Statistical Inference Methods for Two Crossing Survival Curves: A Comparison of Methods

A common problem that is encountered in medical applications is the overall homogeneity of survival distributions when two survival curves cross each other. A survey demonstrated that under this condition, which was an obvious violation of the assumption of proportional hazard rates, the log-rank test was still used in 70% of studies. Several statistical methods have been proposed to solve this problem. However, in many applications, it is difficult to specify the types of survival differences and choose an appropriate method prior to analysis. Thus, we conducted an extensive series of Monte Carlo simulations to investigate the power and type I error rate of these procedures under various patterns of crossing survival curves with different censoring rates and distribution parameters. Our objective was to evaluate the strengths and weaknesses of tests in different situations and for various censoring rates and to recommend an appropriate test that will not fail for a wide range of applications. Simulation studies demonstrated that adaptive Neyman’s smooth tests and the two-stage procedure offer higher power and greater stability than other methods when the survival distributions cross at early, middle or late times. Even for proportional hazards, both methods maintain acceptable power compared with the log-rank test. In terms of the type I error rate, Renyi and Cramér—von Mises tests are relatively conservative, whereas the statistics of the Lin-Xu test exhibit apparent inflation as the censoring rate increases. Other tests produce results close to the nominal 0.05 level. In conclusion, adaptive Neyman’s smooth tests and the two-stage procedure are found to be the most stable and feasible approaches for a variety of situations and censoring rates. Therefore, they are applicable to a wider spectrum of alternatives compared with other tests.     

Production of Bio-Energy from Pig Manure: A Focus on the Dynamics Change of Four Parameters under Sunlight-Dark Conditions

This study investigated the effect of sunlight-dark conditions on volatile fatty acids (VFAs), total ammonium nitrogen (TAN), total alkalinity (TA) and pH during pig manure (PM) digestion and then the subsequent influence on biogas yield of PM. PM₁ and PM₂ were performed in a transparent reactor and a non-transparent reactor, respectively. Two sets of experiments were conducted with a temperature of 35.0±2.0 °C and a total solid concentration of 8.0% to the digestion material. The dynamic change of the four parameters in response to sunlight-dark conditions resulted in variations of the physiological properties in the digester and affected the cumulative biogas production (CBP). PM₁ obtained higher CBP (15020.0 mL) with a more stable pH and a lower TAN concentration (1414.5 mg/L) compared to PM₂ (2675.0 mL and 1670.0 mg/L, respectively). The direct path coefficients and indirect path coefficients between the four parameters and CBP were also analyzed.     

The Combined Effects of Moss-Dominated Biocrusts and Vegetation on Erosion and Soil Moisture and Implications for Disturbance on the Loess Plateau,China

Biological soil crusts (BSCs, or biocrusts) have important positive ecological functions such as erosion control and soil fertility improvement, and they may also have negative effects on soil moisture in some cases. Simultaneous discussions of the two-sided impacts of BSCs are key to the rational use of this resource. This study focused on the contribution of BSCs while combining with specific types of vegetation to erosion reduction and their effects on soil moisture, and it addressed the feasibility of removal or raking disturbance. Twelve plots measuring 4 m × 2 m and six treatments (two plots for each) were established on a 15° slope in a small watershed in the Loess Plateau using BSCs, bare land (as a control, BL), Stipa bungeana Trin. (STBU), Caragana korshinskii Kom. (CAKO), STBU planted with BSCs (STBU+BSCs) and CAKO planted with BSCs (CAKO+BSCs). The runoff, soil loss and soil moisture to a depth of 3 m were measured throughout the rainy season (from June to September) of 2010. The results showed that BSCs significantly reduced runoff by 37.3% and soil loss by 81.0% and increased infiltration by 12.4% in comparison with BL. However, when combined with STBU or CAKO, BSCs only made negligible contributions to erosion control (a runoff reduction of 7.4% and 5.7% and a soil loss reduction of 0.7% and 0.3%). Generally, the soil moisture of the vegetation plots was lower in the upper layer than that of the BL plots, although when accompanied with a higher amount of infiltration, this soil moisture consumption phenomenon was much clearer when combining vegetation with BSCs. Because of the trivial contributions from BSCs to erosion control and the remaining exacerbated consumption of soil water, moderate disturbance by BSCs should be considered in plots with adequate vegetation cover to improve soil moisture levels without a significant erosion increase, which was implied to be necessary and feasible.