A comparison of all-subset Cox and accelerated failure time models with Cox step-wise regression for node-positive breast cancer

Survival outcomes of breast cancer patients with recurrence after surgery according to period and subtype

PURPOSE

To analyze and compare the survival rates of recurrent breast cancer patients in Korea between two periods (period I: 2000-2007; period II: 2008-2013) and to identify the factors associated with outcomes and changes over time in the duration of survival after recurrence.

METHODS

We retrospectively analyzed 2,407 patients who had recurrent breast cancer with treated between January 2000 and December 2013 and divided them into two periods according to the year of recurrence. We reviewed the age at diagnosis, clinical manifestations, pathology report, surgical methods, types of adjuvant treatment, type of recurrence, and follow-up period.

RESULTS

The median follow-up was 30.6 months (range, 0-223.4) from the time of relapse, and the median survival time was 42.3 months. Survival after recurrence (SAR) significantly improved from 38.0 months in period I to 49.7 months in period II (p < 0.001). In the analysis performed according to the hormone receptor and HER2 status subtypes, all subtypes except the triple-negative subtype showed higher SAR in period II than period I. Age at diagnosis, tumor stage, and treatment after recurrence were significantly correlated with survival outcomes.

CONCLUSION

The survival outcomes of Korean patients with breast cancer after the first recurrence have improved in Korea. Such improvements may be attributed to advances in treatment.

Virtual Trials: Causally-validated treatment effects efficiently learned from an observational cancer registry

Randomized controlled trials (RCTs) offer a clear causal interpretation of treatment effects, but are inefficient in terms of information gain per patient. Moreover, because they are intended to test cohort-level effects, RCTs rarely provide information to support precision medicine, which strives to choose the best treatment for an individual patient. If causal information could be efficiently extracted from widely available real-world data, the rapidity of treatment validation could be increased, and its costs reduced. Moreover, inferences could be made across larger, more diverse patient populations. We created a "virtual trial" by fitting a multilevel Bayesian survival model to treatment and outcome records self-reported by 451 brain cancer patients. The model recovers group-level treatment effects comparable to RCTs representing over 3200 patients. The model additionally discovers the feature-treatment interactions needed to make individual-level predictions for precision medicine. By learning from heterogeneous real-world data, virtual trials can generate more causal estimates with fewer patients than RCTs, and they can do so without artificially limiting the patient population. This demonstrates the value of virtual trials as a complement to large randomized controlled trials, especially in highly heterogeneous or rare diseases.

Identification of 6 Hub Proteins and Protein Risk Signature of Colorectal Cancer

Background

Colorectal cancer (CRC) is the second most common cause of cancer death in the United States and the third most common cancer globally. The incidence of CRC tends to be younger, and we urgently need a reliable prognostic assessment strategy.

Methods

Protein expression profile and clinical information of 390 CRC patients/samples were downloaded from the TCPA and TCGA database, respectively. The Kaplan-Meier, Cox regression, and Pearson correlation analysis were applied in this study.

Results

Based on the TCPA and TCGA database, we screened 6 hub proteins and first constructed protein risk signature, all of which were significantly associated with CRC patients' overall survival (OS). The risk score was an independent prognostic factor and significantly related with the size of the tumor in situ (T). 6 hub proteins were differentially expressed in cancer and normal tissues and in different CRC stages, which were validated at the ONCOMINE database. Next, 40 coexpressed proteins of 6 hub proteins were extracted from the TCPA database. In the protein-protein interaction (PPI) network, HER1, HER2, and CTNNB1 were at the center. Function enrichment analysis illustrated that 46 proteins were mainly involved in the EGFR (HER1) tyrosine kinase inhibitor resistance pathway.

Conclusion

Studies indicated that 6 hub proteins might be considered as new targets for CRC therapies, and the protein risk signature can be used to predict the OS of CRC patients.

