Cartas al editor
Response to Dr. de Vries
Dear Dr. de Vries: We appreciate your interest in our work and are grateful for your valuable contributions and comments to clarify the methodology and to facilitate the results interpretation. Your comments relate to two main aspects of the methods used in our estimates and we have focused our response to your two letters in these two aspects:
I - Five-year relative survival estimates
The Cancer Registry of Cali (RPCC) was part of the Concord-2 Study.1 This participation allowed us to evaluate the quality of information2 and optimize the process of linkage between different databases: Cancer registry, mortality, hospital discharges and affiliation to the health insurance system in Cali. Data quality indicators: Morphologically verified: 87.4%, non-specific morphology: 13.3%, lost to follow-up: 0%, censored: 19.5%.2
Five-year relative survival for patients diagnosed during the periods 1995-99 and 2000-04, was estimated using the classic cohort approach with follow-up until 2009. All-cause mortality data were obtained from the Secretaría Municipal de Salud of Cali. We constructed life tables of all-cause mortality from the general population of Cali, stratified by age (single year), sex, and calendar year of death. The intraclass correlation coefficient value was high (0.9937) when comparing estimates of life tables obtained from the teams of RPCC vs. Concord-2 groups. Table 1 shows the comparison between the estimates of relative survival achieved by our working group and those obtained by the team of the London School of Hygiene & Tropical Medicine for the Concord-2 Study.1 In general the results are similar, but our estimates are slightly lower than those obtained by Concord-2, especially for prostate cancer because we did not use the recently developed Pohar Perme estimator for net survival,3 which takes into account the competing risks of death, and these are higher for elderly cancer patients.
2 - Assumption of proportional hazards
With certain types of cancer such as cervical and breast there was no problem with our estimates using the Cox proportional hazards model because there were important explanatory variables such as staging. The Cox proportional hazards model relies on the assumption that the effect of a given covariate does not change over time. Rates nonetheless depend on the particular biological process and the shape of their change over time for the main effect is the most important issue. Violation of the PH assumption for the main effect would effectively invalidate the findings, but the examination of subgroups calls for a more careful examination, where a particular test is less important than the shape of the rates over time. The graphical depiction of the lack of proportionality is probably the best way to assess departures from the assumption. The so-called Arjas plot is generally the most effective at detecting this issue, and the maximum deviation (Kolmogorov-Smirnov like) criterion for rejection the best test.8Figure 1 shows the Arjas plot of estimated cumulative hazard versus number of failures in each stratum of SES and period for prostate and colorectal cancer in Cali, Colombia.
The curves may differ from the 45 degree line as seen in figure 1, but they are still fairly linear. Arjas plot therefore rises the doubt that proportional hazards assumption for these variables is not so heavily questionable.
Our suggestion in the case of a major departure in the proportionality assumption would be Poisson regression.8 Excess hazards can be incorporated by introducing a time-dependent interaction term for that covariate. Table II shows the estimated excess hazard ratios (HR) for colorectal and prostate cancer trough 1995-2004 in Call, Colombia. The HRs obtained with the Cox model have the same direction as those achieved with the GLM-Poisson but with different magnitude, specially for prostate cancer.
Limitations of our estimates: RPCC was not actively tracking participants, and Cali lacked reliable statistics on the migrant population.4 Cause of death information is available to the RPCC via death certificates, but they are often vague and it is difficult to determine whether or not cancer is the primary cause of death Life tables for Cali and Colombia, according to socioeconomic strata, were not available; therefore, the effect of SES on excess mortality due to cancer may be overestimated. During the study period there were changes in follow-up practices. In cases of prostate and breast cancer, there were specific projects that contributed to better tracking compared to colon cancer. Implementation of the new health system in our country improved availability of personal identification number. Since 2000, follow-up practices are similar for all types of cancer. These changes in the practices of follow-up could have caused underestimation of survival for the period 1995-1999, especially for colon cancer. Like any exploratory ecological study, our results must be validated with other designs.
Luis Eduardo Bravo, MD, MSc, Patol,(1) Luz Stella García, Admon de Empresas, Epidem,(1) Edwin Carrascal, Path(1,2) Jaime Rubiano, MSc,(3) Armando Cortés, MD, Pat Clín,(2) Paola Collazos, Ing Sist,(1) Nubia Muñoz, MD, MPH,(4) Jaime Alejandro Restrepo, MD Uról (3) Herney Andrés García-Perdomo, MD, MSc, Uról,(3) Jorge Carbonell, MD Uról.(3)
(1) Registro Poblacional de Cáncer de Cali, Departamento de Patología, Universidad del Valle. Cali, Colombia. firstname.lastname@example.org .
(2) Departamento de Patología, Universidad del Valle. Cali, Colombia.
(3) Departamento de Cirugía, Universidad del Valle. Cali, Colombia.
(4) Instituto Nacional de Cancerologia. Bogotá, Colombia.
1. Allemani C, Weir HK, Carreira H, Harewood R, Spika D,Wang XS, et al. Global surveillance of cancer survival 1995-2009: analysis of individual data for 25 676 887 patients from 279 population-based registries in 67 countries (CONCORD-2). Lancet 2014 Nov 26.pii: S0140-6736(14)62038-9.
2. Allemani C, Weir HK, Carreira H, Harewood R, Spika D, Wang XS, et al,. Global surveillance of cancer survival 1995-2009: analysis of individual data for 25676887 patients from 279 population-based registries in 67 countries (CONCORD-2). Lancet 2014; published online Nov 26. http://dx.doi.org/10.1016/S0140-6736(14)62038-9.
3. Pohar-Perme M, Henderson R, Stare J. An approach to estimation in relative survival regression. Biostatistics 2009; 10:136-146.
4. Muñoz N, Bravo L. Epidemiology of cervical cancer in Colombia. Salud Publica Mex 2014;56(5):431-439.
5. Bravo L, García L, Carrascal E, Rubiano J. Burden of breast cancer in Cali, Colombia: 1962-2012. Salud Publica Mex 2014;56(5):448-456.
6. Restrepo J, Bravo L, García-Perdomo H, García LS, Collazos R Carbonell J. Incidencia, mortalidad y supervivencia al cáncer de próstata en Cali,Colombia, 1962-2011. Salud Publica Mex 2014;56(5):440-447.
7. Cortés A Bravo L, García L, Collazos P. Incidencia, mortalidad y supervivencia por cáncer colorrectal en Cali, Colombia, 1962-2012. Salud Publica Mex 2014;56(5):457-464.
8. Persson, I. Essayson the Assumption of Proportional Hazards in Cox Regression [Elektronisk resurs], Acta Universitatis Upsaliensis, Uppsala, 2002. Available at: http://uu.diva-portal.org/smash/get/diva2:161225/FULLTEXT01.pdf