因素。方法：回顾1997年1月-2006年12月在我科行喉癌手术治疗的89例患者,分析肿瘤因素、宿主因素及辅助治疗因素对术后生存的影响。结果：全组术后5年生存率70．7％（63／89）,肿瘤T分期、颈部淋巴结是否转移及手术切缘状态是影响喉癌手术预后的独立危险因素。对于进展期喉癌,如适应症选择合理,行全喉切除及根治性喉部分切除预后无统计学差异。结论：早期诊断并选择合理的术式,尤其一些保留或重建喉功能的术式加合理的颈淋巴结清扫,同时确保手术安全切缘是提高喉癌术后肿瘤和喉功能效果的关键。     

Efron-type measures of prediction error for survival analysis

Estimates of the prediction error play an important role in the development of statistical methods and models, and in their applications. We adapt the resampling tools of Efron and Tibshirani (1997, Journal of the American Statistical Association92, 548-560) to survival analysis with right-censored event times. We find that flexible rules, like artificial neural nets, classification and regression trees, or regression splines can be assessed, and compared to less flexible rules in the same data where they are developed. The methods are illustrated with data from a breast cancer trial.     

89例喉鳞癌患者术后生存的COX模型多因素分析

目的:探讨影响喉癌手术后生存的相关危险因素。方法:回顾1997年1月-2006年12月在我科行喉癌手术治疗的89例患者,分析肿瘤因素、宿主因素及辅助治疗因素对术后生存的影响。结果:全组术后5年生存率70.7%(63/89),肿瘤T分期、颈部淋巴结是否转移及手术切缘状态是影响喉癌手术预后的独立危险因素。对于进展期喉癌,如适应症选择合理,行全喉切除及根治性喉部分切除预后无统计学差异。结论:早期诊断并选择合理的术式,尤其一些保留或重建喉功能的术式加合理的颈淋巴结清扫,同时确保手术安全切缘是提高喉癌术后肿瘤和喉功能效果的关键。     

A semi-Markov model based on generalized Weibull distribution with an illustration for HIV disease

Multi-state stochastic models are useful tools for studying complex dynamics such as chronic diseases. Semi-Markov models explicitly define distributions of waiting times, giving an extension of continuous time and homogeneous Markov models based implicitly on exponential distributions. This paper develops a parametric model adapted to complex medical processes. (i) We introduced a hazard function of waiting times with a U or inverse U shape. (ii) These distributions were specifically selected for each transition. (iii) The vector of covariates was also selected for each transition. We applied this method to the evolution of HIV infected patients. We used a sample of 1244 patients followed up at the hospital in Nice, France.     

A stochastic model for a progressive chronic disease

For many progressive chronic diseases, there exist useful prognostic indicators for the course of the disease and the survival of the patient. The evolution of such an indicator is modelled as a monotone transformation of a pure birth process with killing. Explicit formulas are derived for the probability distribution of this process at an arbitrary time, the distribution of the first-passage times, the joint distribution of the survival time and the maximum of the process, and the marginals of this joint distribution. In two examples, the general formulas are evaluated in closed form.     

A microscale model for prediction of breast cancer cell damage during cryosurgery

The morphology of cancerous breast tissue is characterized by tightly packed groups of small malignant cells, as found in most duct cell carcinoma. This special structure affects the osmotic responses of the cells to freezing and hence their probability of damage from cellular dehydration or intracellular ice formation. A mathematical model has been developed to study the microscale damage to these breast cancer cells during cryosurgery by accounting for their special structure. The model is based on a spherical unit comprised of an extracellular region that surrounds several layers of cancer cells, as experimentally observed of breast duct cell carcinoma by other researchers. Temperature transients in the breast cancer undergoing cryosurgery are calculated numerically using the Pennes equation. When subjected to various thermal histories, both cellular dehydration and intracellular ice formation in the unit structure are examined by considering the cell-to-cell contact and water transport at the microscale level. It is found that the cells in the inner layers hardly dehydrated while those in the outermost layer do greatly. The results help interpret the previously observed experimental phenomena that breast cancer tissues exhibit intracellular ice formation even at a slow cooling rate of -3 degrees C/min. In the attempt to better define an optimal procedure for breast cancer cryosurgery, various freezing protocols are simulated. The constant heat flux protocol induces greater cellular dehydration and higher intracellular ice formation probability simultaneously compared to the other protocols studied.     

A prediction model for parasitic gastro-enteritis in lambs

Paton G., Thomas R. J. and Waller P. J. 1984. A prediction model for parasitic gastroenteritis in lambs. International Journal for Parasitology14: 439–445. The parasite Ostertagia circumcincta is a major cause of parasitic gastro-enteritis in lambs in temperate countries. A prediction model is described, based on a mathematical representation of the external and internal stages of the life-cycle.The model is used to predict the numbers of infective larvae on a permanent experimental paddock grazed by ewes and lambs in 1973 and 1974. The “moisture status” of the surface layer of the pasture was found to be of fundamental importance for the successful prediction of the development and survival of the pre-infective larval stages. For the years studied the contribution to the summer wave of infection by lamb derived larvae was particularly significant.     

Survival ensembles

We propose a unified and flexible framework for ensemble learning in the presence of censoring. For right-censored data, we introduce a random forest algorithm and a generic gradient boosting algorithm for the construction of prognostic and diagnostic models. The methodology is utilized for predicting the survival time of patients suffering from acute myeloid leukemia based on clinical and genetic covariates. Furthermore, we compare the diagnostic capabilities of the proposed censored data random forest and boosting methods, applied to the recurrence-free survival time of node-positive breast cancer patients, with previously published findings.     

