A cross sectional population is defined as a population of living individuals at the sampling or observational time. Cross‐sectionally sampled data with binary disease outcome are commonly analyzed in observational studies for identifying how covariates correlate with disease occurrence. It is generally understood that cross‐sectional binary outcome is not as informative as longitudinally collected time‐to‐event data, but there is insufficient understanding as to whether bias can possibly exist in cross‐sectional data and how the bias is related to the population risk of interest. As the progression of a disease typically involves both time and disease status, we consider how the binary disease outcome from the cross‐sectional population is connected to birth‐illness‐death process in the target population. We argue that the distribution of cross‐sectional binary outcome is different from the risk distribution from the target population and that bias would typically arise when using cross‐sectional data to draw inference for population risk. In general, the cross‐sectional risk probability is determined jointly by the population risk probability and the ratio of duration of diseased state to the duration of disease‐free state. Through explicit formulas we conclude that bias can almost never be avoided from cross‐sectional data. We present age‐specific risk probability (ARP) and argue that models based on ARP offers a compromised but still biased approach to understand the population risk. An analysis based on Alzheimer's disease data is presented to illustrate the ARP model and possible critiques for the analysis results.

中文翻译：

---

观察性研究中具有二元疾病结果的横断面数据的复杂性和偏倚

横截面人口被定义为抽样或观察时间的活个体人口。具有二元疾病结果的横断面抽样数据通常在观察性研究中进行分析，以确定协变量如何与疾病发生相关。人们普遍认为，横断面二元结果不如纵向收集的事件发生时间数据提供的信息量大，但对于横断面数据中是否可能存在偏倚以及偏倚与人群的关系尚不清楚利息风险。由于疾病的进展通常涉及时间和疾病状态，我们考虑横断面人群的二元疾病结果如何与目标人群的出生疾病死亡过程相关联。我们认为，横断面二元结果的分布不同于目标人群的风险分布，并且在使用横断面数据推断人群风险时通常会出现偏差。一般来说，横截面风险概率是由人口风险概率和患病状态持续时间与无疾病状态持续时间之比共同决定的。通过明确的公式，我们得出结论，从横截面数据中几乎永远无法避免偏差。我们提出了特定年龄风险概率 (ARP)，并认为基于 ARP 的模型提供了一种妥协但仍然有偏见的方法来理解人口风险。提出了基于阿尔茨海默病数据的分析，以说明 ARP 模型和对分析结果的可能批评。