A Bayesian analysis of the two-period crossover design for clinical trials

Statisticians have been critical of the use of the two-period crossover designs for clinical trials because the estimate of the treatment difference is biased when the carryover effects of the two treatments are not equal. In the standard approach, if the null hypothesis of equal carryover effects is not rejected, data from both periods are used to estimate and test for treatment differences; if the null hypothesis is rejected, data from the first period alone are used. A Bayesian analysis based on the Bayes factor against unequal carryover effects is given. Although this Bayesian approach avoids the "all-or-nothing" decision inherent in the standard approach, it recognizes that with small trials it is difficult to provide unequivocal evidence that the carryover effects of the two treatments are equal, and thus that the interpretation of the difference between treatment effects is highly dependent on a subjective assessment of the reality or not of equal carryover effects.     

On the Role of Baseline Measurements for Crossover Designs under the Self and Mixed Carryover Effects Model

Summary .  It is well known that optimal designs are strongly model dependent. In this article, we apply the Lagrange multiplier approach to the optimal design problem, using a recently proposed model for carryover effects. Generally, crossover designs are not recommended when carryover effects are present and when the primary goal is to obtain an unbiased estimate of the treatment effect. In some cases, baseline measurements are believed to improve design efficiency. This article examines the impact of baselines on optimal designs using two different assumptions about carryover effects during baseline periods and employing a nontraditional crossover design model. As anticipated, baseline observations improve design efficiency considerably for two-period designs, which use the data in the first period only to obtain unbiased estimates of treatment effects, while the improvement is rather modest for three- or four-period designs. Further, we find little additional benefits for measuring baselines at each treatment period as compared to measuring baselines only in the first period. Although our study of baselines did not change the results on optimal designs that are reported in the literature, the problem of strong model dependency problem is generally recognized. The advantage of using multiperiod designs is rather evident, as we found that extending two-period designs to three- or four-period designs significantly reduced variability in estimating the direct treatment effect contrast.     

降钙素原在重症腹膜炎患者中的应用

目的:探讨降钙素原(PCT)在重症腹膜炎早期诊断和治疗效果判断中的临床意义。方法:选取2011年3月至2014年9月本院就诊的128例重症腹膜炎患者作为治疗组,并选取同期来我院体检的健康志愿者128例作为对照组,比较治疗组和对照组之间PCT水平;通过治疗后,比较好转组和恶化组患者之间PCT水平的差异。结果:治疗组患者治疗后各时段的PCT水平均显著高于对照组,差异有统计学意义(P0.05),治疗组患者的血清PCT水平在治疗后第1 d开始下降,于第1-3 d PCT水平下降速度较快,之后下降速度减缓。两组患者治疗后各时段PCT水平明显低于治疗前,且差异均具有统计学意义(P0.05)。好转组患者治疗后各时段PCT水平显著低于恶化组患者,差异具有统计学意义(P0.05),其中好转组患者血清PCT水平在治疗后第1 d开始下降,恶化组患者血清PCT水平在治疗后第1 d开始升高。与治疗前相比,好转组患者治疗后各时段PCT水平明显下降,而恶化组患者治疗后各时段PCT水平显著上升,且差异均具有统计学意义(P0.05)。结论:PCT水平不仅是重症腹膜炎的一个重要指示物,也是治疗效果的一个有效指标。     

A Note on the Analysis of the Two-Period Crossover Design When the Period-Treatment Interaction is Significant

In the analysis of a two-period crossover study Grizzle (1965) suggests that, if a preliminary test for a period by treatment interaction (residual effect, carryover effect) is significant at the 10 % level, the direct effects of the treatments should be compared by performing a t-test on the data from the first period only. In this note it is shown that under Grizzle's model the comparison of the direct treatment effects is equivalent to a Behrens-Fisher problem. Depending on one's viewpoint–Bayesian, fiducial, or sampling theory–different solutions are possible. The solutions are illustrated using three well-known data sets.     

