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Comparison of hazard models with and without consideration of competing risks to assess the effect of neoadjuvant chemotherapy on locoregional recurrence among breast cancer patients


1 Division of Biostatistics, Kalinga Institute of Medical Sciences, Bhubaneswar, Odisha; Department of Biostatistics, All India Institute of Medical Sciences, New Delhi, India
2 Department of Surgical Oncology, BRA Institute Rotary Cancer Hospital, All India Institute of Medical Sciences, New Delhi, India
3 Department of Biostatistics, All India Institute of Medical Sciences, New Delhi, India
4 Division of Biostatistics, Kalinga Institute of Medical Sciences, Bhubaneswar, Odisha, India

Date of Submission21-Jan-2019
Date of Decision15-Apr-2019
Date of Acceptance22-Aug-2019
Date of Web Publication06-Jan-2020

Correspondence Address:
Sada Nand Dwivedi,
Department of Biostatistics, All India Institute of Medical Sciences, Ansari Nagar, New Delhi - 110 029
India
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Source of Support: None, Conflict of Interest: None

DOI: 10.4103/jcrt.JCRT_49_19

 > Abstract 


Context: While analyzing locoregional recurrences (LRRs), it is necessary to consider distant metastasis as a competing event. Because, later one is more fatal than LRR. It may change ongoing treatment of breast cancer and may alter the chance of LRR. Although some earlier studies assessed the effect of neoadjuvant chemotherapy (NACT) on LRR, they did not use competing risk regression model for it.
Aims: To identify the risk factors and predict LRR using competing risk hazard model and to compare them with those using conventional hazard model.
Settings and Design: This was a retrospective study from a tertiary care cancer hospital in India.
Subjects and Methods: Data of 2114 breast cancer patients undergoing surgery were used from patient's record files (1993–2014).
Statistical Analysis: Fine and Gray competing risk regression was used to model time from surgery to LRR, considering distant metastasis and death as the competing events. Further, cause-specific Cox regression was used to model time from surgery to LRR without considering competing risk.
Results: Greater than ten positive nodes (hazard ratio [HR] [95% confidence interval (CI)]: 2.19 [1.18–4.03]), skin involvement (HR [95% CI]: 2.75 [1.50–5.05]), NACT (HR [95% CI]: 1.90 [1.06–3.40]), invasive tumor in inner quadrant (HR [95% CI]: 1.78 [0.98–3.24]), and postoperative radiotherapy (HR [95% CI]: 0.52 [0.29–0.94]) were found to be significantly associated with LRR. However, conventional survival analysis ignoring competing risk overestimated cumulative incidence function and underestimated survival. Competing risk regression provided relatively more precise CI.
Conclusions: Competing risks, if any, need to be incorporated in the survival analysis. NACT was found to be associated with higher risk for LRR, which may be because of administering it mainly to patients with bad prognosis.
Conclusions: Competing risks, if any, need to be incorporated in the survival analysis. NACT was found to be associated with higher risk for LRR, which may be because of administering it mainly to patients with bad prognosis.

Keywords: Cause-specific hazard model, cumulative incidence competing risk, distant metastasis, Fine and Gray model, sub-distribution hazard model



How to cite this URL:
Pathak M, S. Deo SN, Dwivedi SN, Vishnubhatla S, Thakur B. Comparison of hazard models with and without consideration of competing risks to assess the effect of neoadjuvant chemotherapy on locoregional recurrence among breast cancer patients. J Can Res Ther [Epub ahead of print] [cited 2020 Mar 31]. Available from: http://www.cancerjournal.net/preprintarticle.asp?id=275236