Survival analysis according to period and analysis of the factors influencing changes in survival in patients with recurrent breast cancer: a large-scale, single-center study

BACKGROUND

We performed this study to analyze changing survival patterns regarding recurrent breast cancer in Korea during the last 16 years (1993-2008). We also sought to determine factors possibly influencing outcomes and changes over time in the duration of survival after recurrence.

METHODS

We retrospectively analyzed 9671 patients with breast cancer treated between January 1993 and December 2008, comparing the periods 1993-2002 and 2003-2008.We retrospectively reviewed the collected database including the age at diagnosis, clinical manifestations, pathology report, surgical methods, types of adjuvant treatment modalities, type of recurrence, and follow-up period.

RESULTS

There were 1944 cases (20.1%) of recurrence. Median age at the first recurrence was 49.5 years (range 21.8-92.9). Median follow-up was 28.8 months (range 0-228.0) from the time of relapse. Median survival time was 35.0 months. Survival after recurrence (SAR) significantly improved in 2003-2008 compared to that in 1993-2002. Median survival time increased from 27.6 months in the period I to 42.3 months in period II (p = 0.001). Independent prognostic factors after the first recurrence by multivariate analysis were age at diagnosis, tumor size, nodal status, tumor grade, subtype, anti-hormonal therapy, time at diagnosis, and disease-free interval.

CONCLUSIONS

Outcomes of breast cancer have been improving recently, and survival time after the first recurrence of breast cancer has steadily increased in recent decades. We confirmed that advances in treatments have contributed to this improvement in survival after the first recurrence.

Modelling survival in hepatocellular carcinoma

OBJECTIVES

To identify the pattern of the risk of death over long-term in unresectable hepatocellular carcinoma by determining the appropriate distribution to extrapolate overall survival and to assess the role of the Weibull distribution as the standard survival model in oncology.

RESEARCH DESIGN AND METHODS

To select the appropriate distribution, three types of data sources have been analysed. Patient level data from two randomized controlled trials and published Kaplan-Meier curves from a systematic literature review provided short term follow-up data. They were supplemented with patient level data, with long-term follow-up from the Cancer Institute New South Wales, Australia. Published Kaplan-Meier curves were read in and a time-to-event dataset was created. Distributions were fitted to the data from the different sources separately. Their fit was assessed visually and compared using statistical criteria based on log-likelihood, the Akaike information criterion (AIC), and the Bayesian information criterion (BIC).

RESULTS

Based on both published and patient-level, and both short- and long-term follow-up data, the Weibull distribution, used very often in cost-effectiveness models in oncology, does not seem to offer a good fit in hepatocellular carcinoma among the different survival models. The best fitting distribution appears to be the lognormal, with loglogistic as the second-best fitting function. Results were consistent between the different sources of data.

CONCLUSIONS

In unresectable hepatocellular carcinoma, the Weibull model, which is often treated at the gold standard, does not appear to be appropriate based on different sources of data (two clinical trials, a retrospective database and published Kaplan-Meier curves). Lognormal distribution seems to be the most appropriate distribution for extrapolating overall survival.

Considerations in the statistical analysis of hemodialysis patient survival

The association of hemodialysis dosage with patient survival is controversial. Here, we tested the hypothesis that methods for survival analysis may influence conclusions regarding dialysis dosage and mortality. We analyzed all-cause mortality by proportional hazards and accelerated failure time regression models in a cohort of incident hemodialysis patients who were followed for 9 yr. Both models identified age, race, heart failure, physical functioning, and comorbidity scores as important predictors of patient survival. Using proportional hazards, there was no statistically significant association between mortality and Kt/V (hazard ratio 0.72; 95% confidence interval 0.45 to 1.14). In contrast, using accelerated failure time models, each 0.1-U increment of Kt/V improved adjusted median patient survival by 3.50% (95% confidence interval 0.20 to 7.08%). Proportional hazard models also yielded less accurate estimates for median survival. These findings are consistent with an additive damage model for the survival of patients who are on hemodialysis. In this conceptual model, the assumptions of the proportional hazard model are violated, leading to underestimation of the importance of dialysis dosage. These results suggest that future studies of dialysis adequacy should consider this additive damage model when selecting methods for survival analysis. Accelerated failure time models may be useful adjuncts to the Cox model when studying outcomes of dialysis patients.

