Maximum of the weighted Kaplan-Meier tests with application to cancer prevention and screening trials

A class of maximum weighted Kaplan-Meier test statistics is described where the weight functions are chosen from a family of smooth functions. The investigated test statistic is robust and sensitive to a variety of alternatives that are often observed in cancer prevention and screening trials. A simulation study is performed to compare the size and power properties between the proposed test statistics and some existing ones. We illustrate the procedure using data from a clinical trial of a breast cancer screening program.     

Supremum weighted log-rank test and sample size for comparing two-stage adaptive treatment strategies

In two-stage adaptive treatment strategies, patients receivean induction treatment followed by a maintenance therapy, giventhat the patient responded to the induction treatment they received.To test for a difference in the effects of different inductionand maintenance treatment combinations, a modified supremumweighted log-rank test is proposed. The test is applied to adataset from a two-stage randomized trial and the results arecompared to those obtained using a standard weighted log-ranktest. A sample-size formula is proposed based on the limitingdistribution of the supremum weighted log-rank statistic. Thesample-size formula reduces to Eng and Kosorok's sample-sizeformula for a two-sample supremum log-rank test when there isno second randomization. Monte Carlo studies show that the proposedtest provides sample sizes that are close to those obtainedby standard weighted log-rank test under a proportional hazardsalternative. However, the proposed test is more powerful thanthe standard weighted log-rank test under non-proportional hazardsalternatives.     

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.     

Berkson's paradox and weighted distributions: An application to Alzheimer's disease

One reason for observing in practice a false positive or negative correlation between two random variables, which are either not correlated or correlated with a different direction, is the overrepresentation in the sample of individuals satisfying specific properties. In 1946, Berkson first illustrated the presence of a false correlation due to this last reason, which is known as Berkson's paradox and is one of the most famous paradox in probability and statistics. In this paper, the concept of weighted distributions is utilized to describe Berskon's paradox. Moreover, a proper procedure is suggested to make inference for the population given a biased sample which possesses all the characteristics of Berkson's paradox. A real data application for patients with dementia due to Alzheimer's disease demonstrates that the proposed method reveals characteristics of the population that are masked by the sampling procedure.     

A Bayesian model with application for adaptive platform trials having temporal changes

Temporal changes exist in clinical trials. Over time, shifts in patients' characteristics, trial conduct, and other features of a clinical trial may occur. In typical randomized clinical trials, temporal effects, that is, the impact of temporal changes on clinical outcomes and study analysis, are largely mitigated by randomization and usually need not be explicitly addressed. However, temporal effects can be a serious obstacle for conducting clinical trials with complex designs, including the adaptive platform trials that are gaining popularity in recent medical product development. In this paper, we introduce a Bayesian robust prior for mitigating temporal effects based on a hidden Markov model, and propose a particle filtering algorithm for computation. We conduct simulation studies to evaluate the performance of the proposed method and provide illustration examples based on trials of Ebola virus disease therapeutics and hemostat in vascular surgery.     

An extension of the weighted dissimilarity test to association study in families

Abstact Association studies for complex diseases based on pedigree haplotype or genotype data have received increasing attention in the last few years. The similarity tests are appealing for these studies because they take into account of the DNA structure, but they have blind areas on which significant association can not be detected. Recently, we developed a dissimilarity method for this problem based on independent haplotype data, which eliminates the blind areas of the existing methods. As DNA collected on families are common in practice, and the data are either of the form of genotype or haplotype. Here we extend our method for association study to data on families. It can be used to evaluate different designs in terms of power. Simulation studies confirmed that the extended method improves the type I error rate and power. Applying this method to the Genetic Analysis Workshop 14 alcoholism data, we find that markers rs716581, rs1017418, rs1332184 and rs1943418 on chromosomes 1, 2, 9 and 18 yield strong signal (with P value 0.001 or lower) for association with alcoholism. Our work can serve as a guide in the design of association studies in families.     

Km typing with PCR: application to population screening.