 > Introduction Top


Contradictory evidence exists regarding association of neoadjuvant chemotherapy (NACT) and locoregional recurrence (LRR) in breast cancers.[1],[2],[3] To assess the impact of NACT on LRR, most of the studies used conventional survival analysis, i.e., Kaplan–Meier for unadjusted survival visualization and Cox proportional hazards (PHs) models, to identify the predictors of LRR. However, while analyzing LRRs, it is necessary to consider distant metastasis as a competing event. Because distant metastasis is more fatal in comparison to LRR and also likely to change the ongoing treatment of breast cancer. Hence, it may alter the chance of LRR. Competing risk (e.g., distant metastasis) can be defined as an event which either hinders the observation of the event of interest (LRR) or alters its probability of occurrence.[4] In the presence of a competing risk, conventional survival analysis may provide incorrect results.[5],[6] Accordingly, researchers have suggested using cumulative incidence competing risk (CICR) method in place of Kaplan–Meier for crude probability estimation.[7] Some of them have also suggested using competing risk regression model instead of conventional Cox PH model for correctly identifying the predictors and subsequently predicting the occurrence of event.[8] Hence, it is necessary to take into consideration the known competing risks while analyzing the time to an event outcome. Although few studies assessed the effect of NACT on LRR, to the best of our knowledge, no study has used competing risk regression model for this purpose. Further, there is need to study the relative change in analytical results between conventional methods of survival analysis, including Kaplan–Meier for crude probability estimation and Cox hazard model to identify the predictors. There is also need to study the crude incidence rate after incorporating competing risks using CICR Method. Similarly, identification of the factors and prediction the event probabilities need to be assessed by Fine and Gray sub-distributional PH model. Accordingly, the present study aimed to identify the risk factors and predict the LRR using conventional as well as competing risk modeling and also to compare the performance of these models.


 > Subjects and Methods Top


The data available under a retrospective cohort of breast cancer patients having surgery and chemotherapy for breast cancer during 1993–2014 at a tertiary care center were considered for the present study. Male breast cancer patients, ductal carcinoma in situ or phyllodes, patients with recurrent or previously treated breast cancer, bilateral breast cancer, any evidence of metastasis, contralateral breast cancer, and breast cancer patients not receiving chemotherapy were excluded. After completion of appropriate treatment decided with clinical expertise, to record data on outcome (e.g., LRR) as well as competing events (e.g., distant metastasis and death), patients were asked to visit the center on 3 monthly or 6 monthly intervals depending on their condition. The present study is approved by the Institutional Ethics Committee of our Institute.

Outcome variables

Time to LRR as the first event was considered as outcome of interest, while times to distant metastasis and death as the first event were considered as two competing events. The patients presented with LRR along with distant metastasis were treated in metastatic group as their treatment is guided by the metastasis. LRR is defined as recurrence either to local or regional area or local as well as regional recurrences. Precisely, local recurrence is come back of cancer in the chest or ipsilateral breast area or in the skin near original site of scar. Further, regional recurrence is the re-appearance of cancer to the lymph nodes near the breast, e.g., axilla. Distant metastasis is recurrence of cancer to distant parts of the body such as brain, lung, bone, and liver. Time to these events is calculated from the surgery because this was the time point when patients become disease-free.

Statistical analysis

The data were checked for internal consistency. Descriptive statistics including mean ± standard deviation (SD) and median (interquartile range) are provided for normally distributed and skewed data, respectively. Proportion is used for categorical variables. The survival probabilities over the time were demonstrated with Kaplan–Meier survival estimates as well as CICR method. Covariate's effect was assessed using Cox PH regression as well as competing risk regression models proposed by Fine and Gray.[9] The PH assumption was tested using time–variant hazard modeling, i.e., by adding time interaction term for given independent variable.[10] The independent variables significant at 25% level of significance under univariable Cox model or competing risk model were considered as candidate variables for stepwise Fine and Gray competing risk model. Final multivariable analysis was performed at 5% level of significance. All the analyses were carried out in Stata 13.1, Stata Corp, Texas, USA.


