Stanley Christopher C, Kazembe Lawrence N, Buchwald Andrea G, Mukaka Mavuto, Mathanga Don P, Hudgens Michael G, Laufer Miriam K, Chirwa Tobias F
School of Public Health, Faculty of Health Sciences, University of the Witwatersrand, Johannesburg, South Africa.
Malaria Alert Center, University of Malawi College of Medicine, Blantyre, Malawi.
J Med Stat Inform. 2019;7. doi: 10.7243/2053-7662-7-1.
In malaria endemic areas such as sub-Saharan Africa, repeated exposure to malaria results in acquired immunity to clinical disease but not infection. In prospective studies, time-to-clinical malaria and longitudinal parasite count trajectory are often analysed separately which may result in inefficient estimates since these two processes can be associated. Including parasite count as a time-dependent covariate in a model of time-to-clinical malaria episode may also be inaccurate because while clinical malaria disease frequently leads to treatment which may instantly affect the level of parasite count, standard time-to-event models require that time-dependent covariates be external to the event process. We investigated whether jointly modelling time-to-clinical malaria disease and longitudinal parasite count improves precision in risk factor estimates and assessed the strength of association between the hazard of clinical malaria and parasite count.
Using a cohort data of participants enrolled with uncomplicated malaria in Malawi, a conventional Cox Proportional Hazards (PH) model of time-to-first clinical malaria episode with time-dependent parasite count was compared with three competing joint models. The joint models had different association structures linking a quasi-Poisson mixed-effects of parasite count and event-time Cox PH sub-models.
There were 120 participants of whom 115 (95.8%) had >1 follow-up visit and 100 (87.5%) experienced the episode. Adults >15 years being reference, log hazard ratio for children <5 years was 0.74 (95% CI: 0.17, 1.26) in the joint model with best fit vs. 0.62 (95% CI: 0.04, 1.18) from the conventional Cox PH model. The log hazard ratio for the 5-15 years was 0.72 (95% CI: 0.22, 1.22) in the joint model vs.0.63 (95% CI: 0.11, 1.17) in the Cox PH model. The area under parasite count trajectory was strongly associated with the risk of clinical malaria, with a unit increase corresponding to-0.0012 (95% CI: -0.0021, -0.0004) decrease in log hazard ratio.
Jointly modelling longitudinal parasite count and time-to-clinical malaria disease improves precision in log hazard ratio estimates compared to conventional time-dependent Cox PH model. The improved precision of joint modelling may improve study efficiency and allow for design of clinical trials with relatively lower sample sizes with increased power.
在撒哈拉以南非洲等疟疾流行地区，反复接触疟疾会导致对临床疾病产生获得性免疫，但不会预防感染。在前瞻性研究中，临床疟疾发病时间和纵向寄生虫计数轨迹通常分别进行分析，这可能会导致估计效率低下，因为这两个过程可能存在关联。在临床疟疾发作时间模型中，将寄生虫计数作为时间依存性协变量纳入也可能不准确，因为虽然临床疟疾疾病常常导致治疗，这可能会立即影响寄生虫计数水平，但标准的生存时间模型要求时间依存性协变量独立于事件过程。我们研究了对临床疟疾发病时间和纵向寄生虫计数进行联合建模是否能提高危险因素估计的精度，并评估了临床疟疾风险与寄生虫计数之间的关联强度。
利用马拉维非复杂性疟疾患者的队列数据，将首个临床疟疾发作时间的传统Cox比例风险（PH）模型与包含时间依存性寄生虫计数的模型，与三个相互竞争的联合模型进行比较。联合模型具有不同的关联结构，将寄生虫计数的拟泊松混合效应与事件时间Cox PH子模型联系起来。
共有120名参与者，其中115名（95.8%）有一次以上的随访，100名（87.5%）经历了发病。以15岁以上成年人作为参照，在拟合度最佳的联合模型中，5岁以下儿童log风险比为0.74（95%CI：0.17，1.26），而传统Cox PH模型为0.62（95%CI：0.04，1.18）。5至15岁儿童在联合模型中的log风险比为0.72（95%CI：0.22，1.22），在Cox PH模型中为0.63（95%CI：0.11，1.17）。寄生虫计数轨迹下的面积与临床疟疾风险密切相关，单位增加对应log风险比降低-0.0012（95%CI：-0.0021，-0.0004）。
与传统的时间依存性Cox PH模型相比，对纵向寄生虫计数和临床疟疾发病时间进行联合建模可提高log风险比估计的精度。联合建模提高的精度可能会提高研究效率，并允许设计样本量相对较小但效能更高的临床试验。
