Non-parametric comparison of relative versus cause-specific survival in Surveillance, Epidemiology and End Results (SEER) programme breast cancer patients.

Cancer-related mortality can be measured by two dissimilar methods: cause-specific survival (based on mortality attributed to a specific cause), and relative survival (based on mortality relative to a matched cohort). We used both methods to determine actuarial survival in a population of 119,502 breast cancer patients from the Surveillance, Epidemiology and End Results (SEER) programme data set, with 20 years of follow-up. The population was divided into four strata by patient age and tumour stage. In all strata, there was only minimal deviation between the two survival methods. Of particular interest was the cause-specific treatment of patients recorded as dead of unknown cause, i.e. those deaths that could not be attributed with certainty to either 'breast cancer' or to 'other causes'. Findings suggest that the most reliable results may be obtained by apportioning these deaths between 'dead of cause' and 'withdrawn at the time of death'. This apportionment is based on the relative number of deaths attributed to 'breast cancer' versus 'other causes'.

Parametric cure models of relative and cause-specific survival for grouped survival times.

With parametric cure models, we can express survival parameters (e.g. cured fraction, location and scale parameters) as functions of covariates. These models can measure survival from a specific disease process, either by examining deaths due to the cause under study (cause-specific survival), or by comparing all deaths to those in a matched control population (relative survival). We present a binomial maximum likelihood algorithm to be used for actuarial data, where follow-up times are grouped into specific intervals. Our algorithm provides simultaneous maximum likelihood estimates for all the parameters of a cure model and can be used for cause-specific or relative survival analysis with a variety of survival distributions. Current software does not provide the flexibility of this unified approach.

Infiltrating ductal carcinoma of the breast: the survival impact of race.

PURPOSE: Breast cancer has a poorer prognosis among black women than among white women. This review was conducted to determine whether this disparity reflects the direct impact of race on likelihood of cure or on time to death from breast cancer or stems from the interaction of race with tumor stage and patient age. PATIENTS AND METHODS: We analyzed data from 115,838 patients with localized (node-negative) and regionally metastatic (node-positive) breast cancer from the Surveillance, Epidemiology, and End-Results (SEER) Program of the National Cancer Institute. Parametric analysis was used to determine the independent prognostic value of age, stage, and race. Linear regression and distribution analyses were also used to examine the interaction of these covariates. RESULTS: The prevalence of regionally metastatic disease, relative to localized disease, declined with increased age among white patients and those classified as "other," but remained relatively constant among black patients. Parametric analysis showed a smaller cured fraction and shorter time to death when patients with regional disease were compared with those with localized disease. A similar disparity was found when black patients were compared with those classified as white or other. CONCLUSION: Age and race have a significant association with tumor stage. In addition, our data show that race has an independent impact on the clinical course of breast cancer and diminishes both the likelihood of cure and time to death among uncured patients.

End points in the analysis of breast cancer survival: relapse versus death from tumor.

BACKGROUND: To determine whether relapse and death from tumor are comparable as survival end points for assessing therapeutic efficacy, five prospective, randomized clinical trials of adjuvant therapy for stage II breast cancer were analyzed. One thousand eight hundred ninety patients were combined from five clinical groups into a single group for analysis. METHODS: Actuarial and parametric survival methods were used to generate three estimates for the likelihood of cure (LOC): (1) for all patients, with relapse as the end point to survival (LOCR); (2) for all patients, with death from tumor as the end point (LOCD); and (3) for patients with relapse only with death from tumor as the end point (LOCRD). Linear regression analysis was used to compare time to relapse for each patient with time from relapse to death. RESULTS: Estimates of LOCR ranged from 33.5% to 38.4%, estimates of LOCD ranged from 36.3% to 44.2%, and estimates of LOCRD ranged from 0% to 6%. Thus LOCR and LOCD are approximately equal for these patients. On the other hand, time to relapse correlated poorly with time from relapse to death (r2 = 0.005). CONCLUSIONS: If therapy affects LOC, relapse and death should ultimately lead to the same conclusion with respect to therapeutic efficacy, because both end points lead to essentially the same LOC. If therapy affects time to relapse, however, these two end points may ultimately lead to different conclusions, because time to relapse correlates poorly with time from relapse to death.

Improvement in the prognosis of breast cancer from 1965 to 1984.