Design and Analysis of Crossover Trials for Absorbing Binary Endpoints

Summary The crossover is a popular and efficient trial design used in the context of patient heterogeneity to assess the effect of treatments that act relatively quickly and whose benefit disappears with discontinuation. Each patient can serve as her own control as within‐individual treatment and placebo responses are compared. Conventional wisdom is that these designs are not appropriate for absorbing binary endpoints, such as death or HIV infection. We explore the use of crossover designs in the context of these absorbing binary endpoints and show that they can be more efficient than the standard parallel group design when there is heterogeneity in individuals' risks. We also introduce a new two‐period design where first period “survivors” are rerandomized for the second period. This design combines the crossover design with the parallel design and achieves some of the efficiency advantages of the crossover design while ensuring that the second period groups are comparable by randomization. We discuss the validity of the new designs and evaluate both a mixture model and a modified Mantel–Haenszel test for inference. The mixture model assumes no carryover or period effects while the Mantel–Haenszel approach conditions out period effects. Simulations are used to compare the different designs and an example is provided to explore practical issues in implementation.     

Non-linear dynamics models characterizing long-term virological data from AIDS clinical trials

Human immunodeficiency virus (HIV) dynamics represent a complicated variant of the text-book case of non-linear dynamics: predator-prey interaction. The interaction can be described as naturally reproducing T-cells (prey) hunted and killed by virus (predator). Virus reproduce and increase in number as a consequence of successful predation; this is countered by the production of T-cells and the reaction of the immune system. Multi-drug anti-HIV therapy attempts to alter the natural dynamics of the predator-prey interaction by decreasing the reproductive capability of the virus and hence predation. These dynamics are further complicated by varying compliance to treatment and insurgence of resistance to treatment. When following the temporal progression of viral load in plasma during therapy one observes a short-term (1-12 weeks) decrease in viral load. In the long-term (more than 12 weeks from the beginning of therapy) the reduction in viral load is either sustained, or it is followed by a rebound, oscillations and a new (generally lower than at the beginning of therapy) viral load level. Biomathematicians have investigated these dynamics by means of simulations. However the estimation of the parameters associated with the dynamics from real data has been mostly limited to the case of simplified, in particular linearized, models. Linearized model can only describe the short-term changes of viral load during therapy and can only predict (apparent) suppression. In this paper we put forward relatively simple models to characterize long-term virus dynamics which can incorporate different factors associated with resurgence: (Fl) the intrinsic non-linear HIV-1 dynamics, (F2) drug exposure and in particular compliance to treatment, and (F3) insurgence of resistant HIV-1 strains. The main goal is to obtain models which are mathematically identifiable given only measurements of viral load, while retaining the most crucial features of HIV dynamics. For the purpose of illustration we demonstrate an application of the models using real AIDS clinical trial data involving patients treated with a combination of anti-retroviral agents using a model which incorporates compliance data.     

丹参多酚酸盐联合凯时注射液治疗慢性肾功能哀竭的临床疗效观察

目的：观察丹参多酚酸盐联合凯时注射液治疗慢性肾功能哀竭（CRF）的临床疗效,探讨提高CRF临床疗效的措施。方法：选择2010年5月至2012年11月我院收治的CRF患者94例,在患者知情同意的前提下,将其随机均分为对照组（n=47例）和观察组（n=47例）,对照组给予常规治疗措施,观察组在以上治疗基础上加用丹参多酚酸盐联合凯时注射液治疗,治疗4周后比较两组患者肾功能指标、临床疗效及不良反应的发生情况。结果：治疗前,两组患者的BUN、Scr和Ccr比较,差异无统计学意义（均P〉0．05）;治疗4周后,两组的BUN、Scr水平均较治疗前显著下降,Ccr水平较治疗前显著升高,且观察组BUN、Scr水平明显低于对照组,而Ccr水平明显高于对照组,差异均具有统计学意义（均P〈0．05）。两组的临床总有效率分别为76．6％和91．5％,观察组显著高于对照组,差异具有统计学意义（均P〈0．05）。治疗过程中,两组不良反应的发生率比较差异无统计学意义（P〉0．05）。结论：丹参多酚酸盐联合凯时注射液辅助治疗CRF可提高临床疗效,且安全性高。     

