Derecho al medio ambiente en relación con el principio de rigor

2.2.1 Person-years at risk (PYR)

We used a standard person-years approach to conduct the analysis 1, 2. Person-years at risk (PYR) started 2 months after a first cancer diagnosis and ended at the date of the second cancer diagnosis, the date of death, or the end of follow-up, whichever came first. Most cancer registries use a 2-month rule to define the development of a MPC because for MPCs occurring within 2 months, it is difficult to determine which one was the first cancer. Below is an example of the calculation of PYR in our study cohort (Figure 2.1).

Figure 2.1: Example illustrating the calculation of person-years at risk (PYR)

The first patient had a first cancer diagnosis in late 2008 and PYR started at the beginning of 2009 (2 months after a first cancer diagnosis). The first patient was still alive at the end of 2013. The PYR for the first patient is 5 years. The PYR for the second patient started at the beginning of 2009 and the patient died in the middle of 2013 and had PYR for 4.5 years. The PYR for the third patient started in the middle of 2009 and the patient developed a second primary cancer in the middle of 2011. The PYR for the third patient is 2.0 years. Similar calculations were applied for the fourth and fifth patients. Therefore, we had the PYR for

P Y R f o r c o h o r t p a t i e n t s i n e a c h c a l e n d a r y e a r P Y R f o r each p at ien t

each patient at each row. If we look at the column, the PYR could also be accumulated within 1-year calendar period strata. Then we could sum the PYR within specific sex, 5-year age group and 1-year calendar period strata.

2.2.2 Outcome measures

2.2.2.1Standardised incidence ratio (SIR)

The standardised incidence ratio (SIR) is a relative measure and was calculated as the ratio of observed to expected numbers of MPCs 2-4. The estimation of expected numbers of MPCs assume that patients with a first cancer experienced the same cancer rates as the general population. The expected number was then calculated using the accumulated person-years within specific sex, 5-year age group and 1-year calendar period strata, multiplied by the corresponding cancer incidence rates in the general population. The SIR is more informative than the crude incidence of MPC because it takes into account the natural increase of cancer risk with age and variation of the background cancer incidence in each year 5_{. In comparison,}

crude incidence of MPCs simply reflects the number of MPC cases occurring in the study cohort during a year. Poisson regression models were used to derive 95% confidence intervals (95% CIs) for SIRs, assuming that the observed number followed a Poisson distribution. The outcome measure used for the model was the observed number of MPCs and offset/exposure variable was the expected number of MPCs. Tests for linear trends in SIRs were performed by entering calendar periods of first cancer diagnosis as a consecutive non-negative integer variable in relevant Poisson regression models. Evidence for a linear trend was assessed by comparing the likelihood function of the model including the variable for calendar periods of first cancer diagnosis with the likelihood function of the model without that variable.

2.2.2.2Absolute excess risk (AER)

The absolute excess risk (AER) is an absolute measure. We subtracted the expected number of MPCs from the observed number of MPCs; the difference was then divided by 10,000 person-years. The AER is often interpreted as the absolute number of excess second cancers per 10,000 PYR among cancer survivors. Generally, the AER is more informative for public health purposes because it measures the absolute impact of the MPC burden among cancer patients. High SIRs may occasionally produce low AERs when the cancer incidence in the general population is low. For example, when the baseline leukaemia incidence in the general adulthood population is low, the AER for treatment-related leukaemia among adult cancer patients may have a low value. However, the relevant SIR value may be high because of the small value of the denominator (the expected number of treatment-related leukaemia using leukaemia incidence in the general adulthood population is low). In contrast, when the relevant cancer incidence in the general population is high, a slight increase in SIRs may produce a great increase in the AERs.

2.3 MPC mortality risk

2.3.1 Competing risk analysis

We applied competing risk models as an alternative to Kaplan-Meier methods to assess the competing mortality from subsequent primary cancers and non-cancer events among cancer patients. Here is a simple example to illustrate the overestimation of cause-specific mortality using the Kaplan-Meier method and the more accurate estimation using competing risk analysis 6. Three patients were diagnosed with lung cancer at the same time. The first patient died one month after lung cancer diagnosis and the cause of death was heart failure. The second patient died two months after lung cancer diagnosis because of the progression of the

lung cancer. The third was still alive at the end of follow-up. The primary outcome of interest is the death due to lung cancer. In Kaplan-Meier (KM) estimates, the patient who died of heart failure is censored in the risk setting (the denominator) at one month. Therefore, the chance of death due to lung cancer at the third month is 1/2 in this group of three patients. In a competing risk (CR) setting, the patient who died of heart failure is still kept in the risk set (the denominator), but the chance of reaching the endpoint of interest (death due to lung cancer) is zero. As a result, the chance of death due to lung cancer at the third month is 1/3.

2.3.2 Outcome measures

As an absolute measure, the cumulative incidence function (CIF) was used to estimate the cumulative incidence of cause-specific deaths in the presence of competing risks 6, 7. For a relative measure, the subdistribution hazard ratios (SHRs) of cause-specific deaths were calculated in competing risk models 8_{. We also derived hazard ratios from Cox regression}

models and made comparisons with the SHRs to illustrate the difference in results in the presence of competing risks. Detailed descriptions of the analyses are presented in Chapter 5.

2.4 Non-cancer mortality among cancer patients

We conducted competing risk analysis to assess the cumulative incidence of non-cancer deaths among cancer patients. Standardised mortality ratios (SMRs) and absolute excess risks

(AERs) for non-cancer deaths were used to compare mortality due to non-cancer events among cancer patients with that expected in the general population. The rationale and calculation of SMRs were similar to that for SIRs.