Dynamic comparison of Kaplan-Meier proportions: monitoring a randomized clinical trial with a long-term binary endpoint.

The approach to early termination for efficacy in a trial where events occur over time but the primary question of interest relates to a long-term binary endpoint is not straightforward. This article considers comparison of treatment groups with Kaplan-Meier (KM) proportions evaluated at increasing times from randomization, at increasing calendar testing times. This strategy is employed to improve the ability to detect important treatment effects and provide critical treatments to patients in a timely manner. This dynamic Kaplan-Meier (DKM) approach is shown to be robust; that is, it produces high power and early termination time across a wide range of circumstances. In contrast, a fixed time KM comparison and the log-rank test are both shown to be more variable in performance. Practical considerations of implementing the DKM method are discussed.     

Implementation of group sequential logrank tests in a maximum duration trial

To control the Type I error probability in a group sequential procedure using the logrank test, it is important to know the information times (fractions) at the times of interim analyses conducted for purposes of data monitoring. For the logrank test, the information time at an interim analysis is the fraction of the total number of events to be accrued in the entire trial. In a maximum information trial design, the trial is concluded when a prespecified total number of events has been accrued. For such a design, therefore, the information time at each interim analysis is known. However, many trials are designed to accrue data over a fixed duration of follow-up on a specified number of patients. This is termed a maximum duration trial design. Under such a design, the total number of events to be accrued is unknown at the time of an interim analysis. For a maximum duration trial design, therefore, these information times need to be estimated. A common practice is to assume that a fixed fraction of information will be accrued between any two consecutive interim analyses, and then employ a Pocock or O'Brien-Fleming boundary. In this article, we describe an estimate of the information time based on the fraction of total patient exposure, which tends to be slightly negatively biased (i.e., conservative) if survival is exponentially distributed. We then present a numerical exploration of the robustness of this estimate when nonexponential survival applies. We also show that the Lan-DeMets (1983, Biometrika 70, 659-663) procedure for constructing group sequential boundaries with the desired level of Type I error control can be computed using the estimated information fraction, even though it may be biased. Finally, we discuss the implications of employing a biased estimate of study information for a group sequential procedure.     

Statistical Properties of the Number of Recombination Events in the History of a Sample of DNA Sequences

Some statistical properties of samples of DNA sequences are studied under an infinite-site neutral model with recombination. The two quantities of interest are R, the number of recombination events in the history of a sample of sequences, and RM, the number of recombination events that can be parsimoniously inferred from a sample of sequences. Formulas are derived for the mean and variance of R. In contrast to R, RM can be determined from the sample. Since no formulas are known for the mean and variance of RM, they are estimated with Monte Carlo simulations. It is found that RM is often much less than R, therefore, the number of recombination events may be greatly under-estimated in a parsimonious reconstruction of the history of a sample. The statistic RM can be used to estimate the product of the recombination rate and the population size or, if the recombination rate is known, to estimate the population size. To illustrate this, DNA sequences from the Adh region of Drosophila melanogaster are used to estimate the effective population size of this species.     

Estimation of temporal gait parameters using Bayesian models on acceleration signals

The purpose of this study is to develop a system capable of performing calculation of temporal gait parameters using two low-cost wireless accelerometers and artificial intelligence-based techniques as part of a larger research project for conducting human gait analysis. Ten healthy subjects of different ages participated in this study and performed controlled walking tests. Two wireless accelerometers were placed on their ankles. Raw acceleration signals were processed in order to obtain gait patterns from characteristic peaks related to steps. A Bayesian model was implemented to classify the characteristic peaks into steps or nonsteps. The acceleration signals were segmented based on gait events, such as heel strike and toe-off, of actual steps. Temporal gait parameters, such as cadence, ambulation time, step time, gait cycle time, stance and swing phase time, simple and double support time, were estimated from segmented acceleration signals. Gait data-sets were divided into two groups of ages to test Bayesian models in order to classify the characteristic peaks. The mean error obtained from calculating the temporal gait parameters was 4.6%. Bayesian models are useful techniques that can be applied to classification of gait data of subjects at different ages with promising results     