PURPOSE: The prognosis of breast cancer has improved over the past three decades. It is uncertain, however, whether this improvement results from an increase in the cure rate, extension of the life span of uncured patients, or some combination. METHODS: From the Connecticut Tumor Registry, we obtained data on 25,091 patients with localized (node-negative) and regionally metastatic (node-positive) breast cancer who were diagnosed over the two decades between 1965 and 1984, with follow-up through 1993. The data for these patients were analyzed using a variety of parametric models to quantitate likelihood of cure and median survival time among uncured patients. These models incorporate the assumption that time to death from breast cancer follows a specific distribution. RESULTS: For patients with node-negative disease, parametric analysis revealed no significant difference in cured-fraction or median survival time over the two decades studied. For patients with node-positive disease, however, a significant increase in median survival time (P < .001) was found during the second decade (1970 to 1979). There was also a trend toward a higher cured-fraction over time, but this was not statistically significant. CONCLUSION: This study confirms that patients with node-positive disease had an improved prognosis over the two decades studied. Parametric analysis suggests that this improvement reflects primarily an increase in the median survival time for uncured patients, although there is a trend toward an increase in the likelihood of cure.

Comparison of parametric and non-parametric survival methods using simulated clinical data.

We derived three parametric survival models (the log-normal, log logit, and Weibull) from the clinical data of chemotherapy trials for stage II breast cancer. We then used these models to generate simulated survival data, which we analysed using both parametric (log-normal) and non-parametric (logrank, Gray-Tsiatis and Laska-Meisner) methods. With limited follow-up (5 years), the non-parametric tests had greater power than the log-normal model. This advantage diminished, however, with extended follow-up (15 years). Furthermore, only the log-normal model could distinguish reliably a survival advantage due to an increase in cured fraction from an advantage due to an increase in time to failure.

Ras oncogene-transformed and nontransformed cell populations are each heterogeneous but respond differently to the chemotherapeutic drug cytosine arabinoside (Ara-C).

In order to determine whether the growth of ras oncogene-transformed cells and nontransformed cells was inhibited differently by the chemotherapuetic drug cytosine arabinoside (Ara-C) their growth was analyzed by a novel colony-based assay that is sensitive and appropriate for heterogeneous cell populations. Colonies of nontransformed NIH3T3 cells, or ras oncogene-transformed NIH(ras) cells, were grown in the absence of drug and then divided into subclones. Subclones were allowed to continue to grow in the absence or presence of drug. Growth inhibition was determined by comparing the growth of drug-treated subclones. Colonies of nontransformed cells grown in the absence of the drug displayed a large variation in growth, and when grown in the presence of the drug displayed a large variation in growth inhibition. Colonies of transformed cells also displayed a large variation in the absence and presence of the drug. For each cell line, related subclones were more similar to each other than to unrelated subclones, implying inheritance of growth rates and drug response. For NIH3T3 cells, the growth of subclones in the presence of drug was highly correlated with the growth of related subclones in the absence of drug. However, for NIH3T3(ras) cells the growth of subclones in the presence of drug was not correlated with the growth of related subclones in the absence of drug. Therefore, ras oncogene-transformed and nontransformed cell populations differ in their response to Ara-C.

The impact of stage and histology on the long-term clinical course of 163,808 patients with breast carcinoma.

BACKGROUND: Stage and histologic type have a significant impact on the long term clinical course of breast carcinoma. Clinical course is governed by two components: likelihood of cure and medial tumor-related survival time among uncured patients. Estimates of these components can be derived only by using survival models that incorporate cured fraction as a specific parameter. METHODS: The prognostic value of stage and histologic type was determined for 163,808 patients with breast carcinoma using the log normal and log logit cure-based survival models. Follow-up ranged from 1 month to 19 years and was obtained from the SEER Program. RESULTS: In approximate terms, ductal carcinoma was diagnosed in 70% of the patients, with estimate cured fractions of 2/3 and 1/3 for local and regional disease, respectively. Estimates of medial survival times for uncured patients were 10 and 5 years. Findings were similar for patients with tumor of miscellaneous histologic types. For patients with medullary carcinoma were 82% and 50%, with median survival times of 6 and 4 years. For patients with mucinous, lobular, and ductolobular carcinomas, parametric analysis gave inconsistent estimates of cured fraction, but findings suggested unusually long tumor-related survival times. CONCLUSIONS: Cured-based parametric survival models offer valuable insight into the impact of stage and histology on the clinical course of breast cancer.

Proliferative rate by S-phase measurement may affect cure of breast carcinoma.

