A Nonparametric Procedure for the Two-Factor Mixed Model with Missing Data

Estimation and Testing of Wilcoxon–Mann–Whitney Effects in Factorial Clustered Data Designs

Clustered data arise frequently in many practical applications whenever units are repeatedly observed under a certain condition. One typical example for clustered data are animal experiments, where several animals share the same cage and should not be assumed to be completely independent. Standard methods for the analysis of such data are Linear Mixed Models and Generalized Estimating Equations—however, checking their assumptions is not easy, especially in scenarios with small sample sizes, highly skewed, count, and ordinal or binary data. In such situations, Wilcoxon–Mann–Whitney type effects are suitable alternatives to mean-based or other distributional approaches. Hence, no specific data distribution, symmetric or asymmetric, is required. Within this work, we will present different estimation techniques of such effects in clustered factorial designs and discuss quadratic- and multiple contrast type-testing procedures for hypotheses formulated in terms of Wilcoxon–Mann–Whitney effects. Additionally, the framework allows for the occurrence of missing data: estimation and testing hypotheses are based on all-available data instead of complete-cases. An extensive simulation study investigates the precision of the estimators and the behavior of the test procedures in terms of their type-I error control. One real world dataset exemplifies the applicability of the newly proposed procedures.

Ranking procedures for repeated measures designs with missing data: Estimation, testing and asymptotic theory

We develop purely nonparametric methods for the analysis of repeated measures designs with missing values. Hypotheses are formulated in terms of purely nonparametric treatment effects. In particular, data can have different shapes even under the null hypothesis and therefore, a solution to the nonparametric Behrens-Fisher problem in repeated measures designs will be presented. Moreover, global testing and multiple contrast test procedures as well as simultaneous confidence intervals for the treatment effects of interest will be developed. All methods can be applied for the analysis of metric, discrete, ordinal, and even binary data in a unified way. Extensive simulation studies indicate a satisfactory control of the nominal type-I error rate, even for small sample sizes and a high amount of missing data (up to 30%). We apply the newly developed methodology to a real data set, demonstrating its application and interpretation.

Rank-based two-sample tests for paired data with missing values

Two-sample location problem is one of the most encountered problems in statistical practice. The two most commonly studied subtypes of two-sample location problem involve observations from two populations that are either independent or completely paired, but a third subtype can oftentimes occur in practice when some observations are paired and some are not. Partially paired two-sample problems, also known as paired two-sample problems with missing data, often arise in biomedical fields when it is difficult for some invasive procedures to collect data from an individual at both conditions we are interested in comparing. Existing rank-based two-sample comparison procedures for partially paired data, however, do not make efficient use of all available data. In order to improve the power of testing procedures for this problem, we propose several new rank-based test statistics and study their asymptotic distributions and, when necessary, exact variances. Through extensive numerical studies, we show that the best overall power come from the proposed tests based on weighted linear combinations of the test statistics comparing paired data and the test statistics comparing independent data, using weights inversely proportional to their variances. We illustrate the proposed methods with a real data example from HIV research for prevention.

Revisiting Fungicide-Based Management Guidelines for Leaf Blotch Diseases in Soft Red Winter Wheat

Standard foliar fungicide applications in wheat are usually made between flag leaf emergence (Feekes [FK] 8) and heading (FK10.5) to minimize damage to the flag leaf. However, over the last few years, new fungicide programs such as applications prior to FK8 and split half-rate applications have been implemented, although there are few data pertaining to the efficacy of these programs. Eight experiments were conducted in Illinois, Indiana, Ohio, and Wisconsin from 2010 to 2012 to compare new programs to standard FK8 and FK10 programs in terms of disease control and yield response. The programs evaluated consisted of single full-rate applications of 19% tebuconazole + 19% prothioconazole (Prosaro) or 23.6% pyraclostrobin (Headline) at FK5 (pseudostem strongly erected), FK8, or FK10, or split half rates at FK5 and 8 (FK5+8), plus an untreated check (CK). Leaf blotch (LB) severity and yield data were collected and random effects meta-analytical models fitted to estimate the overall log odds ratio of disease reaching the flag leaf ( L¯OR ) and mean yield increase ( D¯ ) for each fungicide program relative to CK. For all programs, L¯OR was significantly different from zero (P < 0.05). Based on estimated odds ratios (OR = exp[ L¯OR ]), the two FK8 programs reduced the risk of LB reaching the flag leaf by 55 and 75%, compared with 62 and 69% and 67 and 70% for the two FK10 and FK5+8 programs, respectively, and only 32 and 37% for the two FK5 programs. D¯ was significantly different from zero (P ≤ 0.003) for all FK8, FK10, and FK5+8 programs, with values of 233 and 245, 175 and 220, and 175 and 187 kg ha^-1 for the FK10, FK5+8, and FK8 programs, respectively. Differences in mean yield response between Headline and Prosaro were not statistically significant (P > 0.05). The probability of profitability was estimated for each program for a range of grain prices and fungicide application costs. All FK8, FK10, and FK5+8 programs had more than an 80% chance of resulting in a positive yield response, compared with 63 and 67% for the two FK5 programs. The chance of obtaining a yield increase of 200 kg ha^-1, required to offset an application cost of $36 ha^-1 at a grain price of $0.18 kg^-1, ranged from 44 to 60% for FK8, FK10 and FK5+8 programs compared with 22 and 25% for the two FK5 programs. These findings could be used to help inform fungicide application decisions for LB diseases in soft red winter wheat.