Sample size and power for the weighted log-rank test and Kaplan-Meier based tests with allowance for nonproportional hazards

Asymptotic distributions under alternative hypotheses and their corresponding sample size and power equations are derived for nonparametric test statistics commonly used to compare two survival curves. Test statistics include the weighted log-rank test and the Wald test for difference in (or ratio of) Kaplan-Meier survival probability, percentile survival, and restricted mean survival time. Accrual, survival, and loss to follow-up are allowed to follow any arbitrary continuous distribution. We show that Schoenfeld's equation—often used by practitioners to calculate the required number of events for the unweighted log-rank test—can be inaccurate even when the proportional hazards (PH) assumption holds. In fact, it can mislead one to believe that 1:1 is the optimal randomization ratio (RR), when actually power can be gained by assigning more patients to the active arm. Meaningful improvements to Schoenfeld's equation are made. The present theory should be useful in designing clinical trials, particularly in immuno-oncology where nonproportional hazards are frequently encountered. We illustrate the application of our theory with an example exploring optimal RR under PH and a second example examining the impact of delayed treatment effect. A companion R package npsurvSS is available for download on CRAN.     

重组人血管内皮抑制素联合顺铂化疗治疗老年晚期非小细胞肺癌的临床疗效

目的:分析重组人血管内皮抑制素联合顺铂化疗方案治疗老年晚期非小细胞肺癌(NSCLC)的疗效和安全性。方法:选取82例老年晚期NSCLC患者作为研究对象,应用随机数字表将患者分为观察组和对照组,每组各41例。对照组患者给予含顺铂的两药化疗方案进行治疗,观察组患者在对照组疗法的基础上加用重组人血管内皮抑制素治疗。对两组患者的临床疗效、临床有效率(CRR)、临床受益率(CBR)进行评价。对两组患者治疗前后的Karnofsky评分、血清癌胚抗原(CEA)水平变化进行观察和比较。对两组患者进行随访,对患者的总生存期(OS)和疾病进展时间(TTP)进行观察和比较。对两组患者治疗期间不良反应发生率进行观察和比较。结果:观察组患者CRR和CBR均显著高于对照组,差异均有统计学意义(P0.05)。两组患者治疗前、后Karnofsky评分的上升幅度和血清CEA水平的下降幅度的差异无统计学意义(P0.05)。观察组患者和对照组患者的OS中位数估计值分别为16.720月和14.590月,TTP中位数估计值分别为6.260月和4.770月,两组患者OS和TTP中位数估计值的差异均有统计学意义(P0.05)。两组患者不良反应发生率差异无统计学意义(P0.05)。结论:在老年晚期NSCLC患者的治疗中,在含顺铂治疗方案基础上加用重组人血管内皮抑制素进行治疗,能够提高患者的临床受益和治疗有效率,延长患者的生存期,改善患者的预后,且未增加不良反应的发生率。     

The misuse of the three-point cross for estimating chiasma interference

The building of genetic maps in diploid organisms by crosses between different genotypes and estimation of recombination frequencies from the obtained segregation data has been successfully used since a very young step in the birth of genetics. The three-point cross methodology has facilitated this task and has demonstrated at the same time that genetic distances are not additive, as some recombinant products are not recognised in the progeny. Three-point cross also allows to examine if chiasma interference exists and its evaluation. Here I show that the classical method of this estimation is erroneous and inevitably determines the apparition of a spurious, positive interference, which has been claimed to be an almost general phenomenon. Interference can only be estimated from a precise knowledge of the number of crossing over events occurring in meiocytes.     

