A censored quantile regression approach for the analysis of time to event data

Application of Frailty Quantile Regression Model to Investigate of Factors Survival Time in Breast Cancer: A Multi-Center Study

Background

The prognostic factors of survival can be accurately identified using data from different health centers, but the structure of multi-center data is heterogeneous due to the treatment of patients in different centers or similar reasons. In survival analysis, the shared frailty model is a common way to analyze multi-center data that assumes all covariates have homogenous effects. We used a censored quantile regression model for clustered survival data to study the impact of prognostic factors on survival time.

Methods

This multi-center historical cohort study included 1785 participants with breast cancer from four different medical centers. A censored quantile regression model with a gamma distribution for the frailty term was used, and p-value less than 0.05 considered significant.

Results

The 10^th and 50^th percentiles (95% confidence interval) of survival time were 26.22 (23–28.77) and 235.07 (130–236.55) months, respectively. The effect of metastasis on the 10^th and 50^th percentiles of survival time was 20.67 and 69.73 months, respectively (all p-value < 0.05). In the examination of the tumor grade, the effect of grades 2 and 3 tumors compare with the grade 1 tumor on the 50^th percentile of survival time were 22.84 and 35.89 months, respectively (all p-value < 0.05). The frailty variance was significant, which confirmed that, there was significant variability between the centers.

Conclusions

This study confirmed the usefulness of a censored quantile regression model for cluster data in studying the impact of prognostic factors on survival time and the control effect of heterogeneity due to the treatment of patients in different centers.

Determining Prognostic Factors of Disease-Free Survival in Breast Cancer Using Censored Quantile Regression

Background

The analysis of disease-free survival and related factors leads to a better understanding of the patient's condition and recurrence-related characteristics and provides a basis for more appropriate treatment guidance. In this study, we aimed to investigate the role of prognostic factors on disease-free survival in breast cancer with a quantile regression model.

Methods

This retrospective study was conducted by reviewing data obtained from 2056 breast cancer patients. Age at diagnosis and education status, tumor size, lymph node ratio, tumor grade, estrogen receptor and progesterone receptor, type of surgery, use of radiotherapy, chemotherapy, and hormone therapy were the prognosis factors considered in this study. A quantile regression model was used to investigate prognostic factors of disease-free survival in breast cancer.

Results

Disease recurrence was verified in 251 (13.9%) women, and 39 (0.02%) women died before experience recurrence. The 10th percentile of disease-free survival for patients with the hormone therapy was 23.85 months greater than patients who did not receive this treatment (P value < .001). In the examination of the tumor size, the 10th and 20th percentiles of disease-free survival for patients with tumor size > 5 cm were 31.06 and 27 months less than patients with the tumor size < 2 cm, respectively (P value = .006 and .021, respectively). Compared with grade 1 tumors, the 10th and 20th percentiles of disease-free survival for patients with grade 3 tumors decreased 30.11 and 38.32 months, respectively (P value < .001 and .038, respectively). The 10th and 20th percentiles of disease-free survival decreased 28.16 and 45.32 months with a 1 unit increase in lymph node ratio, respectively (P value = .032 and .032, respectively).

Conclusions

Among the prognostic factors, tumor size, grade, and lymph node ratio showed a close relationship with disease-free survival in breast cancer. The findings indicated that developing public screening and educational programs through the health care system with more emphasis on low-educated women is needed among Iranian women.

The comparison of censored quantile regression methods in prognosis factors of breast cancer survival

The Cox proportional hazards model is a widely used statistical method for the censored data that model the hazard rate rather than survival time. To overcome complexity of interpreting hazard ratio, quantile regression was introduced for censored data with more straightforward interpretation. Different methods for analyzing censored data using quantile regression model, have been introduced. The quantile regression approach models the quantile function of failure time and investigates the covariate effects in different quantiles. In this model, the covariate effects can be changed for patients with different risk and is a flexible model for controlling the heterogeneity of covariate effects. We illustrated and compared five methods in quantile regression for right censored data included Portnoy, Wang and Wang, Bottai and Zhang, Yang and De Backer methods. The comparison was made through the use of these methods in modeling the survival time of breast cancer. According to the results of quantile regression models, tumor grade and stage of the disease were identified as significant factors affecting 20th percentile of survival time. In Bottai and Zhang method, 20th percentile of survival time for a case with higher unit of stage decreased about 14 months and 20th percentile of survival time for a case with higher grade decreased about 13 months. The quantile regression models acted the same to determine prognostic factors of breast cancer survival in most of the time. The estimated coefficients of five methods were close to each other for quantiles lower than 0.1 and they were different from quantiles upper than 0.1.

Predicting Recurrence in Endometrial Cancer Based on a Combination of Classical Parameters and Immunohistochemical Markers

Objective

The aim of this study was to establish a nomogram to predict the recurrence of endometrial cancer (EC) by immunohistochemical markers and clinicopathological parameters and to evaluate the discriminative power of this model.

Methods

The data of 473 patients with stages I–III endometrial cancer who had received primary surgical treatment between October 2013 and May 2018 were randomly split into two sets: a training cohort and a validation cohort at a predefined ratio of 7:3. Univariate and multivariate Cox regression analysis of screening prognostic factors were performed in the training cohort (n=332) to develop a nomogram model for EC-recurrence prediction, which was further evaluated in the validation cohort (n=141).