前列地尔联合氯吡格雷治疗早期糖尿病肾病疗效观察

目的:观察前列地尔与氯吡格雷联合治疗早期糖尿病肾病(DN)的临床疗效。方法:选择我院2013年10月至2014年10月期间收治的早期DN患者120例为研究对象,采用随机数表法将患者随机分为观察组62例和对照组58例,两组患者均给予血管紧张素受体拮抗剂(ARB)或血管紧张素转化酶抑制剂(ACEI)类药物1个月后,对照组给予前列地尔治疗,观察组给予前列地尔联合氯吡格雷治疗,两组患者均进行20d的治疗,观察并比较两组患者治疗前后β2-微球蛋白(β2-MG)、尿微量白蛋白(U-malb)、高敏C反应蛋白(hs-CRP)、尿素氮(BUN)、血肌酐(Cr)、平均动脉压(MPA),全血低切边率、全血高切变率、血浆粘滞度、血小板聚集率的变化情况及不良反应的发生情况。结果:治疗前两组患者间各项指标比较差异均无统计学意义(P0.05);治疗后两组患者β2-MG、U-malb、hs-CRP、血浆粘滞度、全血粘滞度、血小板聚集率较治疗前均出现明显降低,且观察组患者各项指标均低于对照组,差异均有统计学意义(P0.05);治疗前后两组患者Cr、BUN、MPA水平均未发生明显变化(P0.05);两组患者均未发生严重并发症。结论:早期DN患者给予前列地尔联合氯吡格雷治疗可以降低其尿蛋白,减轻炎症反应,缓解疾病进展,具有明显的临床疗效。     

Crossover Designs with Random Periods

Crossover experiments usually are modelled with fixed treatment, carryover, and period effects while the effects of subjects are assumed to be random. In actual realisations of crossover experiments however periods are quite arbitrary intervals of time, depending on administrative affairs for instance and possibly they are even varying from subject to subject. Modelling these arbitrary periods as random effects either globally for all subjects or individually for each one seems to be more adequate than the assumption of fixed period effects. This paper is concerned with the two treatments, two periods crossover design. It is described that—in spite of the somewhat involved covariance structure—the estimators and tests developed for models with fixed period effects remain valid for models with random effects for periods provided that no treatment X period interaction exists.     

血液透析滤过治疗维持性血液透析患者顽固性高血压的临床观察

目的分析血液透析滤过治疗维持性血液透析患者顽固性高血压的临床效果。方法选取2015年1月~2017年2月我院收治的维持性血液透析顽固性高血压患者46例,随机分为对照组与研究组,每组23例。对照组行常规血液透析治疗,研究组采用血液透析滤过方式,观察比较两组患者治疗前后的血压、血浆RA水平及AngII水平变化情况。结果治疗后,研究组的收缩压与舒张压均明显低于对照组(P0.05),血浆RA、AngII水平亦明显低于对照组(P0.05)。结论血液透析滤过治疗维持性血液透析患者顽固性高血压的效果显著,值得临床推广应用。     

Using post-grazing sward height to impose dietary restrictions of varying duration in early lactation: its effects on spring-calving dairy cow production