Elective frozen-thawed embryo transfer (FET) in women at risk for ovarian hyperstimulation syndrome

Elective cryopreservation of cultured embryos has become a treatment option for women at risk for ovarian hyperstimulation syndrome (OHSS). The aim of our study was to investigate the outcome of elective cryopreservation and consecutive frozen-thawed embryo transfer (FET) in a large IVF clinic in Austria. A total of 6104 controlled ovarian hyperstimulation cycles (COH) were performed on 2998 patients including 200 patients (6.7%) who were undergoing elective cryopreservation and FET due to high risk of OHSS. We estimated the cumulative live birth rate using the Kaplan-Meier method and evaluated independent predictors for successful live births with a Cox model. A total of 270 frozen-thawed embryo transfers were performed on 200 patients with up to 4 transfers per patient. The first embryo transfer showed a live birth rate of 42.0%, the second transfer showed a cumulative rate of 58.5%. After a total of 4 FETs from the same COH cycle, a cumulative live birth rate of 61.0% per COH cycle could be achieved. Four cases of OHSS occurred amongst these patients (2.0%), all of them of moderate severity. Multivariate analysis identified maternal age, the use of assisted hatching and the number of embryos transferred at the blastocyst stage as independent predictors for cumulative live birth. Our study clearly suggests that elective FET is safe and shows excellent cumulative live birth rates. This concept can, therefore, be used to avoid the severe adverse events caused by COH and the inefficient use of cultured embryos.     

Isolated Aortocoronary Bypass Operations in Patients Over 70 Years of Age: A Comparison With Results in Patients 50 to 59 Years Old

The early and late morbidity, mortality and beneficial effects of isolated aortocoronary bypass operations in a group of 35 patients 70 years old or older were compared with those factors in patients 50 to 59 years old. The patients in both groups were matched according to the year in which the operation was done and the number of vessels bypassed. Left ventricular function, estimated by the angiographically calculated ejection fraction, was not statistically different in the two groups. Cardiac index, while adequate in both groups, was significantly lower in the older age group. Comparisons were made of “early” events, such as perioperative myocardial infarction, perioperative death and length of post-operative hospital stay; and of “late” events, including myocardial infarction, angina pectoris, congestive heart failure and death, which occurred after patients were discharged from the hospital. The mean length of follow-up of patients was similar in both groups.In comparing early events in the two groups, there was no statistically significant difference in the incidence of perioperative myocardial infarction, perioperative mortality or mean length of postoperative hospital stays. With regard to late events, there was no statistically significant difference in the incidences of myocardial infarction, angina pectoris or mortality.     

系统性纵隔淋巴结清扫对非小细胞肺癌患者预后的影响

目的：探讨系统性纵隔淋巴结清扫术对非小细胞肺癌患者预后的影响。方法：选择2007年1月至2009年12月在我院住院的124例非小细胞肺癌患者为研究对象,并将其随机分为对照组和实验组,对照组60例患者采用采样式纵隔淋巴结清扫术（med．itational lymphnodesampling,LS）治疗,实验组64例患者采用系统纵隔淋巴结清扫术（systematic meditational lymphadenectomy,SML）治疗。比较两组患者的淋巴结清除总数、淋巴结转移数、淋巴结转移率,通过寿命表法和Kaplan—Meier法比较两组患者的累积3年生存率及中位生存时间。结果：两组比较淋巴结转移率无统计学差异,而与对照组相比,实验组术后并发症发生率明显下降,差异具有统计学意义（P〈0．05）。对照组和实验组患者的中位生存期、3年生存率分别为20．1和24．2个月、18．75％和43．33％,两组比较差异显著,有统计学意义（P〈0．05）。结论：系统性纵隔淋巴结清扫治疗非小细胞肺癌可显著降低患者的淋巴结转移率,并提高患者的3年生存率,延长患者的寿命。     