The immunoglobulin kappa light chain (IgK) locus may play a significant role in the pathology of both infectious and autoimmune diseases. Most of the work on IgK genetics has been conducted using immunological techniques for allelic typing and sequence analysis. This is restricted by availability of reagents and can be both expensive and time-consuming. PCR primers were designed to amplify the kappa constant gene (Ck), and four allele-specific oligonucleotides (ASOs) were used to distinguish the alleles in the amplified PCR products. Direct sequencing of PCR products was performed to confirm that the primers specifically amplified the Ck region and the ASOs differentiated the Km alleles. Sequencing of an average of 209 nucleotides of DNA from 50 individuals revealed no variation except at codon 191, which is known to be involved in a frequent polymorphism. An analysis of 347 different individual DNAs from 10 human populations was conducted to determine Km allelic frequencies within these populations and to apply this type of data collection to population studies.     

An up to date look at lung cancer screening

Lung cancer is the leading cause of cancer-related death worldwide. At the time of initial presentation, most patients are at an advance stage of disease and have a poor associated prognosis. Those diagnosed and treated at earlier stages have a significantly better outcome with five year survival for stage I disease approaching 75%. Ideally a screening strategy for lung cancer would detect disease at an earlier stage and allow for potential surgical cure. The purpose of this review is to examine past and current evidence as it relates to lung cancer screening.     

Quantification of length‐bias in screening trials with covariate‐dependent test sensitivity

Length‐biased sampling exists in screening programs where longer duration disease is detected during the preclinical stage because a longer sojourn time (preclinical duration) has a higher probability of being screen detected. By modeling the course of disease, we quantify the effect of length‐biased sampling on clinical duration when cases are subject to periodic screening with variable test sensitivity. We use the highly flexible bivariate lognormal density to jointly model preclinical and clinical durations, and we model screening test sensitivity as a function of the sojourn time and number of previous false negative screens. We show that the mean clinical duration among screen‐detected cases can be up to 40% higher, with shrinking standard deviation, than those among nonscreen‐detected cases, due to biased sampling alone, irrespective of any possible benefit (increased survival time arising from earlier detection or reduction in mortality). These findings will aid in the design and interpretation of screening trials.     

Correcting for noncompliance and dependent censoring in an AIDS Clinical Trial with inverse probability of censoring weighted (IPCW) log-rank tests

AIDS Clinical Trial Group (ACTG) randomized trial 021 compared the effect of bactrim versus aerosolized pentamidine (AP) as prophylaxis therapy for pneumocystis pneumonia (PCP) in AIDS patients. Although patients randomized to the bactrim arm experienced a significant delay in time to PCP, the survival experience in the two arms was not significantly different (p = .32). In this paper, we present evidence that bactrim therapy improves survival but that the standard intent-to-treat comparison failed to detect this survival advantage because a large fraction of the subjects either crossed over to the other therapy or stopped therapy altogether. We obtain our evidence of a beneficial bactrim effect on survival by artificially regarding the subjects as dependently censored at the first time the subject either stops or switches therapy; we then analyze the data with the inverse probability of censoring weighted Kaplan-Meier and Cox partial likelihood estimators of Robins (1993, Proceedings of the Biopharmaceutical Section, American Statistical Association, pp. 24-33) that adjust for dependent censoring by utilizing data collected on time-dependent prognostic factors.     

Multidimensional adaptive P-splines with application to neurons' activity studies

The receptive field (RF) of a visual neuron is the region of the space that elicits neuronal responses. It can be mapped using different techniques that allow inferring its spatial and temporal properties. Raw RF maps (RFmaps) are usually noisy, making it difficult to obtain and study important features of the RF. A possible solution is to smooth them using P-splines. Yet, raw RFmaps are characterized by sharp transitions in both space and time. Their analysis thus asks for spatiotemporal adaptive P-spline models, where smoothness can be locally adapted to the data. However, the literature lacks proposals for adaptive P-splines in more than two dimensions. Furthermore, the extra flexibility afforded by adaptive P-spline models is obtained at the cost of a high computational burden, especially in a multidimensional setting. To fill these gaps, this work presents a novel anisotropic locally adaptive P-spline model in two (e.g., space) and three (space and time) dimensions. Estimation is based on the recently proposed SOP (Separation of Overlapping Precision matrices) method, which provides the speed we look for. Besides the spatiotemporal analysis of the neuronal activity data that motivated this work, the practical performance of the proposal is evaluated through simulations, and comparisons with alternative methods are reported.