The objective of this study was to investigate the immediate and carryover effects of imposing two post-grazing sward heights (PGSH) for varying duration during early lactation on sward characteristics and dairy cow production. The experiment was a randomised block design with a 2×2 factorial arrangement of treatments. A total of 80 spring-calving (mean calving date – 6 February) dairy cows were randomly assigned, pre-calving, to one of the two (n=40) PGSH treatments – S (2.7 cm) and M (3.5 cm) – from 13 February to 18 March, 2012 (P1). For the subsequent 5-week period (P2: 19 March to 22 April, 2012), half the animals from each P1 treatment remained on their treatment, whereas the other half of the animals switched to the opposing treatment. Following P2, all cows were managed similarly for the remainder of the lactation (P3: 23 April to 4 November, 2012) to measure the carryover effect. Milk production, BW and body condition score were measured weekly, and grass dry matter intake (GDMI) was measured on four occasions – approximately weeks 5, 10, 15 and 20 of lactation. Sward utilisation (above 2.7 cm; P1 and P2) was significantly improved by reducing the PGSH from 3.5 (0.83) to 2.7 cm (0.96). There was no effect of PGSH on cumulative annual grass dry matter (DM) production (15.3 t DM/ha). Grazing to 2.7 cm reduced GDMI by 1.7 and 0.8 kg DM/cow in P1 and P2, respectively, when compared with 3.5 cm (13.3 and 14.0 kg/cow per day, respectively). Cows grazing to 2.7 cm for both P1 and P2 (SS) tended to have reduced cumulative 10-week milk yield (−105 kg) and milk solids yield (−9 kg) when compared with cows grazing to 3.5 cm for both periods (MM; 1608 and 128 kg/cow, respectively). Treatments that alternated PGSH at the end of P1, SM and MS had intermediate results. There was no interaction between P1 and P2 treatments. There was also no carryover effect of early lactation grazing regime on milk and milk solids production in P3, given the reduction in early lactation milk yield. The results indicate that the diet of dairy cows should not be restricted by imposing a severe PGSH for all of the first 10 weeks of lactation, cows should graze to 3.5 cm for at least 5 of these weeks.     

Carryover effects and climatic conditions influence the postfledging survival of greater sage‐grouse

Prebreeding survival is an important life history component that affects both parental fitness and population persistence. In birds, prebreeding can be separated into pre‐ and postfledging periods; carryover effects from the prefledging period may influence postfledging survival. We investigated effects of body condition at fledging, and climatic variation, on postfledging survival of radio‐marked greater sage‐grouse (Centrocercus urophasianus) in the Great Basin Desert of the western United States. We hypothesized that body condition would influence postfledging survival as a carryover effect from the prefledging period, and we predicted that climatic variation may mediate this carryover effect or, alternatively, would act directly on survival during the postfledging period. Individual body condition had a strong positive effect on postfledging survival of juvenile females, suggesting carryover effects from the prefledging period. Females in the upper 25th percentile of body condition scores had a postfledging survival probability more than twice that (Φ = 0.51 ± 0.06 SE) of females in the bottom 25th percentile (Φ = 0.21 ± 0.05 SE). A similar effect could not be detected for males. We also found evidence for temperature and precipitation effects on monthly survival rates of both sexes. After controlling for site‐level variation, postfledging survival was nearly twice as great following the coolest and wettest growing season (Φ = 0.77 ± 0.05 SE) compared with the hottest and driest growing season (Φ = 0.39 ± 0.05 SE). We found no relationships between individual body condition and temperature or precipitation, suggesting that carryover effects operated independently of background climatic variation. The temperature and precipitation effects we observed likely produced a direct effect on mortality risk during the postfledging period. Conservation actions that focus on improving prefledging habitat for sage‐grouse may have indirect benefits to survival during postfledging, due to carryover effects between the two life phases.     

Sequential Testing with Recurrent Events over Multiple Treatment Periods

Recurrent event outcomes are adopted increasingly often as a basis for evaluating experimental interventions. In clinical trials involving recurrent events, patients are frequently observed for a baseline period while under standard care, and then randomised to receive either an experimental treatment or continue on standard care. When events are generated according to a mixed Poisson model, having baseline data permits a conditional analysis which can eliminate the subject-specific random effect and yield a more efficient analysis regarding treatment effect. When studies are expected to recruit a large number of patients over an extended period of accrual, or if the period of follow-up is long, sequential testing is desirable to ensure the study is stopped as soon as sufficient data have been collected to establish treatment benefits. We describe methods which facilitate sequential analysis of data arising from trials with recurrent event responses observed over two treatment periods where one is a baseline period of observation. Formulae to help schedule analyses at approximately equal increments of information are given. Simulation studies show that the sequential testing procedures have rejection rates compatible with the nominal error rates under the null and alternative hypotheses. Data from a trial of patients with herpes simplex virus infection are analysed to illustrate the utility of these methods.     