Continuous time Markov models for binary longitudinal data

Longitudinal data usually consist of a number of short time series. A group of subjects or groups of subjects are followed over time and observations are often taken at unequally spaced time points, and may be at different times for different subjects. When the errors and random effects are Gaussian, the likelihood of these unbalanced linear mixed models can be directly calculated, and nonlinear optimization used to obtain maximum likelihood estimates of the fixed regression coefficients and parameters in the variance components. For binary longitudinal data, a two state, non-homogeneous continuous time Markov process approach is used to model serial correlation within subjects. Formulating the model as a continuous time Markov process allows the observations to be equally or unequally spaced. Fixed and time varying covariates can be included in the model, and the continuous time model allows the estimation of the odds ratio for an exposure variable based on the steady state distribution. Exact likelihoods can be calculated. The initial probability distribution on the first observation on each subject is estimated using logistic regression that can involve covariates, and this estimation is embedded in the overall estimation. These models are applied to an intervention study designed to reduce children's sun exposure.     

比伐卢定联合替罗非班在高血栓负荷拟行PPCI治疗的急性ST段抬高型心肌梗死患者中的应用价值

目的:探讨替罗非班与比伐卢定联合治疗在高血栓负荷拟行直接经皮冠状动脉介入(PPCI)的急性ST段抬高型心肌梗死(STEMI)患者中的应用价值。方法:选取我院于2018年3月~2020年3月期间收治的127例高血栓负荷拟行PPCI治疗的STEMI患者。将所有患者按照入院顺序,单号分为对照组(替罗非班治疗),双号分为观察组(比伐卢定联合替罗非班治疗),分别为63例和64例。对比两组术后24 h、术后30 d支架内血栓事件、30 d内的出血事件发生率,对比两组心肌梗死溶栓试验(TIMI)血流分级变化、心功能及肌酸激酶同工酶(CKMB)峰值时间及CKMB峰值,记录两组术后不良心血管事件发生率及住院时间。结果:两组术后24 h、术后30 d均未发生支架内血栓事件,观察组30 d内的出血事件发生率较对照组低(P<0.05)。两组住院时间组间对比无明显差异(P>0.05)。两组术后1个月TIMI血流分级为Ⅲ级的占比高于术前同一分级,TIMI血流分级为0~Ⅰ级、Ⅱ级的占比低于术前同一分级(P<0.05)。观察组术后7 d左心室收缩末期内径(LVESD)、CKMB峰值小于对照组,左心室射血分数(LVEF)高于对照组,CKMB峰值时间短于对照组(P<0.05)。两组心血管不良事件总发生率对比无差异(P>0.05)。结论:比伐卢定联合替罗非班治疗高血栓负荷拟行PPCI的STEMI患者,可改善患者心功能,减少心肌损伤,改善TIMI血流分级,同时还可减少30 d内的出血事件发生率。     

A multistate model for bivariate interval-censored failure time data

SUMMARY: Interval-censored life-history data arise when the events of interest are only detectable at periodic assessments. When interest lies in the occurrence of two such events, bivariate-interval censored event time data are obtained. We describe how to fit a four-state Markov model useful for characterizing the association between two interval-censored event times when the assessment times for the two events may be generated by different inspection processes. The approach treats the two events symmetrically and enables one to fit multiplicative intensity models that give estimates of covariate effects as well as relative risks characterizing the association between the two events. An expectation-maximization (EM) algorithm is described for estimation in which the maximization step can be carried out with standard software. The method is illustrated by application to data from a trial of HIV patients where the events are the onset of viral shedding in the blood and urine among individuals infected with cytomegalovirus.     

A two-sample comparison for multiple ordered event data

A longitudinal study is conducted to compare the process of particular disease between two groups. The process of the disease is monitored according to which of several ordered events occur. In the paper, the sojourn time between two successive events is considered as the outcome of interest. The group effects on the sojourn times of the multiple events are parameterized by scale changes in a semiparametric accelerated failure time model where the dependence structure among the multivariate sojourn times is unspecified. Suppose that the sojourn times are subject to dependent censoring and the censoring times are observed for all subjects. A log-rank-type estimating approach by rescaling the sojourn times and the dependent censoring times into the same distribution is constructed to estimate the group effects and the corresponding estimators are consistent and asymptotically normal. Without the dependent censoring, the independent censoring times in general are not available for the uncensored data. In order to complete the censoring information, pseudo-censoring times are generated from the corresponding nonparametrically estimated survival function in each group, and we can still obtained unbiased estimating functions for the group effects. A real application and a simulation study are conducted to illustrate the proposed methods.     