 > Results Top


A total of 2114 breast cancer patients having surgery and chemotherapy were included in the analysis. The mean age of breast cancer patients was 46.6 years with SD of 10.2. Around 50% of the women already experienced menopause. Distribution of relevant baseline characteristics is presented in [Table 1].
Table 1: Distribution of outcomes in relation to demographic, clinical, and treatment.related characteristics

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A total of 64 patients had LRR. However, 409 patients had distant metastasis. Further, 82 patients who presented with LRR along with metastasis were considered in metastasis group. Furthermore, 21 patients died without having recurrence.

Crude estimation of cumulative incidence function

The cumulative incidence of LRR up to a given time is the probability that an individual experiences LRR by that time. Conventionally ignoring the presence of competing risk, it is a complement of Kaplan–Meier survival function.[7] However, CICR method incorporates competing risk while calculating cumulative incidence. As evident from [Figure 1], ignorance of competing risks (distant metastasis and deaths) overestimated cumulative risk and hence underestimated survival in comparison to method incorporating these competing risks.
Figure 1: Cumulative incidence function by conventional method (complement of Kaplan–Meier method) and cumulative incidence competing risk method

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Hazard models

Univariable analysis

Univariable analysis was performed with each of the considered explanatory variables using cause-specific PHs model and competing risk model for LRR, considering distant metastasis and death as two competing events. In univariable analysis for LRR, uniparous, more than 30 years of age at first birth, history of breast cancer, average general condition, tumor at inner or multiple quadrant, auxiliary node involvement, presence of matted nodes, pathologically N3 stage, pathological skin involvement, larger tumor size, negative hormone receptor status, NACT, not receiving adjuvant hormone therapy, and lower number of chemotherapy cycles were found to be associated with higher risk of LRR at 25% level significance under each of the two models, i.e., cause-specific Cox PH model as well as competing risk regression. However, higher duration of symptoms and not receiving postoperative radiotherapy were found significant only under competing risks method. Keeping in view the objective of comparison of models, these two variables were also included as candidate variables for stepwise regression using each of the models. In addition, inner quadrant was not found significant under multivariable step-wise cause-specific Cox regression model. However, keeping in view defined objective to compare with and without competing risk models, as it was significant under multivariable stepwise competing risk model, it was included in final set of covariates to run complete multivariable regression models. In similar ways, keeping in view the significance of hormone receptor status under multivariable stepwise Cox model, hormone receptor status was considered in final set of covariates for multivariable competing risk model despite being nonsignificant under stepwise competing risk regression model.

Multivariable analysis

Under multivariable cause-specific Cox PH model of LRR, among the candidate variables, >10 positive nodes (hazard ratio [HR] [95% confidence interval (CI)] =2.84 [1.58–5.12]), skin involvement (HR [95% CI]: 3.23 [1.80–5.79]), and NACT (HR [95% CI]: 2.74 [1.55–4.84]) were found to be significantly associated with higher risk of LRR. In addition, invasive tumor in inner quadrant (HR [95% CI]: 1.82 [0.99–3.33]) was associated with higher rate of LRR but with borderline significance. However, positive hormone receptor status (HR [95% CI]: 0.58 [0.34–0.99]) and postoperative radiotherapy (HR [95% CI]: 0.47 [0.27–0.82]) were found to be the protective factors for LRR. It is worthwhile to mention here that postoperative radiotherapy which was not significant under univariable cause-specific regression analysis turned up to be significant in multivariable analysis.

Like cause-specific Cox model, among the candidate variables, under multivariable competing risk regression analysis of LRR, >10 positive nodes (HR [95% CI]: 2.19 [1.18–4.03]), skin involvement (HR [95% CI]: 2.75 [1.50–5.05]), and NACT (HR [95% CI]: 1.90 [1.06–3.40]) were retained to be significantly associated at 5% level of significance with higher risk of LRR. In addition, invasive tumor in inner quadrant (HR [95% CI]: 1.78 [0.98–3.24]) was retained to be borderline significant. In contrary, only postoperative radiotherapy (HR [95% CI]: 0.52 [0.29–0.94]) was retained to be protective factors for LRR. As a matter of fact, the comparative results under this model indicated more precise CI in comparison to those under cause-specific Cox PH model.