Ascertaining prognosis for breast cancer in node-negative patients with innovative survival analysis

Clinical decisions to administer adjuvant systemic therapy to women with early breast cancer require knowledge about baseline prognosis, which is only assessable in the absence of such adjuvant treatment, which most patients currently do receive. The Cox model is the standard tool for assessing the effect of prognostic factors; however, there may be substantive differences in the estimated prognosis obtained by the Cox model rather than a log-normal model. For more than 50 years, clinical breast cancer data for cohorts of patients have supported the choice of a log-normal model. The prognostic impact of model type is examined here for a cohort of breast cancer patients, only 7% of whom received adjuvant systemic therapy. We quantitated prognosis utilizing Kaplan-Meier, Cox, and log-normal survival analyses for 415 consecutive T1-T3, M0, histologically node-negative patients who were operated on for primary breast cancer at Women's College Hospital between 1977 and 1986. Recurrence outside the breast for disease-free interval (DFI) and breast cancer death for disease-specific survival (DSS) were the events of interest. The patient follow-up for these investigations was 96% complete: a median 8 years for those surviving. Factors used in these investigations were age, weight, tumor size, histology, tumor grade, nuclear grade, lymphovascular invasion, estrogen receptor (ER), progesterone receptor (PR), combined ER/PR receptor, overexpression of neu oncoprotein, DNA ploidy, S-phase, and adjuvant therapy. In our study we found evidence against the Cox assumption of proportional hazards, which is not an assumption for the log-normal approach. We identified patients with greater than 96% and others with less than 40% DSS at 10 years. The difference in prognosis determined by using the Cox versus the log-normal model ranged for DFI from 1.2% to 8.1%, and for DSS from 0.4% to 6.2%; interestingly, the difference was more substantial for patients with a high risk of recurrence or death from breast cancer. Estimated prognoses may differ substantially by survival analysis model type, by amounts that might affect patient management, and we think that the log-normal model has a major advantage over the Cox model for survival analysis.

The effect of age, race, tumor size, tumor grade, and disease stage on invasive ductal breast cancer survival in the U.S. SEER database

PURPOSE

To examine the effect of patient and tumor characteristics on breast cancer survival as recorded in the U.S. National Cancer Institute's Surveillance, Epidemiology, and End Results (SEER) database from 1973 to 1998.

METHODS

A sample of 72,367 female cases from 1973 to 1998 aged 21-90 years with invasive ductal breast cancer were examined with Cox proportional hazards regression to determine the effect of age at diagnosis, race, tumor size, tumor grade, disease stage, and year of diagnosis on disease-specific survival.

RESULTS

Larger tumor size and higher tumor grade were found to have large negative effects on survival. Blacks had a 47 % greater risk of death than whites. Year of diagnosis had a positive effect, with a 15 % reduction in risk for each decade in the time period under study. The effects of patient age and disease stage violated the proportional hazards assumption, with distant disease having much poorer short-term survival than one would expect from a proportional hazards model, and younger age groups matching or even falling below the survival rate of the oldest group over time.

CONCLUSION

Tumor size, grade, race, and year of diagnosis all have significant constant effects on disease-specific survival in breast cancer, while the effects of age at diagnosis and disease stage have significant effects that vary over time.

Factors affecting distant disease-free survival for primary invasive breast cancer: use of a log-normal survival model

BACKGROUND

Invasive breast cancer is a frequently diagnosed disease that now comes with an ever expanding array of therapeutic management options. We assessed the effects of 20 prognostic factors in a multivariate context.