BACKGROUND: Standard, nonparametric statistical methods measure the interaction of covariates with survival rate or relative risk. Conversely, parametric methods measure the interaction of covariates with the two cardinal features of malignant potential: the likelihood of cure and the median time to relapse among uncured patients. METHODS: The authors performed parametric analysis on data from 810 patients with breast cancer using relapse as the survival end point. Prognostic covariates included lymph node status, tumor size, patient age, nuclear size, S-phase by thymidine or bromodeoxy-uridine labeling, and type of adjuvant therapy (chemotherapy, radiation, or hormone therapy). Also included was the cross-product term (labeling index X chemotherapy). RESULTS: Multivariate analysis revealed that: likelihood of cure was associated positively with labeling index X chemotherapy and associated negatively with lymph node status, tumor size, and patient age; and time to relapse was associated negatively with node status, nuclear size, and labeling index. CONCLUSION: The associations of labeling index and chemotherapy with the clinical course suggest that rapidly dividing tumors have a high likelihood of cure, especially with adjuvant chemotherapy, but those not cured may have early relapse.

Choroidal-ciliary body melanoma. A multivariate survival analysis of tumor location.

BACKGROUND: Posterior uveal melanomas with ciliary body involvement have greater mortality when compared with choroidal melanomas. This study was conducted to determine if this association is due to an independent effect or to correlations with other parameters. METHODS: From the 4335 cases of uveal melanoma with follow-up data in the Registry of Ophthalmic Pathology, 664 were selected; therefore, approximately two thirds of the patients died of metastatic melanoma. Ciliary body involvement was determined by the location of the anterior tumor margin. Kaplan-Meier survival, Cox regression, and Gamel-Boag log-normal regression analyses were performed. Covariables included ciliary body involvement, largest tumor dimension, mean diameter of the largest ten nucleoli, and modified Callender classification. RESULTS: Kaplan-Meier and univariate Cox analyses indicated a significant association between ciliary body involvement and tumor-related death but when included in a multivariate Cox model, ciliary body involvement was not statistically significant. Similarly, when ciliary body involvement was included in a multivariate Gamel-Boag model, ciliary body involvement was not statistically significant. Melanomas that involve the ciliary body were more likely to be larger (Student's t = 10.5; P = 10(-6)), contain larger nucleoli (Student's t = 2.43; P = 0.015), and be of mixed cell type (chi-square = 17.2; P = 3 x 10(-5)). CONCLUSIONS: Ciliary body involvement is associated with tumor-related mortality but this association is primarily due to ciliary body tumors being larger with more malignant cytology.

Parametric survival analysis of adjuvant therapy for stage II breast cancer.

BACKGROUND: Standard, nonparametric statistical methods estimate only the impact of therapy on survival rate up to a selected follow-up interval. In contrast, parametric methods can estimate the impact of treatment on the two cardinal parameters of malignancy: likelihood of cure and recurrence free survival time among uncured patients. METHODS: The authors screened a total of six parametric survival models. Three of these, including the log normal model, were applied to survival data from five clinical trials of adjuvant therapy for Stage II breast cancer. For comparison, the log rank test, a standard nonparametric method, was also applied to the same data. RESULTS: Both parametric and nonparametric methods identified a significant therapeutic in three of the five trials. In only one of these three trials, however, did parametric analysis identify a significant difference in the likelihood of cure between treatment groups. In the remaining two trials, a significant difference was found in recurrence free survival time among uncured patients. The three parametric survival models gave similar results. CONCLUSION: These findings suggest that parametric analysis may warrant further study as a method for measuring the long term clinical impact of adjuvant therapy on Stage II breast cancer.

A stable, multivariate extension of the log-normal survival model.

When applied to survival data from a population of cancer patients, the log-normal model provides estimates of three important parameters: cured fraction, mean log survival time, and standard deviation log survival time. In the original model, however, these parameters are unrelated to prognostic covariates. Furthermore, the original algorithm is computationally unstable and highly dependent on initial parameter estimates. We have developed an extension of the log-normal model that stabilizes computation and expresses survival parameters as functions of prognostic covariates. We have also developed an ancillary algorithm that provides reliable initial estimates.

Blood levels in macular cystoid spaces and their relationship to retinal vein obstruction.

BACKGROUND: Blood levels in macular cystoid spaces are commonly seen in patients with branch or central retinal vein obstruction, but have not been previously reported. METHODS: To determine blood levels in cystoid spaces, a retrospective study was conducted of 102 eyes with branch retinal vein obstruction, 54 eyes with central retinal vein obstruction, 207 eyes with clinically significant diabetic macular edema, and 109 eyes with aphakic or pseudophakic cystoid macular edema seen over a 5-year period. RESULTS: Definite blood levels in cystoid spaces were found in 26 eyes (25%) with branch vein obstruction and in 4 eyes (8%) with central vein obstruction. In contrast, this clinical change was detected in only 1 of 207 eyes (1%) with diabetic cystoid macular edema, and in only 2 of 109 eyes (2%) with aphakic or pseudophakic cystoid macular edema (P < 0.001). When blood levels in cystoid spaces were detected in patients with branch vein obstruction, the site of obstruction tended to be superotemporal (P < 0.05). CONCLUSION: Blood levels in cystoid spaces are an important sign of retinal vein obstruction, and may help establish the diagnosis in certain cases.

