Randomization Tests for Censored Survival Distributions

This paper discusses the application of randomization tests to censored survival distributions. The three types of censoring considered are those designated by MILLER (1981) as Type 1 (fixed time termination), Type 2 (termination of experiment at r-th failure), and random censoring. Examples utilize the Gehan scoring procedure. Randomization tests for which computer programs already exist can be applied to a variety of experimental designs, regardless of the presence of censored observations.     

Generalized Rank Transformations for Tests of Survival

The asymptotic equivalence of nonparametric tests and parametric tests based on rank-transformed data (CONOVER and IMAN , 1981) can be extended to the case of censoring. This paper presents generalized rank transformations for analyses of censored data, of interval-censored data and of survival data with uncertain causes of death. A Monte Carlo study and an analysis of leukemia remission times demonstrate excellent agreement of suggested procedures with GEHAN 'S (1965) and PRENTICE 'S (1978) tests.     

Diallel analysis for sex-linked and maternal effects

Genetic models including sex-linked and maternal effects as well as autosomal gene effects are described. Monte Carlo simulations were conducted to compare efficiencies of estimation by minimum norm quadratic unbiased estimation (MINQUE) and restricted maximum likelihood (REML) methods. MINQUE(1), which has 1 for all prior values, has a similar efficiency to MINQUE(), which requires prior estimates of parameter values. MINQUE(1) has the advantage over REML of unbiased estimation and convenient computation. An adjusted unbiased prediction (AUP) method is developed for predicting random genetic effects. AUP is desirable for its easy computation and unbiasedness of both mean and variance of predictors. The jackknife procedure is appropriate for estimating the sampling variances of estimated variances (or covariances) and of predicted genetic effects. A t-test based on jackknife variances is applicable for detecting significance of variation. Worked examples from mice and silkworm data are given in order to demonstrate variance and covariance estimation and genetic effect prediction.     

Comparison of Several Relative Risk Estimators with Interval‐Censored Data

Several simple, intuitive, explicitly computable estimation procedures for relative risk with interval‐censored data are proposed. These procedures are the modified versions of relative risk estimators for right‐censored data developed by Peto, Pike, and Andersen. Simulation study is conducted to demonstrate the performances of the proposed estimators.     

Using Weighted Kaplan-Meier Statistics in Nonparametric Comparisons of Paired Censored Survival Outcomes

This research introduces methods for nonparametric testing of weighted integrated survival differences in the context of paired censored survival designs. The current work extends work done by Pepe and Fleming (1989, Biometrics 45, 497-507), which considered similar test statistics directed toward independent treatment group comparisons. An asymptotic closed-form distribution of the proposed family of tests is presented, along with variance estimates constructed under null and alternative hypotheses using nonparametric maximum likelihood estimates of the closed-form quantities. The described method allows for additional information from individuals with no corresponding matched pair member to be incorporated into the test statistic in sampling scenarios where singletons are not prone to selection bias. Simulations presented over a range of potential dependence in the paired censored survival data demonstrate substantial power gains associated with taking into account the dependence structure. Consequences of ignoring the paired nature of the data include overly conservative tests in terms of power and size. In fact, simulation results using tests for independent samples in the presence of positive correlation consistently undershot both size and power targets that would have been attained in the absence of correlation. This additional worrisome effect on operating characteristics highlights the need for accounting for dependence in this popular family of tests.     

A comparison of two methods for making statistical inferences on Nei's measure of genetic distance

The delta and jackknife methods can be used to estimate Nei's measure of genetic distance and calculate confidence intervals for this estimate. Computer stimulations were used to study the bias and variance of each estimator and the accuracy of the corresponding approximate 95% confidence intervals. The simulations were conducted using 3 sets of data and several sample sizes. The results showed: (1) the jackknife reduced bias; (2) in 8 out of 9 cases the variance and mean square error of the jackknife estimator were less; (3) a second order jackknife reduced the bias the most but suffered a corresponding increase in variance; (4) both the first order jackknife and delta methods yielded intervals whose confidence levels were approximately equal but less than 95%.     

Confidence intervals for the similarity between algal communities

While researchers commonly use similarity measures to compare algal communities, very few researchers have considered the variability of these estimated measures. This paper discusses a recent method for estimating the variance of and confidence intervals for similarity measures proposed by Johnson & Millie (1982, Hydrobiologia 89: 3–8). Applications of this method to data have produced confidence intervals that are too narrow. Two alternative methods, the jackknife method and the bootstrap, are shown to provide superior estimates of the variability.     