METHODS

We accrued clinical data for 156 consecutive patients with stage 1-3 primary invasive breast cancer who were diagnosed in 1989-1990 at the Henrietta Banting Breast Center, and followed to 1995. There is complete follow-up for 91% of patients (median follow-up of 4.9 years). The event of interest was distant recurrence (for distant disease-free survival, DFS). We used Cox and log-normal step-wise regression to assess the multivariate effects of the following factors on DFS: age, tumor size, nodal status, histology, tumor and nuclear grade, lymphovascular and perineural invasion (LVPI), ductal carcinoma-in-situ (DCIS) type, DCIS extent, DCIS at edge of tumor, ER and PgR, ERICA, adjuvant systemic therapy, ki67, S-phase, DNA index, neu oncogene, and pRb.

RESULTS

There was strong evidence against the Cox assumption of proportional hazards for nodal status, and nodal status was not in the Cox step-wise model. With step-wise log-normal regression, a large tumor size (P < .001), positive nodes (P = .002), high nuclear grade (P = .01), presence of LVPI (P = .03), and infiltrating duct carcinoma not otherwise specified (P = .05) were associated with a reduction in DFS.

CONCLUSIONS

For nodal status, there was strong evidence against the Cox assumption of proportional hazards, and it was not included in the Cox model although it was in the log-normal model. Only traditional factors were included in the step-wise models. Thus, this statistical management of prognostic markers in breast cancer appears to be very important.

Dose and dose intensity as determinants of outcome in the adjuvant treatment of breast cancer. The Cancer and Leukemia Group B

BACKGROUND

Both total dose and dose intensity of adjuvant chemotherapy are postulated to be important variables in the outcome for patients with operable breast cancer. The Cancer and Leukemia Group B study 8541 examined the effects of adjuvant treatment using conventional-range dose and dose intensity in female patients with stage II (axillary lymph node-positive) breast cancer.

METHODS

Within 6 weeks of surgery (radical mastectomy, modified radical mastectomy, or lumpectomy), 1550 patients with unilateral breast cancer were randomly assigned to one of three treatment arms: high-, moderate-, or low-dose intensity. The patients received cyclophosphamide, doxorubicin, and 5-fluorouracil on day 1 of each chemotherapy cycle, with 5-fluorouracil administration repeated on day 8. The high-dose arm had twice the dose intensity and twice the drug dose as the low-dose arm. The moderate-dose arm had two thirds the dose intensity as the high-dose arm but the same total drug dose. Disease-free survival and overall survival were primary end points of the study.

RESULTS

At a median follow-up of 9 years, disease-free survival and overall survival for patients on the moderate- and high-dose arms are superior to the corresponding survival measures for patients on the low-dose arm (two-sided P<.0001 and two-sided P = .004, respectively), with no difference in disease-free or overall survival between the moderate- and the high-dose arms. At 5 years, overall survival (average +/- standard error) is 79% +/- 2% for patients on the high-dose arm, 77% +/- 2% for the patients on the moderate-dose arm, and 72% +/- 2% for patients on the low-dose arm; disease-free survival is 66% +/- 2%, 61% +/- 2%, and 56% +/- 2%, respectively.

CONCLUSION

Within the conventional dose range for this chemotherapy regimen, a higher dose is associated with better disease-free survival and overall survival.

Competing causes of death for primary breast cancer

BACKGROUND

A patient's likelihood of dying from breast cancer or another cause can be assessed with competing risks analyses.

METHODS

Data for a cohort of 678 patients with primary invasive breast cancer accrued from 1971 to 1990, updated to 1995, included cause of death (e.g., breast cancer vs. other cause). We investigated the effects of age, tumor size, nodal status, ER, PgR, and adjuvant therapy (hormones, chemotherapy, radiotherapy) on type of death and time to death for patients of all ages and for those over the age of 65 years.