Risk factors for breast cancer in the breast cancer risk model study of Guam and Saipan

BackgroundChamorro Pacific Islanders in the Mariana Islands have breast cancer incidence rates similar to, but mortality rates higher than, those of U.S. women. As breast cancer risk factors of women of the Mariana Islands may be unique because of ethnic and cultural differences, we studied established and suspected risk factors for breast cancer in this unstudied population.MethodsFrom 2010–2013, we conducted retrospective case-control study of female breast cancer (104 cases and 185 controls) among women in the Mariana Islands. Odds ratios (ORs) and 95% confidence intervals (CIs) were calculated for each of various lifestyle-related factors from logistic regression of breast cancer, in all women and in pre- and postmenopausal women separately. Tests for interaction of risk factors with ethnicity were based on the Wald statistics for cross-product terms.ResultsOf the medical and reproductive factors considered — age at menarche, breastfeeding, number of live births, age at first live birth, hormone use, and menopause — only age at first live birth was confirmed. Age at first live birth, among parous women, was higher among cases (mean 24.9 years) than controls (mean 23.2 years); with increased breast cancer risk (OR = 2.53; 95% CI, 1.04–6.19 for age ≥ 30y compared to <20y, P for trend = 0.01). Of the lifestyle factors —body mass index, waist circumference, physical activity, alcohol and betel-nut intake, and education — only waist circumference (OR = 1.65; 95% CI 0.87–3.14 for the highest tertile group compared to the lowest, P for trend = 0.04) was significantly associated with breast cancer risk and only in Filipino women. The association with many other established risk factors, such as BMI, hormone use and physical activity, were in the expected direction but were not significant. Associations for family history of breast cancer and alcohol intake were not evidentConclusionsThe results provide a basis for cancer prevention guidance for women in the Mariana Islands.     

Estimating Completeness in Cancer Registries – Comparing Capture‐Recapture Methods in a Simulation Study

Completeness of registration is one of the quality indicators usually reported by cancer registries. This allows researchers to assess how useful and representative the data is. Several methods have been suggested to estimate completeness. In this paper a multi‐state model for the process of cancer diagnosis and treatment is presented. In principle, every contact with a doctor during diagnosis, treatment, and aftercare can give rise to a cancer registry notification with a certain probability. Therefore the states included in the model are “incident tumour” and “death” but also contacts with doctors such as consultation of a general practitioner or specialised doctor, diagnostic procedures, therapeutic interventions, and aftercare. In this model transitions between states and possible notifications to a cancer registry after entering a state are simulated. Transition intensities are derived and used in simulation. Several capture‐recapture methods have been applied to the simulated data. Simulated “true” numbers of new cases and simulated numbers of registrations are both available. This allows to assess the validity of the completeness estimates and to compare the relative merits of the methods. In the scenarios investigated here, all capture‐recapture estimators tended to underestimate completeness. While a modified DCN method and one type of log‐linear model yielded quite reasonable estimates other methods exhibited large variability or grossly underestimated completeness. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A model for the prediction of Oncomelania hupensis in the lake and marshland regions, China

A model has been developed for predicting the density of Oncomelania hupensis, the intermediate host snail of Schistosoma japonicum. The model takes into account different environmental factors, including elevation, air and soil temperature, type of vegetation, mean height of preponderant vegetation and soil humidity. Deviance and Akaike information criteria were used to determine the best model fits. Model diagnostics and internal and external validations of model efficiency were also performed. From the final prediction model, two important results emerge. First, air temperature should be used with care to study the distribution of O. hupensis and to predict its potential survival because the impact is indirect, and it is weaker and more unstable than soil temperature. Second, the more important environmental factor for O. hupensis prediction at the microscale is soil humidity, but the more important macroscale environmental factor is soil temperature. This finding might help in selecting different environmental features for studying O. hupensis at different spatial scales. Our model is promising for predicting the density of O. hupensis, and hence can provide more objective information about snail dispersal, which might eventually replace the tedious and imprecise field work for annual surveillance of O. hupensis.     

Homological radiomics analysis for prognostic prediction in lung cancer patients

PurposeThis study explored a novel homological analysis method for prognostic prediction in lung cancer patients.Materials and methodsThe potential of homology-based radiomic features (HFs) was investigated by comparing HFs to conventional wavelet-based radiomic features (WFs) and combined radiomic features consisting of HFs and WFs (HWFs), using training (n = 135) and validation (n = 70) datasets, and Kaplan–Meier analysis. A total of 13,824 HFs were derived through homology-based texture analysis using Betti numbers, which represent the topologically invariant morphological characteristics of lung cancer. The prognostic potential of HFs was evaluated using statistically significant differences (p-values, log-rank test) to compare the survival curves of high- and low-risk patients. Those patients were stratified into high- and low-risk groups using the medians of the radiomic scores of signatures constructed with an elastic-net-regularized Cox proportional hazard model. Furthermore, deep learning (DL) based on AlexNet was utilized to compare HFs by stratifying patients into the two groups using a network that was pre-trained with over one million natural images from an ImageNet database.ResultsFor the training dataset, the p-values between the two survival curves were 6.7 × 10⁻⁶ (HF), 5.9 × 10⁻³ (WF), 7.4 × 10⁻⁶ (HWF), and 1.1 × 10⁻³ (DL). The p-values for the validation dataset were 3.4 × 10⁻⁵ (HF), 6.7 × 10⁻¹ (WF), 1.7 × 10⁻⁷ (HWF), and 1.2 × 10⁻¹ (DL).ConclusionThis study demonstrates the excellent potential of HFs for prognostic prediction in lung cancer patients.