The waiting game: how long is long enough?
The time it takes to recruit patients into a clinical trial has a major impact on whether a drug development programme completes on time. Here Byron Jones explains how simple statistical models can be very useful in predicting the time to complete recruitment.
The design of multicentre trials
The analysis of data collected in multicentre trials offers challenges because the data from the individual centres must be combined in some way to give an overall evaluation of the differences between the treatments in the trial. We propose that the combined response to treatment (CRT) be used as this overall measure. The definition and estimation of the CRT can be derived from either a fixed-effects or a random-effects model. For the latter we introduce the ECRT - the expected combined response to treatment. We describe and compare both types of model and express our preference for the random-effects model. We stress that the number of patients enrolled at a centre is a random variable and show that this source of randomness inflates the variance of the estimated ECRT. Variability in enrolment rates over the centres further inflates this variance. A simple conclusion from our results is that if variability in the treatment and centre effects, in the enrolment time, in the number of patients enrolled at a centre and in the enrolment rates is not properly accounted for, then an underpowered trial may result. Using properties of estimators generated by the random-effects model we propose methods for determining the optimal number of centres and total number of patients to enrol in a trial to minimize a loss function that accounts for centre and patient costs and loss of revenue. We discuss variants of the loss function and corresponding optimization problems for different types of enrolment. We end the paper with brief generalizations of the developed techniques to the case where the response is binary.
Molecular diversity of skin mucus lectins in fish.
Among lectins in the skin mucus of fish, primary structures of four different types of lectin have been determined. Congerin from the conger eel Conger myriaster and AJL-1 from the Japanese eel Anguilla japonica were identified as galectin, characterized by its specific binding to beta-galactoside. Eel has additionally a unique lectin, AJL-2, which has a highly conserved sequence of C-type lectins but displays Ca(2+)-independent activity. This is rational because the lectin exerts its function on the cutaneous surface, which is exposed to a Ca(2+) scarce environment when the eel is in fresh water. The third type lectin is pufflectin, a mannose specific lectin in the skin mucus of pufferfish Takifugu rubripes. This lectin showed no sequence similarity with any known animal lectins but, surprisingly, shares sequence homology with mannose-binding lectins of monocotyledonous plants. The fourth lectin was found in the ponyfish Leiognathus nuchalis and exhibits homology with rhamnose-binding lectins known in eggs of some fish species. These lectins, except ponyfish lectin, showed agglutination of certain bacteria. In addition, pufflectin was found to bind to a parasitic trematode, Heterobothrium okamotoi. Taken together, these results demonstrate that skin mucus lectins in fish have wide molecular diversity.