Some t-tests for N-of-1 trials with serial correlation

N-of-1 trials allow inference between two treatments given to a single individual. Most often, clinical investigators analyze an individual's N-of-1 trial data with usual t-tests or simple nonparametric methods. These simple methods do not account for serial correlation in repeated observations coming from the individual. Existing methods accounting for serial correlation require simulation, multiple N-of-1 trials, or both. Here, we develop t-tests that account for serial correlation in a single individual. The development includes effect size and precision calculations, both of which are useful for study planning. We then evaluate and compare their Type I and II errors and interval estimators to those of usual t-tests analogues via Monte Carlo simulation. The serial t-tests clearly outperform the usual t-tests commonly used in reporting N-of-1 results. Examples from N-of-1 clinical trials in fibromyalgia patients and from a behavioral health setting exhibit how accounting for serial correlation can change inferences. These t-tests are easily implemented and more appropriate than simple methods commonly used; however, caution is needed when analyzing only a few observations. Keywords: Autocorrelation; Cross-over studies; Repeated measures analysis; Single-case experimental design; Time-seriesComment: 23 pages, 6 figures, 6 table

Efficient wald tests for fractional unit roots

In this article we introduce efficient Wald tests for testing the null hypothesis of the unit root against the alternative of the fractional unit root. In a local alternative framework, the proposed tests are locally asymptotically equivalent to the optimal Robinson Lagrange multiplier tests. Our results contrast with the tests for fractional unit roots, introduced by Dolado, Gonzalo, and Mayoral, which are inefficient. In the presence of short range serial correlation, we propose a simple and efficient two-step test that avoids the estimation of a nonlinear regression model. In addition, the first-order asymptotic properties of the proposed tests are not affected by the preestimation of short or long memory parameters.Publicad

Development of Threshold Levels and a Climate-Sensitivity Model of the Hydrological Regime of the High-Altitude Catchment of the Western Himalayas, Pakistan

Water shortages in Pakistan are among the most severe in the world, and its water resources are decreasing significantly due to the prevailing hydro-meteorological conditions. We assessed variations in meteorological and hydrological variables using innovative trend analysis (ITA) and traditional trend analysis methods at a practical significance level, which is also of practical interest. We developed threshold levels of hydrological variables and developed a non-parametric climate-sensitivity model of the high-altitude catchment of the western Himalayas. The runoff of Zone I decreased, while the temperature increased and the precipitation increased significantly. In Zone II, the runoff and temperature increased but the precipitation decreased. A two-dimensional visualization of the Pardé coefficient showed extreme drought events, and indicated greater sensitivity of the hydrological regime to temperature than to precipitation. The threshold levels of runoff for Zones I and II were 320 and 363 mm using the Q80 fixed method, while the mean runoff amounts were estimated to be 79.95 and 55.61 mm, respectively. The transient threshold levels varied by month, and the duration of droughts in Zones I and II ranged from 26.39 to 78.98 days. The sensitivity of the hydrological regime was estimated based on a modified climate-elasticity model (εp = 0.11–0.23, εt = −0.04–2.39) for Zones I and II, respectively. These results highlight the sensitivity of the hydrological regime to temperature, which influences the melting process. However, it is important to establish thresholds for hydrological variables and understand the climate sensitivity of the hydrological regime of the entire basin, so that policy makers and water managers can make sustainable water-resource-management decisions for this region