Results

Univariate analysis found that FIGO stage, histological type, histological grade, myometrial invasion, cervical stromal invasion, postoperative adjuvant treatment, and four immunohistochemical markers (Ki67, ER, PR, and p53) were associated with recurrence in EC. Multivariate analysis showed that FIGO stage, histological type, ER, and p53 were superior parameters to generate the nomogram model for recurrence prediction in EC. Recurrence-free survival was better predicted by the proposed nomogram, with a C-index value of 0.79 (95% CI 0.66–0.92) in the validation cohort.

Conclusion

This nomogram model involving immunohistochemical markers can better predict recurrence in FIGO stages I–III EC.

Statistical issues and methods in designing and analyzing survival studies

BACKGROUND

Cancer studies that are designed for early detection and screening, or used for identifying prognostic factors, or assessing treatment efficacy and health outcome are frequently assessed with survival or time-to-event outcomes. These studies typically require specific methods of data analysis. Appropriate statistical methods in the context of study design and objectives are required for obtaining reliable results and valid inference. Unfortunately, variable methods for the same study objectives and dubious reporting have been noticed in the survival analysis of oncology research. Applied researchers often face difficulties in selecting appropriate statistical methods due to the complex nature of cancer studies.

RECENT FINDINGS

In this report, we describe briefly major statistical issues along with related challenges in planning, designing, and analyzing of survival studies. For applied researchers, we provided flow charts for selecting appropriate statistical methods. Various available statistical procedures in common statistical packages for applying survival analysis were classified according to different objectives of the study. In addition, an illustration of the statistical analysis of some common types of time-to-event outcomes was shown with STATA codes.

CONCLUSIONS

We anticipate that this review article assists oncology researchers in understanding important statistical concepts involved in survival analysis and appropriately select the statistical approaches for survival analysis studies. Overall, the review may help in improving designing, conducting, analyzing, and reporting of data in survival studies.

Lasso regularization for left-censored Gaussian outcome and high-dimensional predictors

Background

Biological assays for the quantification of markers may suffer from a lack of sensitivity and thus from an analytical detection limit. This is the case of human immunodeficiency virus (HIV) viral load. Below this threshold the exact value is unknown and values are consequently left-censored. Statistical methods have been proposed to deal with left-censoring but few are adapted in the context of high-dimensional data.

Methods

We propose to reverse the Buckley-James least squares algorithm to handle left-censored data enhanced with a Lasso regularization to accommodate high-dimensional predictors. We present a Lasso-regularized Buckley-James least squares method with both non-parametric imputation using Kaplan-Meier and parametric imputation based on the Gaussian distribution, which is typically assumed for HIV viral load data after logarithmic transformation. Cross-validation for parameter-tuning is based on an appropriate loss function that takes into account the different contributions of censored and uncensored observations. We specify how these techniques can be easily implemented using available R packages. The Lasso-regularized Buckley-James least square method was compared to simple imputation strategies to predict the response to antiretroviral therapy measured by HIV viral load according to the HIV genotypic mutations. We used a dataset composed of several clinical trials and cohorts from the Forum for Collaborative HIV Research (HIV Med. 2008;7:27-40). The proposed methods were also assessed on simulated data mimicking the observed data.

Results

Approaches accounting for left-censoring outperformed simple imputation methods in a high-dimensional setting. The Gaussian Buckley-James method with cross-validation based on the appropriate loss function showed the lowest prediction error on simulated data and, using real data, the most valid results according to the current literature on HIV mutations.

Conclusions

The proposed approach deals with high-dimensional predictors and left-censored outcomes and has shown its interest for predicting HIV viral load according to HIV mutations.

Determining Overall Survival and Risk Factors in Esophageal Cancer Using Censored Quantile Regression

Background: Esophageal cancer is one of the leading causes of death worldwide. The global increasing rate of this type of cancer requires more attention. The purpose of this study was to determine the overall survival probability of esophageal cancer after diagnosis and to assess the potential risk factors in a population of Iranian patients. Materials and Methods: This retrospective cohort study was conducted on 127 cases with esophageal cancer in the Azarbaijan province, East of Iran. Participants in the study were diagnosed during 2009-2010 and were followed up for 5 years. The event was considered death due to esophageal cancer and those who survived until the end of the study were assumed as right censored. Censored quntile regression was fitted to find the overall survival of the patients using adjusted effects of variables and was compared with Cox regression model. Results: Patients’ mean and median survival time were 16.99 and 10.06 months respectively and 89% off cases died by the end of the study. The 1, 3, 6, 12 and 36-month survival probabilities were 0.95, 0.76, 0.60, 0.43, and 0.18. The median survival time for females and males without surgery were 21.79 and 14.76 month respectively. The accuracy of predictions were 0.99 and 0.74 for the censored quantile regression and Cox, respectively. Conclusion: We concluded that being male, not having surgery, longer wait time between having symptoms and being diagnosed, low socioeconomic status and old age to be significant risk factors in reducing the probability of survival from esophageal cancer.