Improved confidence intervals for a difference of two cause-specific cumulative incidence functions estimated in the presence of competing risks and random censoring

A cause-specific cumulative incidence function (CIF) is the probability of failure from a specific cause as a function of time. In randomized trials, a difference of cause-specific CIFs (treatment minus control) represents a treatment effect. Cause-specific CIF in each intervention arm can be estimated based on the usual non-parametric Aalen–Johansen estimator which generalizes the Kaplan–Meier estimator of CIF in the presence of competing risks. Under random censoring, asymptotically valid Wald-type confidence intervals (CIs) for a difference of cause-specific CIFs at a specific time point can be constructed using one of the published variance estimators. Unfortunately, these intervals can suffer from substantial under-coverage when the outcome of interest is a rare event, as may be the case for example in the analysis of uncommon adverse events. We propose two new approximate interval estimators for a difference of cause-specific CIFs estimated in the presence of competing risks and random censoring. Theoretical analysis and simulations indicate that the new interval estimators are superior to the Wald CIs in the sense of avoiding substantial under-coverage with rare events, while being equivalent to the Wald CIs asymptotically. In the absence of censoring, one of the two proposed interval estimators reduces to the well-known Agresti–Caffo CI for a difference of two binomial parameters. The new methods can be easily implemented with any software package producing point and variance estimates for the Aalen–Johansen estimator, as illustrated in a real data example.     

A method for the analysis of biological transduction phenomena

Biological transduction can be defined as the triggering of a cellular response by the binding of molecules of effector substances to specific cellular sites. An example of biological transduction, analyzed in this report, is the triggering of T-cell proliferation by the binding of T-cell growth factor (TCGF) to specific TCGF-binding sites on responsive T-cells. Sigmoidal or S-shaped curves often result when measurements of biological response are plotted as a function of concentration of effector substance. Such curves suggest that effector molecules must bind a critical number of cellular sites, and this critical number of bound complexes must undergo secondary events (cross-linking, association, internalization, second messenger release, etc.) in order to initiate the biological response. The method described here estimates the critical number of cellular sites (R) and the probability of these secondary events (PS/B) as follows: (1) The total number of cellular sites (N) is estimated from binding data, and the probabilities (PB) of effector molecules binding to a site are estimated from response data. (2) The response data are assumed to follow the summed binomial distribution function, which is equated to the incomplete beta function. (3) R and PS/B are estimated by applying nonlinear regression to the incomplete beta function. The T-cell data to which the method was applied gave N = 15,000, R = 5, and PS/B = 7.22 x 10(-4). These results show that the binding of very few TCGF molecules is required for activation of T-cells and that the probability of the secondary events leading to cell proliferation is much smaller than the probability of TCGF binding to T-cells. The method described can be used to analyze any biological transduction experiments where both binding and biological response data are available.     

In or Out-of-Madagascar?—Colonization Patterns for Large-Bodied Diving Beetles (Coleoptera: Dytiscidae)

