The simultaneous use of weighted logrank and weighted Kaplan-Meier statistics with clustered right-censored data

P-values and confidence intervals for weighted log-rank tests under truncated binomial design based on clustered medical data

The randomization design employed to gather the data is the basis for the exact distributions of the permutation tests. One of the designs that is frequently used in clinical trials to force balance and remove experimental bias is the truncated binomial design. The exact distribution of the weighted log-rank class of tests for censored cluster medical data under the truncated binomial design is examined in this paper. For p-values in this class, a double saddlepoint approximation is developed using the truncated binomial design. With the right censored cluster data, the saddlepoint approximation's speed and accuracy over the normal asymptotic make it easier to invert the weighted log-rank tests and find nominal 95 % confidence intervals for the treatment effect.

The weighted log-rank tests based on stratified clustered survival data: saddle-point p-values and confidence intervals

Clinical studies sometimes provide clustered data with censored failure times. A crucial factor of the randomized design that lessens selection bias is the random allocation rule. Given this, the weighted rank tests' p-values for stratified survival clustered sampling based on the random allocation rule are approximated using the double saddle-point approximation technique. For tests of significance and confidence intervals for the treatment effect, this approximation can be utilized. Through simulation experiments, the accuracy of the saddle-point approximation is examined by comparing saddle-point and normal approximations to the exact underlying permutation distribution.

Log-rank tests for censored clustered data under generalized randomized block design: Saddlepoint approximation

The weighted log-rank class is the common and widely used class of two-sample tests for clustered data. Clustered data with censored failure times often arise in tumorigenicity investigations and clinical trials. The randomized block design is a significant design that reduces both unintentional bias and selection bias. Accordingly, the p-values of the null permutation distribution of weighted log-rank class for clustered data are approximated using the double saddlepoint approximation technique. Comprehensive simulation studies are carried out to appraise the accuracy of the saddlepoint approximation. This approximation exhibits a significant improvement in precision over the asymptotic approximation. This precision motivates us to determine the approximated confidence intervals for the treatment impact.

Sample size determination for paired right-censored data based on the difference of Kaplan-Meier estimates

Sample size determination is essential to planning clinical trials. Jung (2008) established a sample size calculation formula for paired right-censored data based on the logrank test, which has been well-studied for comparing independent survival outcomes. An alternative to rank-based methods for independent right-censored data, advocated by Pepe and Fleming (1989), tests for differences between integrated weighted Kaplan-Meier estimates and is more sensitive to the magnitude of difference in survival times between groups. In this paper, we employ the concept of the Pepe-Fleming method to determine an adequate sample size by calculating differences between Kaplan-Meier estimators considering pair-wise correlation. We specify a positive stable frailty model for the joint distribution of paired survival times. We evaluate the performance of the proposed method by simulation studies and investigate the impacts of the accrual times, follow-up times, loss to follow-up rate, and sensitivity of power under misspecification of the model. The results show that ignoring the pair-wise correlation results in overestimating the required sample size. Furthermore, the proposed method is applied to two real-world studies, and the R code for sample size calculation is made available to users.

Utilizing the integrated difference of two survival functions to quantify the treatment contrast for designing, monitoring, and analyzing a comparative clinical study

BACKGROUND

Consider a comparative, randomized clinical study with a specific event time as the primary end point. In the presence of censoring, standard methods of summarizing the treatment difference are based on Kaplan-Meier curves, the logrank test, and the point and interval estimates via Cox's procedure. Moreover, for designing and monitoring the study, one usually utilizes an event-driven scheme to determine the sample sizes and interim analysis time points.

PURPOSE

When the proportional hazards (PHs) assumption is violated, the logrank test may not have sufficient power to detect the difference between two event time distributions. The resulting hazard ratio estimate is difficult, if not impossible, to interpret as a treatment contrast. When the event rates are low, the corresponding interval estimate for the 'hazard ratio' can be quite large due to the fact that the interval length depends on the observed numbers of events. This may indicate that there is not enough information for making inferences about the treatment comparison even when there is no difference between two groups. This situation is quite common for a postmarketing safety study. We need an alternative way to quantify the group difference.

METHODS

Instead of quantifying the treatment group difference using the hazard ratio, we consider an easily interpretable and model-free parameter, the integrated survival rate difference over a prespecified time interval, as an alternative. We present the inference procedures for such a treatment contrast. This approach is purely nonparametric and does not need any model assumption such as the PHs. Moreover, when we deal with equivalence or noninferiority studies and the event rates are low, our procedure would provide more information about the treatment difference. We used a cardiovascular trial data set to illustrate our approach.

RESULTS

The results using the integrated event rate differences have a heuristic interpretation for the treatment difference even when the PHs assumption is not valid. When the event rates are low, for example, for the cardiovascular study discussed in this article, the procedure for the integrated event rate difference provides tight interval estimates in contrast to those based on the event-driven inference method.

LIMITATIONS

The design of a trial with the integrated event rate difference may be more complicated than that using the event-driven procedure. One may use simulation to determine the sample size and the estimated duration of the study.

CONCLUSIONS

The procedure discussed in this article can be a useful alternative to the standard PHs method in the survival analysis.