gives demographic, medical, and treatment characteristics of the study sample. WHEL women had an average age of 51 years (standard deviation, 8.8; range, 26–71) at diagnosis and were primarily Caucasian (85%) and college graduates (54%). The prevalence of stage I tumors was 38.6%; 15.7% of tumors displayed well-differentiated pathology; 63.1% of tumors were ER+ and PR+; and 85.9% of tumors were of the ductal (with or without lobular) type. Regarding treatment, 52% of WHEL women underwent a mastectomy (the remainder underwent lumpectomy with radiation therapy), 70% received adjuvant chemotherapy, and 68% received antiestrogen therapy (66% took tamoxifen, 1% took raloxifene, 0.1% took anastrazole/arimidex, and for 1% the type of antiestrogen medication prescribed was unknown). Median time from diagnosis was 8.99 years (range, 0.79–15.01).
Demographic and Medical Characteristics of a Sample of 3,088 Women Diagnosed With Primary Breast Cancer Between 1991 and 2000, Women's Healthy Eating and Living Study, 1995–2006
In the univariate analysis, age at diagnosis, education, tumor stage, tumor type, tumor grade, ER/PR status, receipt of chemotherapy, receipt of antiestrogens, and clinical site were significantly associated with outcomes (P < 0.05), while age at diagnosis, tumor stage, tumor type, tumor grade, ER/PR status, and antiestrogen therapy exhibited non-proportional-hazards effects (P < 0.1). These results guided the development of multiple regression models ( and ).
Hazard Ratios for Prognostic Factors From Multiple Cox Regression Models Applied to a Sample of 3,088 Women Diagnosed With Primary Breast Cancer Between 1991 and 2000, Women's Healthy Eating and Living Study, 1995–2006
Time-varying Hazard Ratiosa for Prognostic Factors for Second Breast Cancer Events Applied to a Sample of 3,088 Women Diagnosed With Primary Breast Cancer Between 1991 and 2000, Women's Healthy Eating and Living Study, 1995–2006
In Cox models (), stage II or III tumors were associated with the highest risk of breast cancer events in the early model; this effect appeared to diminish with time, although it was still a major risk factor in the late model. Interestingly, although the finding was not statistically significant, having an ER+ tumor was protective against early disease but was associated with poorer prognosis more than 5 years postdiagnosis. Similar time-related inversions of risks were apparent for tumor type; that is, having a ductal tumor was associated with higher risk for earlier disease in our sample but not for risk more than 5 years postdiagnosis. As expected, the log hazard ratios in the overall model were a weighted average of the log hazard ratios from the early and late models. Older age at diagnosis, having completed college, and having received antiestrogen therapy exhibited similar protective effects across all 3 models.
The Cox models in involved stratification on each year from diagnosis to study entry, with different baseline hazard functions being computed for these 4 strata; thus, varying recurrence risks were modeled by year from diagnosis. Additionally, we fitted delayed-entry Cox models (10
) to further examine possible biases due to variability in time from diagnosis to study entry. The results (not presented) were almost identical to those of , with changes of less than 1% in the delayed-entry model hazard ratios, suggesting that this source of bias was not a factor in our analyses.
Time-varying coefficient models (5
) further explicate the Cox model findings by formally testing the proportional hazards assumption. They permit more flexibility by allowing the estimation of hazard ratios across shorter time intervals. and present results from the time-varying coefficient model with 4 knots and 2 degrees of freedom. Hazard ratios for education, age at diagnosis, PR status, and receipt of antiestrogen therapy were constant over time and similar to those for the overall Cox model (). Tumor stage, ER status, and tumor grade violated the proportional hazards assumption. Higher stage was associated with a 3-fold greater hazard of breast cancer events than a stage I tumor during the first 2.5 years after diagnosis; this effect diminished to a hazard ratio of 2.1 after 7.7 years, but higher stage remained a significant risk factor. Similarly, poorly differentiated tumors were associated with higher risk (hazard ratios ranging from 1.25 to 1.5) of a breast cancer event up to 5.5 years postdiagnosis, with no apparent effect after 7.7 years. Interestingly, although it was not statistically significant at the 5% level in each time interval, having ER+ status was protective up to 4 years after diagnosis; this trend was reversed in later years, with ER+ status exhibiting a hazard ratio of 1.5 after 7.7 years.
Figure 1. Log hazard ratios for prognostic factors for second breast cancer events based on a penalized spline model (time-varying coefficient models with 4 knots and 2 df) applied to a sample of 3,088 women diagnosed with primary breast cancer between 1991 and (more ...)
We also fitted a time-varying coefficient model with 10 knots. The results (not shown) were similar to those of for ER status and stage, with ER+ status conferring striking protection early (for <1.7 years since diagnosis, hazard ratio = 0.63, 95% confidence interval: 0.4, 0.98) and detrimental effects later (for >9.5 years since diagnosis, hazard ratio = 2.01, 95% confidence interval: 1.22, 3,30). Interestingly, in the 10-knot model, tumor type violated the proportional hazards assumption, with hazard ratios increasing up to 5 years postdiagnosis and decreasing thereafter for ductal tumors versus nonductal tumors.
In additional sensitivity analyses, we included other covariates (e.g., ethnicity, receipt of radiation or chemotherapy, clinical site, and diet group (intervention vs. comparison)) in the model. These covariates were excluded from the final parsimonious models because either they were not significantly associated with outcomes or including them did not meaningfully alter the hazard ratios for other factors in the model.
It is important to contrast the Cox model findings () with those from the spline approach (). At first glance, both give similar results—namely, that ER status and stage exhibit time-dependent effects on disease-free survival. However, the spline approach affords many advantages. First, it formally tests the proportional hazards assumption and identifies variables that violate it. Second, the spline approach does not arbitrarily choose a time point of 5 years to delineate early versus late recurrence. Instead, this method partitions the time axis on the basis of knot locations and estimates hazard ratios for each prognostic factor on each time subinterval. For instance, using splines, WHEL data suggest that the risk of second breast cancer events is 50% higher for poorly differentiated tumors in the first 2.5 years after diagnosis, whereas ER+ tumors appear to be associated with higher risk after 7.7 years. Thus, Gray's method allows for the possibility that time periods in which hazard ratios change are different for different prognostic factors, rather than imposing an a priori cutpoint of 5 years. Third, this approach also provides finer estimates of hazard ratios (with 95% confidence intervals) for each time subinterval, whereas the early and late models simply provide “averaged” hazard ratio estimates for time intervals of ≤5 years versus >5 years. In particular, the lack of a significant effect for poorly differentiated tumors in the early model () is probably due to this factor's only having an impact on very early breast cancer events (<2.5 years), so that using a 5-year time scale nullifies the risk. Finally, most analyses of such data would simply use the Cox model for the entire follow-up period (i.e., our “overall” model), which would lead to potentially incorrect conclusions regarding the prognostic effects of ER status.