Comparing Trials with Multiple Outcomes: The Multivariate One-Sided Hypothesis with Unknown Covariances

The paper deals with a problem arising for tests in clinical trials. The outcomes of a standard and a new treatment to be compared are multivariate normally distributed with common but unknown covariance matrix. Under the null hypothesis the means of the outcomes are equal, under the alternative the new treatment is assumed to be superior, i.e. the means are larger without further quantification. For known covariance matrix there is a variety of tests for this problem. Some of these procedures can be extended to the case of unknown covariances if one is willing to accept a bias. There is, however, also an efficient unbiased test. The paper contains some numerical comparisons of these different procedures and takes a look on the minimax properties of the unbiased test.     

东菱迪芙治疗急性脑梗死的效果观察

目的探讨东菱迪芙治疗急性脑梗死的临床疗效及安全性。方法随机将收治的80例急性脑梗死患者分为治疗组40例,对照组40例。两组均给予抗血小板聚集、钙拮抗剂等基础治疗,并将血塞通0．25g加入生理盐水或5％葡萄糖液250ml中静脉点滴,连用14天。在此基础上,治疗组于治疗第1、3、5日给予东菱迪芙10u、5u、5u加入生理盐水250ml中静滴,每次滴注时间不少于1h。观察两组疗效、治疗前后神经功能缺损评分及治疗前后血浆FIB水平。结果治疗组显效率（75．00％）明显优于对照组（47．50％）,χ2=6．37,P〈0．05;神经功能缺损评分明显低于对照组（P〈0．05或0．01）;治疗组FIB由治疗前（3.98±0．86）g／L降至（1．84±0．42）g／L,治疗前后比较有显著性差异（P〈0．01）。结论东菱迪芙通过降低血浆FIB,增强纤溶活性,降低血粘度,改善脑循环等综合作用,对治疗急性脑梗死疗效显著、安全性好,值得推广应用。     

承气活血通腑汤联合穴位贴敷治疗粘连性肠梗阻的疗效及对胃肠功能和血清炎性因子的影响

目的:探讨承气活血通腑汤联合穴位贴敷治疗粘连性肠梗阻的疗效及对胃肠功能和血清炎性因子的影响。方法:选取2018年2月到2020年7月期间于我院接受诊治的粘连性肠梗阻患者60例。分组方法采用随机数字表法,将入选患者分为对照组(n=30,常规治疗)、研究组(n=30,对照组的基础上给予承气活血通腑汤联合穴位贴敷治疗),对比两组疗效、胃肠功能、炎性因子、住院时间、住院费用、临床症状评分。结果:研究组的临床总有效率较对照组高(P<0.05)。两组治疗12d后血清降钙素原(PCT)、C反应蛋白(CRP)水平较治疗前降低,且研究组较对照组低(P<0.05)。两组治疗12d后腹部胀痛、排便排气、恶心呕吐、口苦口干评分较治疗前降低,且研究组较对照组低(P<0.05)。研究组胃管拔除时间、恢复正常饮食时间均短于对照组(P<0.05)。研究组住院时间短于对照组,住院费用少于对照组(P<0.05)。结论:承气活血通腑汤联合穴位贴敷治疗粘连性肠梗阻的疗效确切,可改善患者临床症状和胃肠功能,促进患者早日恢复,减少住院费用,降低机体炎性因子水平。     

董氏指压法治疗积滞患儿的临床疗效及对血清Ghrelin水平和胃肠动力的影响

目的:探讨董氏指压法治疗积滞患儿临床疗效及对血清Ghrelin水平和胃肠动力的影响。方法:选取2015年12月-2016年12月上海中医药大学附属岳阳中西医结合医院儿科收治的积滞乳食内积证患儿120例作为研究对象,按随机数字表法分为两组,其中治疗组60例予以董氏指压法,对照组60例予以针刺四缝,两组均治疗8周。比较两组治疗前后血清Ghrelin水平以及胃半排空时间、胃窦收缩频次,并对比两组的临床疗效。结果:治疗组总有效率为98.33%(59/60),与对照组的95.00%(57/60)比较无统计学差异(P0.05)。两组治疗4周后、8周后胃半排空时间均显著低于治疗前,而胃窦收缩频次以及血清Ghrelin水平均显著高于治疗前(均P0.05),且治疗组治疗4周后、8周后胃半排空时间显著低于对照组(均P0.05),治疗8周后治疗组胃窦收缩频次和血清Ghrelin水平显著高于对照组,差异均有统计学意义(均P0.05)。结论:董氏指压法治疗小儿积滞的疗效良好,可显著升高血清Ghrelin水平,增进食欲,改善胃肠蠕动,值得临床推广。     