Both the models fitted well to the observed data. The standard error (SE) of predicted risk score was significantly higher in cause-specific PH model (mean SE [95% CI]: 0.891 [0.856–0.927]) in comparison to competing risk survival model (mean SE [95% CI]:0.508 [0.503–0.513]). This supports the precise CI under competing risk model. In addition, as evident from [Table 2], competing risk regression model provided precise estimates in comparison to Cox PHs model. Further, comparatively point estimates under competing risk model were found to be toward null value.
Table 2: Univariable and multivariable results under cause.specific Cox model and sub.distribution competing risk model for locoregional recurrence

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 > Discussion Top


The predictors found associated with LRR have similar as well as contradictory findings from global literature. The present study supports the finding of the previous study that NACT is significantly associated with LRR.[3] Tumor size, although being significant under univariable, could not retain its significance under multivariable analysis in some global literature as well.[11],[12],[13],[14] The radiotherapy showing significant protective effect under present study was in contrary to those reported in previous studies.[15],[16],[17] Some of the factors not considered in multivariable analysis have mixed reporting over their effect on LRR.[11],[12],[13],[14],[15],[16],[17],[18],[19]

Although the present study identified NACT as a risk factor for LRR, this is worthwhile to mention here that as per treatment strategy, NACT is generally given to patients having bad prognosis. It may be worthwhile to mention here that majority of the patients were of higher stages at the time of presentation. Further, some of the variables related to these bad prognosis decided on the basis of clinical wisdom could not be adjusted as they were either not reported in the database or reported for very less proportion of the patients.

The competing risk regression models provided precise estimates toward null in comparison to Cox PHs model. It may be due to the fact that the survival time for the patients experiencing competing events is considered infinite because it is known that event of interest will never happen as the first failure. Accordingly, the patients having competing failure remain in the risk set forever. This implies that while calculating the HR, despite having same numerator, denominator is larger under competing risk model in comparison to Cox PH model. On the other hand, cause-specific Cox PH model considers competing event as censored assuming that they have similar risk of event of interest as that of at-risk patients, over sighting the fact that the event of interest will never happen to these patients. To be more specific, point estimate under competing risk model was found to have comparatively lower HR with precise CI in comparison to those under Cox PH model except in some situation. The hazard associated with cumulative incidence function was found higher under competing risk method only in the case when competing event and event of interest were found to be associated with the covariates in reverse direction. At the same time, maybe because of considering competing events as censored and assuming that they have similar risk, Cox PH model overestimates the HR.


 > Conclusion Top


Neoadjuvant chemotherapy was found to be associated with higher risk for loco-regional recurrence, which may be because of administering it mainly to patients with bad prognosis. Competing risk regression provides precise estimates. Ignorance of known competing risk may result into overestimation of hazard and hence underestimation of survival. Competing risks, if any, need to be incorporated in the survival analysis

Acknowledgement

We thank All India Institute of Medical Sciences (AIIMS), New Delhi, to register MP as a Ph. D. student in the Department of Biostatistics and make available access to patient record files, computer laboratory facility, library, online accessibility of articles, and other resources.

Financial support and sponsorship

This study was not funded by any external funding agency. It is part of Ph.D. work of the first author, Dr. Mona Pathak.

Conflicts of interest

There are no conflicts of interest.



 
 > References Top

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Mauriac L, MacGrogan G, Avril A, Durand M, Floquet A, Debled M, et al. Neoadjuvant chemotherapy for operable breast carcinoma larger than 3 cm: A unicentre randomized trial with a 124-month median follow-up. Institut Bergonié Bordeaux Groupe Sein. Ann Oncol 1999;10:47-52.  Back to cited text no. 1
    
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