Parameter estimates of the joint model.

One of the key tools to understand and reduce the spread of the SARS-CoV-2 virus is testing. The total number of tests, the number of positive tests, the number of negative tests, and the positivity rate are interconnected indicators and vary with time. To better understand the relationship between these indicators, against the background of an evolving pandemic, the association between the number of positive tests and the number of negative tests is studied using a joint modeling approach. All countries in the European Union, Switzerland, the United Kingdom, and Norway are included in the analysis. We propose a joint penalized spline model in which the penalized spline is reparameterized as a linear mixed model. The model allows for flexible trajectories by smoothing the country-specific deviations from the overall penalized spline and accounts for heteroscedasticity by allowing the autocorrelation parameters and residual variances to vary among countries. The association between the number of positive tests and the number of negative tests is derived from the joint distribution for the random intercepts and slopes. The correlation between the random intercepts and the correlation between the random slopes were both positive. This suggests that, when countries increase their testing capacity, both the number of positive tests and negative tests will increase. A significant correlation was found between the random intercepts, but the correlation between the random slopes was not significant due to a wide credible interval.

检测是理解并遏制严重急性呼吸综合征冠状病毒2型（SARS-CoV-2）传播的关键手段之一。检测总人次、阳性检测数、阴性检测数以及阳性率均为相互关联的指标，且随时间动态变化。为更好地明晰此类指标间的关联关系，在持续演变的新冠疫情背景下，本研究采用联合建模方法探究阳性检测数与阴性检测数之间的相关性。本分析纳入欧盟所有成员国、瑞士、英国以及挪威。本研究提出一种联合惩罚样条（penalized spline）模型，该模型将惩罚样条重新参数化为线性混合模型。该模型通过平滑各国家相对于整体惩罚样条的偏差，实现灵活的轨迹拟合；同时通过允许自相关参数与残差方差在各国间存在差异，解决了异方差性问题。阳性检测数与阴性检测数之间的相关性由随机截距与随机斜率的联合分布推导得出。随机截距间的相关性与随机斜率间的相关性均为正值，这表明当各国提升检测能力时，阳性检测数与阴性检测数均会随之增加。研究发现随机截距间的相关性具有统计学显著性，但由于可信区间较宽，随机斜率间的相关性未达到显著水平。