Reduced sensitivity to hidden bias at upper quantiles in observational studies with dilated treatment effects

When a treatment has a dilated effect, with larger effects when responses are higher, there can be much less sensitivity to bias at upper quantiles than at lower quantiles; i.e., small, plausible hidden biases might explain the ostensible effect of the treatment for many subjects, and yet only quite large hidden biases could explain the effect on a few subjects having dramatically elevated responses. An example concerning kidney function of cadmium workers is discussed in detail. In that example, the treatment effect is far from additive: It is plausibly zero at the lower quartile of responses to control, and it is large and fairly insensitive to bias at the upper quartile.     

Quantile regression for longitudinal data using the asymmetric Laplace distribution

In longitudinal studies, measurements of the same individuals are taken repeatedly through time. Often, the primary goal is to characterize the change in response over time and the factors that influence change. Factors can affect not only the location but also more generally the shape of the distribution of the response over time. To make inference about the shape of a population distribution, the widely popular mixed-effects regression, for example, would be inadequate, if the distribution is not approximately Gaussian. We propose a novel linear model for quantile regression (QR) that includes random effects in order to account for the dependence between serial observations on the same subject. The notion of QR is synonymous with robust analysis of the conditional distribution of the response variable. We present a likelihood-based approach to the estimation of the regression quantiles that uses the asymmetric Laplace density. In a simulation study, the proposed method had an advantage in terms of mean squared error of the QR estimator, when compared with the approach that considers penalized fixed effects. Following our strategy, a nearly optimal degree of shrinkage of the individual effects is automatically selected by the data and their likelihood. Also, our model appears to be a robust alternative to the mean regression with random effects when the location parameter of the conditional distribution of the response is of interest. We apply our model to a real data set which consists of self-reported amount of labor pain measurements taken on women repeatedly over time, whose distribution is characterized by skewness, and the significance of the parameters is evaluated by the likelihood ratio statistic.     

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.     

Tree fern trunks facilitate seedling regeneration in a productive lowland temperate rain forest

Seedling regeneration on forest floors is often impaired by competition with established plants. In some lowland temperate rain forests, tree fern trunks provide safe sites on which tree species establish, and grow large enough to take root in the ground and persist. Here we explore the competitive and facilitative effects of two tree fern species, Cyathea smithii and Dicksonia squarrosa, on the epiphytic regeneration of tree species in nutrient-rich alluvial forests in New Zealand. The difficulties that seedlings have in establishing on vertical tree fern trunks were indicated by the following observations. First, seedling abundance was greatest on the oldest sections of tree fern trunks, near the base, suggesting that trunks gradually recruited more and more seedlings over time, but many sections of trunk were devoid of seedlings, indicating the difficulty of establishment on a vertical surface. Second, most seedlings were from small-seeded species, presumably because smaller seeds can easily lodge on tree fern trunks. Deer browsing damage was observed on 73% of epiphytic seedlings growing within 2 m of the ground, whereas few seedlings above that height were browsed. This suggests that tree ferns provide refugia from introduced deer, and may slow the decline in population size of deer-preferred species. We reasoned that tree ferns would compete with epiphytic seedlings for light, because below the tree fern canopy photosynthetically active radiation (PAR) was about 1% of above-canopy PAR. Frond removal almost tripled %PAR on the forest floor, leading to a significant increase in the height growth rate (HGR) of seedlings planted on the forest floor, but having no effects on the HGRs of epiphytic seedlings. Our study shows evidence of direct facilitative interactions by tree ferns during seedling establishment in plant communities associated with nutrient-rich soils.     

Generational effects and gender height dimorphism in contemporary Spain

We examine the influence of socio-environmental (and birth cohort specific) effects on both adult height and gender dimorphism (height gap). Our data set is from contemporary Spain, a country governed by an authoritarian regime for about 40 years. Both OLS and quantile regression approaches are used to examine these patterns. Furthermore, we then draw upon a Blinder-Oaxaca decomposition approach to explain the influence of socio-political environment in explaining gender dimorphism. Our findings point to a significant increase in adult height in the generations that benefited from the country's economic liberalization in the 1950s, and especially among those brought up after the transition to democracy in the 1970s. In contrast, individual heterogeneity suggests that only in recent generations has "height increased more among the tallest". We also find that the effects of education on height are greater among shorter individuals. Although the mean gender difference in height is 11.7cm, birth cohort and capabilities effects along with other controls explain on average roughly 4% of the gender height dimorphism, irrespective of the quantile considered.