A model of long-term survival following adjuvant therapy for stage 2 breast cancer.

Following adjuvant therapy for breast cancer, some patients will die of this tumour while the remainder will die of other causes. Deaths from breast cancer tend to follow a lognormal distribution, while deaths from other causes can be approximated by national demographic data. By combining these two survival models, we have generated an age-specific method for estimating the impact of treatment on overall long-term survival. Treatment was designed to operate by one of two mechanisms: an increase in cured fraction, or an increase in median tumour-related survival time among uncured patients. This analysis revealed that, for young and middle-aged patients, an increase in cured fraction has substantially greater long-term clinical impact than an increase in median survival time. Unfortunately, the non-parametric tests traditionally used in prospective clinical trials cannot distinguish between these two mechanisms of action.

Skin melanoma. Cured fraction and survival time as functions of thickness, site, histologic type, age, and sex.

BACKGROUND: Previously, nonparametric or semiparametric methods have been used to determine the relationship of various prognostic covariates with survival of skin cancer. Unfortunately, these methods do not readily distinguish between factors that modulate cure and those that modulate survival time among uncured patients. METHODS: The multivariate lognormal model can be used to detect the association of cured fraction and median survival time with specific prognostic covariates. This model was applied to survival data from 2004 patients with skin melanoma using the following prognostic covariates: thickness, site, and histologic type of the tumor and sex and age of the patient. RESULTS: This analysis revealed that a low cured fraction was associated with thick lesions and location other than trunk or extremity, whereas a short median survival time was associated with thick lesions and tumor located on the trunk. Advanced age was highly associated only with short median survival time. CONCLUSION: The lognormal survival model offers insight into the biology of skin melanoma by distinguishing the roles played by likelihood of cure and survival time. The differential associations of various covariates with these two parameters suggest that biologic mechanisms that govern cure are not identical to those that govern survival time.

Assessing the impact of adjuvant therapy on cure rate for stage 2 breast carcinoma.

The log-rank test is commonly used to assess therapeutic effect in prospective, randomised clinical trials. This test is sensitive to differences in survival between treatment groups at a specific endpoint, but cannot determine whether such a difference is due to an enhanced cure rate or an enhanced survival time among uncured patients. To investigate the clinical impact of such limitations, an algorithm was constructed to simulate clinical, randomised, adjuvant therapy trials in patients with a cured fraction of 0.27 and a median survival time for uncured patients of 3.4 years. Hypothetical therapies were introduced to increase rate of cure, increase median survival time, or achieve a combination of these effects. For 500 simulated patients recruited over a 5 year period and then followed for three additional years, a 50% enhancement of median survival time (to 5.1 years) led to a survival increase detectable at the P = 0.05 level in 780 of 1000 trials, whereas a 50% enhancement of cured fraction (to 40.5%) led to a detectable increase at the same level in only 449 of 1000 trials. These findings suggest that, in clinical trials of adjuvant therapy for stage 2 breast cancer, the log rank test may be more sensitive to increases in tumour-related survival time than to increases in cured fraction.

Stereologic estimation of nucleolar volume in ocular melanoma: a comparative study of size estimators with prognostic impact.

The aim of this study was to investigate the relationships between one-, two-, and three-dimensional histomorphometric estimators of nucleolar size in ordinary histologic sections of uveal melanomas from 144 patients. In addition, the prognostic value of the various size parameters was studied. The following estimates were obtained: the mean diameter of the 10 largest nucleoli, the mean nucleolar profile area and associated standard deviation of the nucleolar profile area, the volume-weighted mean nucleolar volume (nucleolar vv), and the macroscopic, largest tumor dimension. All histomorphometric parameters were highly intercorrelated (r > .75). The correlation between the largest tumor dimension and the nucleolar vv was rather poor (r = .35). The efficiency of the sampling scheme for estimation of the nucleolar vv was very high; more than 95% of the totally observed variation was contributed by biologic differences between tumors. Single-term Cox analyses demonstrated a highly significant prognostic value of all five investigated, quantitative variables. Evaluation in a multivariate Cox model showed, however, that only the nucleolar vv and the largest tumor dimension were independent prognostic covariates at the chosen level of significance (5%). Unbiased, shape-independent estimates of the nucleolar vv offered superior prediction of clinical outcome, as compared with lower-dimensional, shape-dependent histomorphometric estimators of nucleolar size.