High species diversity and endemism within Madagascar is mainly the result of species radiations following colonization from nearby continents or islands. Most of the endemic taxa are thought to be descendants of a single or small number of colonizers that arrived from Africa sometime during the Cenozoic and gave rise to highly diverse groups. This pattern is largely based on vertebrates and a small number of invertebrate groups. Knowledge of the evolutionary history of aquatic beetles on Madagascar is lacking, even though this species-rich group is often a dominant part of invertebrate freshwater communities in both standing and running water. Here we focus on large bodied diving beetles of the tribes Hydaticini and Cybistrini. Our aims with this study were to answer the following questions 1) How many colonization events does the present Malagasy fauna originate from? 2) Did any colonization event lead to a species radiation? 3) Where did the colonizers come from—Africa or Asia—and has there been any out-of-Madagascar event? 4) When did these events occur and were they concentrated to any particular time interval? Our results suggest that neither in Hydaticini nor in Cybistrini was there a single case of two or more endemic species forming a monophyletic group. The biogeographical analysis indicated different colonization histories for the two tribes. Cybistrini required at least eight separate colonization events, including the non-endemic species, all comparatively recent except the only lotic (running water) living Cybister operosus with an inferred colonization at 29 Ma. In Hydaticini the Madagascan endemics were spread out across the tree, often occupying basal positions in different species groups. The biogeographical analyses therefore postulated the very bold hypothesis of a Madagascan origin at a very deep basal node within Hydaticus and multiple out-of-Madagascar dispersal events. This hypothesis needs to be tested with equally intense taxon sampling of mainland Africa as for Madagascar.     

Detection of Transmission Clusters of HIV-1 Subtype C over a 21-Year Period in Cape Town,South Africa

Introduction

Despite recent breakthroughs in the fight against the HIV/AIDS epidemic within South Africa, the transmission of the virus continues at alarmingly high rates. It is possible, with the use of phylogenetic methods, to uncover transmission events of HIV amongst local communities in order to identify factors that may contribute to the sustained transmission of the virus. The aim of this study was to uncover transmission events of HIV amongst the infected population of Cape Town.

Methods and Results

We analysed gag p24 and RT-pol sequences which were generated from samples spanning over 21-years with advanced phylogenetic techniques. We identified two transmission clusters over a 21-year period amongst randomly sampled patients from Cape Town and the surrounding areas. We also estimated the origin of each of the identified transmission clusters with the oldest cluster dating back, on average, 30 years and the youngest dating back roughly 20 years.

Discussion and Conclusion

These transmission clusters represent the first identified transmission events among the heterosexual population in Cape Town. By increasing the number of randomly sampled specimens within a dataset over time, it is possible to start to uncover transmission events of HIV amongst local communities in generalized epidemics. This information can be used to produce targeted interventions to decrease transmission of HIV in Africa.     

Measuring kinetics of complex single ion channel data using mean-variance histograms.

The measurement of single ion channel kinetics is difficult when those channels exhibit subconductance events. When the kinetics are fast, and when the current magnitudes are small, as is the case for Na+, Ca2+, and some K+ channels, these difficulties can lead to serious errors in the estimation of channel kinetics. I present here a method, based on the construction and analysis of mean-variance histograms, that can overcome these problems. A mean-variance histogram is constructed by calculating the mean current and the current variance within a brief "window" (a set of N consecutive data samples) superimposed on the digitized raw channel data. Systematic movement of this window over the data produces large numbers of mean-variance pairs which can be assembled into a two-dimensional histogram. Defined current levels (open, closed, or sublevel) appear in such plots as low variance regions. The total number of events in such low variance regions is estimated by curve fitting and plotted as a function of window width. This function decreases with the same time constants as the original dwell time probability distribution for each of the regions. The method can therefore be used: 1) to present a qualitative summary of the single channel data from which the signal-to-noise ratio, open channel noise, steadiness of the baseline, and number of conductance levels can be quickly determined; 2) to quantify the dwell time distribution in each of the levels exhibited. In this paper I present the analysis of a Na+ channel recording that had a number of complexities. The signal-to-noise ratio was only about 8 for the main open state, open channel noise, and fast flickers to other states were present, as were a substantial number of subconductance states. "Standard" half-amplitude threshold analysis of these data produce open and closed time histograms that were well fitted by the sum of two exponentials, but with apparently erroneous time constants, whereas the mean-variance histogram technique provided a more credible analysis of the open, closed, and subconductance times for the patch. I also show that the method produces accurate results on simulated data in a wide variety of conditions, whereas the half-amplitude method, when applied to complex simulated data shows the same errors as were apparent in the real data. The utility and the limitations of this new method are discussed.