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.     

Diffusion of extracellular K+ can synchronize bursting oscillations in a model islet of Langerhans.

Electrical bursting oscillations of mammalian pancreatic beta-cells are synchronous among cells within an islet. While electrical coupling among cells via gap junctions has been demonstrated, its extent and topology are unclear. The beta-cells also share an extracellular compartment in which oscillations of K+ concentration have been measured (Perez-Armendariz and Atwater, 1985). These oscillations (1-2 mM) are synchronous with the burst pattern, and apparently are caused by the oscillating voltage-dependent membrane currents: Extracellular K+ concentration (Ke) rises during the depolarized active (spiking) phase and falls during the hyperpolarized silent phase. Because raising Ke depolarizes the cell membrane by increasing the potassium reversal potential (VK), any cell in the active phase should recruit nonspiking cells into the active phase. The opposite is predicted for the silent phase. This positive feedback system might couple the cells' electrical activity and synchronize bursting. We have explored this possibility using a theoretical model for bursting of beta-cells (Sherman et al., 1988) and K+ diffusion in the extracellular space of an islet. Computer simulations demonstrate that the bursts synchronize very quickly (within one burst) without gap junctional coupling among the cells. The shape and amplitude of computed Ke oscillations resemble those seen in experiments for certain parameter ranges. The model cells synchronize with exterior cells leading, though incorporating heterogeneous cell properties can allow interior cells to lead. The model islet can also be forced to oscillate at both faster and slower frequencies using periodic pulses of higher K+ in the medium surrounding the islet. Phase plane analysis was used to understand the synchronization mechanism. The results of our model suggest that diffusion of extracellular K+ may contribute to coupling and synchronization of electrical oscillations in beta-cells within an islet.     

Mechanistic studies on aromatase and related C---C bond cleaving P-450 enzymes

Some P-450 systems, notably aromatase and 14-demethylase catalyse not only the hydroxylate reaction but also the oxidation of an alcohol into a carbonyl compound as well as a C---C bond cleavage process. All these reactions occur at the same active site. A somewhat analogous situation is noted with 17-hydroxylase-17,20-lyase that participates in hydroxylation as well as C---C bond cleavage process. The C---C bond cleavage reactions catalysed by the above enzymes conform to the general equation:

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It is argued that all three types of reaction catalyzed by these enzymes may be viewed as variations on a common theme. In P-450 dependent hydroxylation the initially formed Fe^III---O---O^. species is converted into Fe^III---O---OH and the heterolysis of the oxygen—oxygen bond of the latter then gives the oxo-derivative for which a number of canonical structures are possible; for example Fe^V = O ↔ (+^.)Fe^IV = O ↔ Fe^IV---O^.. One of these, Fe^IV---O^. behaves like an alkoxyl radical and participates in hydrogen abstraction from C---H bond to produce Fe^IV---OH and carbon radical. The latter is then quenched by the delivery of hydroxyl radical from Fe^IV---OH. The latter species may thus be regarded as a carrier of hydroxyl radical. We have proposed that the C---C bond cleavage reaction occurs through the participation of the Fe^III---O---OH species that is trapped by the electrophilic property of the carbonyl compound giving a peroxide adduct that fragments to produce an acyl—carbon cleavage. Scientific developments leading up to this conclusion are considered. In the first author's views,

“The study of mechanisms is not a scientific but a cultural activity. Mechanisms do not aim at an absolute truth but are intended to be a “running” commentary on the status of knowledge in a field. As the structural knowledge in a field advances Mechanisms evolve to take note of the new findings. Just as a constructive “running” commentary provides the stimulus for higher standards of performance, so Mechanisms call for better and firmer structural information from their practitioners”.     

Functional and genetic plasticities of the poliovirus genome: quasi-infectious RNAs modified in the 5'-untranslated region yield a variety of pseudorevertants.

Poliovirus RNA species with nucleotides 564 to 571 deleted or with a secondary structure domain (positions 564 to 629) replaced by a shorter irregular oligonucleotide have been engineered previously; these RNAs have been considered quasi-infectious (yielding a single late revertant plaque) and dead, respectively (E. Pilipenko, A. Gmyl, Y. Svitkin, S. Maslova, A. Sinyakov, and V. Agol, Cell 68:119-131, 1992). By using large amounts of these RNAs for transfections, revertant clones with a great variety of genetic changes (point mutations, insertions of foreign sequences, short or extended deletions) were isolated. The pattern of these changes supported the notion that an appropriately spaced oligopyrimidine-AUG tandem is important for efficient poliovirus RNA translation. Structural features within and around this tandem modulated the initiation efficiency. The functional and genetic plasticities of the poliovirus genome are briefly discussed.