Department of Medical Epidemiology and Biostatistics, Karolinska Institutet, Stockholm, Sweden.
Clinical Epidemiology Division, Department of Medicine Solna, Karolinska Institutet, Stockholm, Sweden.
BMC Med Res Methodol. 2022 May 2;22(1):130. doi: 10.1186/s12874-022-01597-7.
A relative survival approach is often used in population-based cancer studies, where other cause (or expected) mortality is assumed to be the same as the mortality in the general population, given a specific covariate pattern. The population mortality is assumed to be known (fixed), i.e. measured without uncertainty. This could have implications for the estimated standard errors (SE) of any measures obtained within a relative survival framework, such as relative survival (RS) ratios and the loss in life expectancy (LLE). We evaluated the existing approach to estimate SE of RS and the LLE in comparison to if uncertainty in the population mortality was taken into account.
The uncertainty from the population mortality was incorporated using parametric bootstrap approach. The analysis was performed with different levels of stratification and sizes of the general population used for creating expected mortality rates. Using these expected mortality rates, SEs of 5-year RS and the LLE for colon cancer patients in Sweden were estimated.
Ignoring uncertainty in the general population mortality rates had negligible (less than 1%) impact on the SEs of 5-year RS and LLE, when the expected mortality rates were based on the whole general population, i.e. all people living in a country or region. However, the smaller population used for creating the expected mortality rates, the larger impact. For a general population reduced to 0.05% of the original size and stratified by age, sex, year and region, the relative precision for 5-year RS was 41% for males diagnosed at age 85. For the LLE the impact was more substantial with a relative precision of 1286%. The relative precision for marginal estimates of 5-year RS was 3% and 30% and for the LLE 22% and 313% when the general population was reduced to 0.5% and 0.05% of the original size, respectively.
When the general population mortality rates are based on the whole population, the uncertainty in the estimates of the expected measures can be ignored. However, when based on a smaller population, this uncertainty should be taken into account, otherwise SEs may be too small, particularly for marginal values, and, therefore, confidence intervals too narrow.
在基于人群的癌症研究中，通常使用相对生存率方法，其中假定其他原因（或预期）死亡率与特定协变量模式下的一般人群死亡率相同。假定人群死亡率是已知的（固定的），即没有不确定性地测量。这可能会对相对生存率框架内获得的任何测量值的估计标准误差（SE）产生影响，例如相对生存率（RS）比和预期寿命损失（LLE）。我们评估了现有的方法来估计 RS 和 LLE 的 SE，并将其与考虑人群死亡率不确定性的情况进行了比较。
使用参数自举方法纳入人群死亡率的不确定性。在不同的分层水平和用于创建预期死亡率的一般人群大小下进行了分析。使用这些预期死亡率，估计了瑞典结肠癌患者的 5 年 RS 和 LLE 的 SE。
当预期死亡率基于整个一般人群（即居住在一个国家或地区的所有人）时，忽略一般人群死亡率的不确定性对 5 年 RS 和 LLE 的 SE 影响可以忽略不计（小于 1%）。然而，用于创建预期死亡率的人群越小，影响越大。对于预期死亡率降低到原始大小的 0.05%并按年龄、性别、年份和地区分层的一般人群，85 岁时诊断为男性的 5 年 RS 的相对精度为 41%。对于 LLE 的影响更为显著，相对精度为 1286%。当一般人群减少到原始大小的 0.5%和 0.05%时，5 年 RS 的边缘估计的相对精度分别为 3%和 30%，而 LLE 的相对精度分别为 22%和 313%。
当一般人群死亡率基于整个人群时，可以忽略预期测量值估计中的不确定性。然而，当基于较小的人群时，应考虑这种不确定性，否则 SE 可能太小，尤其是对于边缘值，因此置信区间可能太窄。