Median Tests for Censored Survival Data; a Contingency Table Approach

Summary The median failure time is often utilized to summarize survival data because it has a more straightforward interpretation for investigators in practice than the popular hazard function. However, existing methods for comparing median failure times for censored survival data either require estimation of the probability density function or involve complicated formulas to calculate the variance of the estimates. In this article, we modify a K ‐sample median test for censored survival data ( Brookmeyer and Crowley, 1982 , Journal of the American Statistical Association 77, 433–440) through a simple contingency table approach where each cell counts the number of observations in each sample that are greater than the pooled median or vice versa. Under censoring, this approach would generate noninteger entries for the cells in the contingency table. We propose to construct a weighted asymptotic test statistic that aggregates dependent χ² ‐statistics formed at the nearest integer points to the original noninteger entries. We show that this statistic follows approximately a χ² ‐distribution with k? 1 degrees of freedom. For a small sample case, we propose a test statistic based on combined p ‐values from Fisher’s exact tests, which follows a χ² ‐distribution with 2 degrees of freedom. Simulation studies are performed to show that the proposed method provides reasonable type I error probabilities and powers. The proposed method is illustrated with two real datasets from phase III breast cancer clinical trials.     

Exact,Distribution Free Confidence Intervals for Late Effects in Censored Matched Pairs

When comparing censored survival times for matched treated and control subjects, a late effect on survival is one that does not begin to appear until some time has passed. In a study of provider specialty in the treatment of ovarian cancer, a late divergence in the Kaplan–Meier survival curves hinted at superior survival among patients of gynecological oncologists, who employ chemotherapy less intensively, when compared to patients of medical oncologists, who employ chemotherapy more intensively; we ask whether this late divergence should be taken seriously. Specifically, we develop exact, permutation tests, and exact confidence intervals formed by inverting the tests, for late effects in matched pairs subject to random but heterogeneous censoring. Unlike other exact confidence intervals with censored data, the proposed intervals do not require knowledge of censoring times for patients who die. Exact distributions are consequences of two results about signs, signed ranks, and their conditional independence properties. One test, the late effects sign test, has the binomial distribution; the other, the late effects signed rank test, uses nonstandard ranks but nonetheless has the same exact distribution as Wilcoxon's signed rank test. A simulation shows that the late effects signed rank test has substantially more power to detect late effects than do conventional tests. The confidence statement provides information about both the timing and magnitude of late effects (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of genotype,growth regulators,carbon source,and pH on shoot induction and plant regeneration in tomoto

Summary Ten cultivars of tomato were screened for their ability to produce shoots and shoot primordia on media containing a range of 6-benzyladenine (BA) concentrations (0.0–4.0 mgl⁻¹; 0.0–17.7 μM) in combination with indole-3-acetic acid (IAA; 0.0, 0.1, 0.2 mgl⁻¹; 0.0, 0.57, 1.14 μM, respectively). Both genotypes and growth regulator levels showed significant differences at α=0.05. However, their interaction was not significantly different. A comparison of the mean number of shoots produced six cultivar classes, with UC82, UC97-3, Castlerock, Red Rock, and Peto86 producing the highest means. There were four cultiver frequency classes, the highest including cultivars Peto Rock (93.7%), Peto86 (92.3%), and Strain B (90.7%). Growth regulator mean comparisons produced eight classes, the highest included three different BA/IAA combinations, with media containing 2.0 mgl⁻¹ (8.87 μM) BA and 0.2 mgl⁻¹ (1.14. μM) IAA giving the highest mean and frequency (94.1%). The effect of carbon source was studied using glucose, fructose, maltose, and sucrose at 3.0% concentration. Three high regenerating genotypes and four media were used in combination with each sugar. Sugars were significantly different with maltose giving the highest number of shoots (31.6) followed by glucose (20.9). Growth regulator means, sugar-growth regulator interaction, and cultivar-sugar interaction were significant. A three-way interaction was nonsignificant. The effect of maltose and sucrose concentration (1.5–9.0%) showed the positive effect of maltose over sucrose in inducing shoots and in reducing loss rates of shoots on the regeneration media. Maltose at 1.5, 3.0, and 4.5% was the most effective. Six pH values (4.0–6.5) were used to test their effect on shoot induction in three cultivars (Peto86, UC97-3 and Castlerock). pH effects and cultivar-pH interaction were not significant.     

