| Backgrounds and ObjectivesHierarchical data,also known as multilevel 'data,are very common in medical research,such as large-scale epidemiological studies using multi-stage cluster sampling design,or intervention comparative studies with cluster randomized trial design.The hierarchical data are characterized by the intra-cluster correlation.Hierarchical models are commonly used to analyze multilevel data.There are substantially fewer studies on methods for analyzing hierarchical survival data compared with those on approaches for analyzing continuous or discrete multilevel data(i.e.,generalized linear multilevel models).The frailty model is one of the most popular hierarchical survival models and able to handle multiple types of hierarchical survival data,such as elustered data and recurrent events.The Cox shared frailty model,which is a semiparametric model,is the most commonly used one.Compared with parametric frailty models,semiparametric frailty models are not required to specify the baseline hazard function and may not take full advantage of data,which may lead to a compromise of estimation accuracy and efficiency.It is unclear whether Cox shared frailty models are comparable with parametric shared frailty models from the perspective of effect estimation and hypothesis test.With Monte Carlo simulation,the first part of this thesis aims to compare the accuracy,efficiency and robustness of Cox and parametric shared frailty models under different simulated scenarios(various total sample sizes and cluster sizes,varying censoring levels and degrees of correlation)In the second part,we illustrate the application of frailty models using follow-up data of a large-scale epidemiological study with multi-stage cluster sampling.Individuals spend about a third of their lives sleeping.Sleep is essential to human health and is increasingly recognized as an important lifestyle behavior that can affect cardiovascular diseases(CVDs)and deaths.Previous studies on the association of sleep and CVDs or deaths were mostly from certain countries or regions and the results were controversial.This part of the thesis aims to examine the associations of estimated total sleep duration and daytime naps with deaths or major cardiovascular events based on a population cohort from 21 high-,middle-,and low-income countries.MethodsFor the model comparative study,Monte Carlo simulation was used to generate the two-level survival data that meet different scenario settings,and the Cox and parametric shared frailty model were compared in each simulated scenario from the perspective of effect estimation and hypothesis test.All the scenarios depend on four factors including the total sample size and cluster size,denoted by N(200,500)and k(50,25,10)respectively,censoring level c(10%,30%,50%),and intra-cluster correlation,indicated by Kendall,s ?(0.2,0.5,0.6).For each scenario we conducted 1000 simulations.Performance measures are as follows:the mean of fixed-effect regression coefficient estimations and its standard error,average percent relative bias(bias%)and mean squared error(MSE)as accuracy measures,the mean of parameter estimations of frailty distributions,empirical coverage,power or type I error as hypothesis-testing measures.For the association study,data were obtained from the Prospective Urban Rural Epidemiological Study(PURE),which used a multi-stage cluster sampling approach to recruit individuals aged 35-70 from 21 high-,middle-,and low-income countries,Baseline recruitment began in 2003,and standardized questionnaires or case report forms 'were used to collect data and do all follow-up events adjudication.A total of 116,632 participants were included in the analysis.Until September 2017,the median follow-up time was 7.8 years(interquartile range:5.1-9.2 years).The estimated nocturnal sleep duration is defined as the time interval between bedtime and wake-up time.The napping duration is estimated by self-reported daytime sleep time.Total daily sleep duration is estimated by the sum of the two parameters.The primary outcome is time to death plus major cardiovascular events(defined as fatal cardiovascular events and non-fatal myocardial infarction,stroke,and heart failure).The Cox shared frailty model was used to assess the associations of estimated total daily sleep duration and daytime naps with events.We also explored whether the associations were consistent in different regions of world.In addition,sensitivity analyses were performed to further examine the robustness of the associations.Re^ultsThe simulation results are summarized as follows:(1)When the true fixed effect value p is not O,that is hazard ratio(HR)?1,in all scenarios,the regression coefficients of the Cox shared frailty model(hereinafter referred to as"Cox model")and the Weibull shared frailty model(hereinafter referred to as "Weibullmoder")are both well estimated,with the bias%below 5%and the MSE less than 0.05.The differences of bias%and MSE between the two models are<1.5%and<0.01,respectively,indicating the equivalent accuracy.In the case that N=200,the power of the Weibull model is a little better than the Cox model(2%or so).This subtle difference reduces to<0.5%as N increases to 500.The parameter ? of frailty distribution gets slightly better estimation in Cox model,closer to the true value.The accuracy of fixed effect estimation and power slightly increase with the increase of the cluster size and the decrease of the censoring proportion for both models,while the accuracy of 0 estimation relatively decreases.The intra-cluster correlation has little effect on the parameter estimation but might weaken the power.(2)When the true fixed effect value P equals 0,that is HR=1,the MSEs of regression coefficient estimations in both models are<0.05 and their differences are very small(<0.001),leading to the comparable accuracy.Mostly,? is better estimated in Cox model.Type ? error rate of both models meets expectations(around 0.05)in most scenarios,although it is slightly smaller in certain cases.The difference of Type ? error rate between the two models is within 0.005.The increase of the cluster size and the reduction of the censoring proportion can improve the accuracy of regression coefficient estimations in both models,while the intra-cluster correlation has little influence on the estimation of the model parameters.In the epidemiological study,we recorded 4381 deaths and 4365 major cardiovascular events until September 2017.We observed a J-shaped association between estimated total sleep duration and the composite outcome.To be specific,taking 6-8 hours of sleep per day as reference,after adjusting for demographic characteristics,lifestyle behaviors and health status,longer sleep duration was associated with increased risk of composite outcome and a significant trend for a greater risk of composite events was observed as sleep time increased(HR of 1.05[0.99-1.12],1.17[1.09-1.25]and 1.41[1.30-1.53]for 8-9h/day,9-10h/day and>10h/day respectively,P for trend<0.0001);people who slept no more than 6 hours per day showed a non-significant trend for higher risk of composite outcome(HR of 1.09[0.99-1.20]).The results were consistent in regions with different sleep patterms(whether daytime naps are common or not).It also showed the similar pattern for each of deaths and major cardiovascular events.The results of sensitivity analyses were unchanged.In addition,compared with not taking naps,daytime naps were associated with a graded increased risk of composite outcome(HR of 1.13[1.07-1.20]and 1.31[1.21-1.43]for 0-1h/day and>lh/day)in those with sufficient or longer nocturnal sleep(>6h per night)but not in those who lacked sleep at night(?6h per night).ConclusionsThe semi-parametric Cox shared frailty model is comparable with the parametric shared frailty model in handling hierarchical survival data,without a compromise of the accuracy and efficiency.In studies with large sample sizes,the Cox shared frailty model is a good choice for analyzing hierarchical survival data.It shows a J-shaped association between estimated 24-hour sleep duration and deaths plus major cardiovaseular events,with those who sleep about 6-8 hours a day having the lowest risk.Daytime naps are associated with increased risk of all-cause mortality and major cardiovascular events among those with>6h of nocturnal sleep but not among those sleeping ?6h/night. |
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