RESULTS

Although there were no significant univariate differences in breast cancer death rates by age group (P=0.94), more patients over the age of 65 years died from other causes (41/207 [20%] of those older than 65 years vs. 16/471 [3%] of those younger than 65 years; P <.001). In competing risks analyses, older age was associated with non-breast cancer death, whereas larger tumor size was associated with breast cancer death. PgR was positively, and nodal status negatively, associated with survival, regardless of type. In the older patient group, the competing risks analyses identified similar effects for age and tumor size; in addition, higher ER assay values were less likely to be associated with breast cancer death.

CONCLUSIONS

With increased lifespan, there will be more breast cancer cases in women older than 65 years; we have shown that women in this group have more non-breast cancer deaths. It becomes important, then, to delineate differential effects of prognostic factors on competing causes of death.

Survival analysis in public health research

This paper reviews the common statistical techniques employed to analyze survival data in public health research. Due to the presence of censoring, the data are not amenable to the usual method of analysis. The improvement in statistical computing and wide accessibility of personal computers led to the rapid development and popularity of nonparametric over parametric procedures. The former required less stringent conditions. But, if the assumptions for parametric methods hold, the resulting estimates have smaller standard errors and are easier to interpret. Nonparametric techniques include the Kaplan-Meier method for estimating the survival function and the Cox proportional hazards model to identify risk factors and to obtain adjusted risk ratios. In cases where the assumption of proportional hazards is not tenable, the data can be stratified and a model fitted with different baseline functions in each stratum. Parametric modeling such as the accelerated failure time model also may be used. Hazard functions for the exponential, Weibull, gamma, Gompertz, lognormal, and log-logistic distributions are described. Examples from published literature are given to illustrate the various methods. The paper is intended for public health professionals who are interested in survival data analysis.

An improved statistical approach: can it clarify the role of new prognostic factors for breast cancer?

Recently, there has been a proliferation of new biomarkers, some of which may lead to an improved prognostic index or may influence treatment selection. However, there are methodological and statistical issues that require attention in assessing the role and use of these prognostic factors. Between 1977 and 1986, 1097 primary breast cancer patients were accrued for multidisciplinary research at the Henrietta Banting Breast Centre, Women's College Hospital; follow-up to 1990 is complete for 96% of the patients. Data for these patients are used here to illustrate strategies: (1) for the comparison of results from diverse assessments of biomarkers; (2) for the improved comparability of inter-laboratory results; (3) for the examination of the results from monoclonal or polyclonal antibody assays for possible clinically relevant bimodality; (4) for good statistical resolution of overlapping distributions; (5) that involve the use of quantitative values for prognostic factors whenever possible; and (6) for improved multivariate analyses. Good data handling and analyses may enable more accurate and rapid assessment of new prognostic factors, thereby expediting and improving their clinical application.

Alternative multivariate modelling for time to local recurrence for breast cancer patients receiving a lumpectomy alone

Certain prognostic factors (patient and/or tumour characteristics) may be associated with low (or high) risk for local recurrence. Patients with these characteristics could be candidates for less (or more) adjuvant therapy or a less (or more) aggressive surgical approach. However, the assessment of many factors can be problematic with the standard multivariate technique-a Cox proportional hazards model and step-wise regression. We compared the results obtained when using a Cox model with those from four alternative models (exponential, Weibull, log logistic and log Normal) in step-wise and all subset regressions. Between 1977 and 1986, 293 primary invasive breast cancer patients were treated at the Henrietta Banting Breast Centre with a lumpectomy with or without an axillary dissection, and with no postoperative adjuvant therapy. The variables considered were age, lymph node status, tumour size, estrogen receptor (ER), progesterone receptor (PgR), histologic grade, nuclear grade, carcinoma in situ (CIS), amount of CIS, and presence of tumour emboli. With follow-up to 1991, nodal status was not found to be included in the step-wise Cox model, although it was in the step-wise exponential, Weibull and log Normal models, and in the best all subset models for all model types. The variables tumour emboli, ER, age, CIS and nodal status were consistently included in the best all subset regressions, regardless of model type. In the 1993 follow-up, the variables in the step-wise Cox model were tumour emboli, ER, age, CIS and nodal status. The multivariate consideration of all possible subsets of regression variables led to an earlier indication of the importance of nodal status, while the data strongly supported accelerated failure time models over the Cox model.