Use of the weighted jackknife method to calculate the variance in cellular-specific protein secretion rate: application to monoclonal antibody secretion rate kinetics in response to osmotic stress

The specific secretion rate (q, mug protein secreted/viable cell-h) and its variance are very useful to compare the capability of cell lines for protein secretion. An assessment of specific secretion rate variability is also beneficial and important when the specific secretion rate is to be used as an on-line process parameter to monitor culture production behavior or for in-process decisionmaking. Experimental errors in mammalian cell culture (e.g., protein concentration measurement and cell counting) and estimation error in the method of calculating q contribute to the total variance of the specific secretion rate. Although the variance of q is essential for comparing the differences between cell lines and the response of the same cell line to different nutrient or environmental conditions, few methods for calculating the variance of the specific secretion rate have been reported. As a model system, we have used the weighted jackknife method and the delta method to calculate the variance in the specific secretion rate of a murine monoclonal antibody (q(mAb)) determined by a differential method. These methods were applied to calculate q(mAb) and its standard deviation to determine the change in q(mAb) kinetics during batch culture of the 9.2.27 hybridoma in response to growth in hyperosmotic media or osmotic stress. Without osmotic stress, during exponential growth in DMEM + 5% FBS spinner culture, the estimate of q(mAb) decreases at least threefold. Results indicate that the 9.2.27 hybridoma responds to hyperosmotic media (400 mOsm, 470 mOsm) by significantly reducing the degree of q(mAb) decrease in the exponential phase, thus maintaining a higher q(mAb) through the stationary phase. The trend of q(mAb) during the batch cultures studied is further confirmed by t-test. Osmotic stress is statistically shown to be able to alter significantly the hybridoma-specific mAb secretion kinetics during batch culture. Determination of the variance of specific secretion rate using the weighted jackknife method offers a powerful approach for establishing the confidence limits of specific protein secretion rate between cell cultures in different nutritional or osmotic environments. (c) 1996 John Wiley & Sons, Inc.     

Proposal of k Sample Tests for Bivariate Censored Data for Nondecreasing Ordered Alternatives

Tests are introduced which are designed to test for a nondecreasing ordered alternative among the survival functions of k populations consisting of multiple observations on each subject. Some of the observations could be right censored. A simulation study is conducted comparing the proposed tests on the basis of estimated power when the underlying distributions are multivariate normal. Equal sample sizes of 20 with 25% censoring, and 40 with both 25% and 50% censoring are considered for 3 and 4 populations. All of the tests hold their α‐values well. A recommendation is made as to the best overall test for the situations considered.     

Tree-Structured Exponential Regression Modeling

A method for fitting piecewise exponential regression models to censored survival data is described. Stratification is performed recursively, using a combination of statistical tests and residual analysis. The splitting criterion employed in cross-validation is the average squared error of the residuals. The bootstrap is employed to keep the probability of a type I error (the error of discovering two or more strata when there is only one) of the method close to a predetermined value. The proposed method can thus also serve as a formal goodness-of-fit test for the exponential regression model. Real and simulated data are used for illustration.     

Some Tests for k£2 Upper Outliers in an Exponential Sample

The sequential procedure for testing up to k upper outliers proposed by Kimber (1982) for one-parameter exponential distribution is modified to a two-parameter exponential distribution. Further null distributions of some test statistics for an upper outlier-pair in a complete or censored sample from a two-parameter exponential distribution are given. Percentage points of the statistic T₁ are tabulated.     

Some Inference Results in Modified Freund's Bivariate Exponential Distribution

This paper obtains MLE of the parameters and large sample tests for independence as well as symmetry of two components in modified Freund's model of bivariate exponential distribution proposed by PROSCHAN and SULLO (1974). The Modified Freund's model is more general model than the other models like MARSHALL and OLKIN (1967), FREUND (1961) and BASU (1974) which are the sub-models of Modified Freund's model. It satisfies the most important Loss of Memory Property (LMP) which implies the other three sub-models also satisfy LMP. We also obtain the confidence interval for the parameters in the above model. We extend the above results in fixed time censored and random censored samples.     