连续性血液净化治疗对急性胰腺炎的临床效果和预后状况分析

目的:探讨连续性血液净化(CBP)对急性胰腺炎(AP)的治疗效果及预后的影响。方法:选取2010年1月至2016年12月间我院1200例AP患者作为研究对象,按照随机数字表法分为常规治疗组及CBP治疗组,每组600例。常规治疗组接受常规药物治疗,CBP治疗组在常用药物治疗的基础上联合应用CBP治疗。对比治疗后两组患者临床症状消失时间以及治疗前、治疗后72h炎性因子水平变化情况和肠道功能变化情况,并对比两组治疗后7 d的死亡率。结果:CBP治疗组治疗后的腹痛消失时间、腹胀消失时间及腹部压痛消失时间均低于常规治疗组(P0.05)。两组治疗前内毒素、C反应蛋白(CRP)、淀粉酶(AMS)、二胺氧化酶及丙二醛比较无统计学差异(P0.05);治疗后72 h,内毒素、CRP、AMS、二胺氧化酶及丙二醛水平均较治疗前降低,且CBP治疗组低于常规治疗组(P0.05)。治疗后7 d CBP治疗组死亡率低于常规治疗组,差异具有统计学意义(P0.05)。结论:CBP可有效的提高AP的临床治疗效果,并改善患者的临床预后。     

r-tpa合并甘露醇治疗血管壁病变性脑梗死的临床疗效分析

目的:观察r-tpa合并甘露醇治疗血管壁病变性脑梗死临床疗效。方法:将临床发病6 h以内的急性脑梗死患者随机分为治疗组与对照组,每组60例,治疗组用r-tpa合并甘露醇静脉滴注,对照组用川芎嗪注射液静脉滴注,对治疗组和对照组连续使用15天观察对照组和治疗组的临床疗效及神经功能恢复情况。结果:采用r-tpa合并甘露醇静脉滴注和川芎嗪静脉注射液疗效比较,治疗组总有效率93.33%,明显优于常规治疗组78.33%,两组差异有统计学意义(P0.05)。两组患者治疗后CSS评分均显著低于治疗前,且治疗组明显低于对照组(P0.05);两组患者治疗后ADL评分均显著高于治疗前,且治疗组明显高于对照组(P0.05)。结论:r-tpa合并甘露醇治疗血管壁病变性脑梗死临床疗效显著,且对6个小时内没有出血倾向的血管病变性脑梗死安全实用,患者后期恢复效果良好。     

非布司他对急性痛风性关节炎患者血清SUA水平及氧化应激的影响

目的:研究非布司他治疗急性痛风性关节炎(AGA)患者的临床疗效及对血清尿酸(SUA)水平及氧化应激的影响。方法:研究对象选取我院2014年6月到2016年10月收治的200例AGA患者,采用随机数字法将其分为对照组和观察组,每组各100例。对照组患者口服别嘌呤醇治疗,观察组患者口服非布司他治疗,均连续治疗24周。比较两组患者治疗前后各时间点的血清SUA、8-羟基脱氧鸟苷(8-OHdG)、3-硝基络氨酸修饰蛋白(3-NT)、甘油三酯(TG)、总胆固醇(TC)、低密度脂蛋白(LDL)、高密度脂蛋白(HDL)水平的变化。结果:治疗后,观察组各时间点的血清SUA、8-OHdG和3-NT水平均明显低于对照组(P0.01)。治疗后,对照组患者的血清TG、TC、HDL、LDL水平较治疗前无明显变化(P0.05),观察组患者的血清TG水平明显低于治疗前(P0.01),血清HDL水平明显高于治疗前(P0.01),而血清TC和LDL水平比较无明显差异(P0.05)。结论:非布司他治疗AGA的疗效明显,能有效降低血清SUA水平,抑制氧化应激状态,并能改善血脂代谢。