An investigation of cut-points for primary breast cancer oestrogen and progesterone receptor assays

Oestrogen and progesterone receptor (ER and PgR) assay values are frequently used in medical decision-making for breast cancer patients. We have proposed statistical standardization of receptor assay values to improve inter-laboratory comparability, and now report the use of standardized log units (SLU) to investigate the effects of ER and PgR cut-points on time to first recurrence outside the breast (DFS). Between 1980 and 1986, there were 678 primary breast cancer patients treated at the Henrietta Banting Breast Centre (HBBC). The effects of ER and PgR cut-points were examined with multivariate analyses considering the variables: age, tumour size, nodal status, weight and adjuvant treatment. We considered receptor assay cut-points ranging from - 1.0 to + 1.0 SLU (ER between 7 and 166 fmol/mg protein; PgR between 7 and 181 fmol/mg protein). PgR was included in the multivariate prognostic models more often than ER, although patients had a better prognosis with both larger ER and PgR values. There was no best cut-point for ER or PgR, and there was strong evidence that ER and PgR should be considered as continuous rather than dichotomous (negative, positive) variables. Patient prognosis should also be more comparable with SLU.

The Henrietta Banting Breast Centre database: a model for clinical research utilizing a hospital-based inception cohort

The cohort study design has been used successfully in clinical cancer research. Cohorts, however, are valuable only if they produce results which are valid and generalizable. Some hospital-based inception cohorts satisfy both these requirements and may thus be useful research tools. The development of one such hospital-based cohort, the Henrietta Banting Breast Centre database, is described. This cohort is composed of 1097 women diagnosed with primary breast cancer at Women's College Hospital, Toronto, from January 1977 through December 1986. Details of diagnostic procedures, pathology, treatment, dates and sites of recurrence, and date of death are available on 96% of women. By comparison with published series and with the Ontario Cancer Registry, we have demonstrated validity and generalizability. A major advantage is the ready availability of paraffin tissue blocks on virtually all cases, facilitating analyses of the prognostic importance of specific biologic variables and immunocytochemical hormone assays. Other completed studies and future uses of the cohort are described.

Host markers and prognosis in recurrent rectal carcinomas treated with radiotherapy

The value of blood tests as prognostic factors in patients with recurrent rectal carcinomas treated with radiotherapy was studied in one retrospective (n = 114, 1976-1984) and one prospective (n = 100, 1985-1989) group of patients. The retrospective group was used for validation of the results from the prospective group. In univariate survival analyses, 19 of totally 38 variables significantly correlated to the survival. Of 13 significant blood parameters, lactate dehydrogenase (LD), erythrocyte sedimentation rate (ESR), alpha 1-, alpha 2-globulin, fibrinogen, carcinoembryonic antigen (CEA), C-reactive protein (CRP), haptoglobin, granulocytosis and thrombocytosis were the most important ones (p < or = 0.01). In the multivariate analyses (Cox regression) of the prospective group, LD, alpha 1-globulin, diagnosed liver metastases and CEA were found to be significant predictors of survival. A prognostic index was derived from the prospective group including ESR, LD and relapse-free interval. This clearly separated the patients in the retrospective group into one low- and one high-risk group.

Prognostic factors: rationale and methods of analysis and integration

With the proliferation of potential prognostic factors for breast cancer, it is becoming increasingly more difficult for physicians and patients to integrate the information provided by these factors into a single accurate prediction of clinical outcome. Here we review Cox's proportional hazards model, recursive partitioning, correspondence analysis, and neural networks for their respective capabilities in analyzing censored survival data in the presence of multiple prognostic factors, and we present some clinical applications where these models have been used.