Observations below multiple lower limits of quantification: How to estimate the mean and variance

Multiple lower limits of quantification (MLOQs) result if various laboratories are involved in the analysis of concentration data and some observations are too low to be quantified. For normally distributed data under MLOQs there exists only the multiple regression method of Helsel to estimate the mean and variance. We propose a simple imputation method and two new maximum likelihood estimation methods: the multiple truncated sample method and the multiple censored sample method. A simulation study is conducted to compare the performances of the newly introduced methods to Helsel's via the criteria root mean squared error (RMSE) and bias of the parameter estimates. Two and four lower limits of quantification (LLOQs), various amounts of unquantifiable observations and two sample sizes are studied. Furthermore, the robustness is investigated under model misspecification. The methods perform with decreasing accuracy for increasing rates of unquantified observations. Increasing sample sizes lead to smaller bias. There is almost no change in the performance between two and four LLOQs. The magnitude of the variance impairs the performance of all methods. For a smaller variance, the multiple censored sample method leads to superior estimates regarding the RMSE and bias, whereas Helsel's method is superior regarding the bias for a larger variance. Under model misspecification, Helsel's method was inferior to the other methods. Estimating the mean, the multiple censored sample method performed better, whereas the multiple truncated sample method performs best in estimating the variance. Summarizing, for a large sample size and normally distributed data we recommend to use Helsel's method. Otherwise, the multiple censored sample method should be used to obtain estimates of the mean and variance of data including MLOQs.     

Testing the correlation for clustered categorical and censored discrete time-to-event data when covariates are measured without/with errors

In the analysis of clustered categorical data, it is of common interest to test for the correlation within clusters, and the heterogeneity across different clusters. We address this problem by proposing a class of score tests for the null hypothesis that the variance components are zero in random effects models, for clustered nominal and ordinal categorical responses. We extend the results to accommodate clustered censored discrete time-to-event data. We next consider such tests in the situation where covariates are measured with errors. We propose using the SIMEX method to construct the score tests for the null hypothesis that the variance components are zero. Key advantages of the proposed score tests are that they can be easily implemented by fitting standard polytomous regression models and discrete failure time models, and that they are robust in the sense that no assumptions need to be made regarding the distributions of the random effects and the unobserved covariates. The asymptotic properties of the proposed tests are studied. We illustrate these tests by analyzing two data sets and evaluate their performance with simulations.     

One- and Two-Sample Tests of Kendall's τ

Several methods of testing general one-sample and two-sample hypotheses of Kendall's τ are discussed. The performance of these procedures in typical situations likely to occur in practice was investigated by numerous Monte Carlo experiments. The common one-sample test (H₀: τ = 0) based on the permutational variance performs very similar to bootstrap or jackknife testing for true τ near zero. For true |τ| perhaps greater than 0.4 and moderate sample sizes bootstrap techniques are the methods of choice.     

Partitioning of genetic variance and selection efficiency for alternative vegetative deployment strategies for white spruce in Eastern Canada

Genetic variances and selection efficiencies for growth traits of white spruce (Picea glauca (Moench) Voss) were estimated from clonally replicated full-sib progeny tests established both in nursery and field environments in New Brunswick, Canada. The available data included heights at 4, 5, and 6 years in the nursery test; height at 9 years, height, DBH, and volume at 14 years in the field test. Estimated variance components were interpreted according to an additive-dominance-epistasis model. For heights in the nursery test, while both non-additive and additive variances were important sources of genetic variation, the former decreased but the latter increased with age; among the non-additive genetic variance, the epistatic variance was much more important than the dominance variance. Different from the nursery traits, for traits in the field test, additive variance accounted for an average of 81% of the total genetic variance, whereas dominance variance explained most of the remaining genetic variance. Genetic parameters and selection efficiencies for three vegetative deployment strategies: deploying half-sib families (VD_FAM_HS), full-sib families (VD_FAM_FS), and multi-varietal forestry (MVF), were compared. Heritability estimates were moderate for VD_FAM_HS and VD_FAM_FS (0.61–0.72), high for MVF (>0.82) for the nursery heights, and high (>0.79) for the field traits for all strategies. Genetic correlations of volume at age 14 in the field test, the target trait for improvement, were strong (>0.85) with other field traits. Genetic correlations of VOL14 with the nursery heights were also strong (>0.71) at the half-sib and full-sib family levels, but were only moderate (>0.59) for MVF. Overall, practicing MVF is the most effective deployment strategy, yielding the highest genetic gains, followed by VD_FAM_FS and VD_FAM_HS, regardless of traits and selection methods. Furthermore, early selections for HT9 or for HT4–HT6 were very encouraging, resulting in higher gain in volume at age 14 on a per year basis.