Combining centres

The ideal situation in a multi-centre trial is to have a small number of large centres (or pre-defined pseudo-centres). This gives the necessary consistency and control yet still allows the evaluation of heterogeneity. In practice, however, we do not always end up in this situation and combining centres at the data analysis stage inevitably needs to be considered. From a statistical perspective adjusting for small centres in the analysis is problematic and leads to unreliable estimates of treatment effect so we generally have to combine. 

There are no fixed rules for these combinations but several points should be noted  

We will discuss the decision-making process with regard to the Statistical Analysis Plan and the Blind Review in Section 16.3. 

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Combining centres just because they are small or combining centres to produce centres of similar size has no scientific justification (see CPMP (2003) Points to Consider on Adjustment for Baseline Covariates ). 

Ideally, rules for combining centres should be detailed in the Statistical Analysis Plan. 

Finalisation of algorithms for combining centres should this be required... 

In South Wales, the Welsh Combined Centres for Public Health compared indices of health in a population living near a landfill site with a population matched for socioeconomic status and examined environmental monitoring data.28 Using odour complaints as a proxy for exposure in five wards near the site, the authors compared mortality, rates of hospital admission and measures of reproductive health (proportion of all births and stillbirths of infants weighing... 

Austenitic Steel weld has a well defined transcrystalline (oriented) macrostructure with continuously changing orientation of the crystal axis - from the periphery towards the centre the angle between the axis of the crystal and the axis of the weld is changed from 90 to 0 degrees. Weld metal eould be possible to approximate in the form of a discrete combination of crystals with parallel axes of the crystallites. 

One of the most important fiinctions in the application of light scattering is the ability to estimate the object dimensions. As we have discussed earlier for dilute solutions containing large molecules, equation (B 1.9.38) can be used to calculate tire radius of gyration , R, which is defined as the mean square distance from the centre of gravity [12]. The combined use of equation (B 1.9.3 8) equation (B 1.9.39) and equation (B 1.9.40) (tlie Zimm plot) will yield infonnation on R, A2 and molecular weight. 

Figure Bl.16.9. Background-free, pseudo-steady-state CIDNP spectra observed in the photoreaction of triethylamine with different sensitizers ((a), antliraquinone (b), xanthone, CIDNP net effect (c), xanthone, CIDNP multiplet effect, amplitudes multiplied by 1.75 relative to the centre trace) in acetonitrile-d3. The stmctiiral formulae of the most important products bearing polarizations (1, regenerated starting material 2, N,N-diethylvinylamine 3, combination product of amine and sensitizer) are given at the top R denotes the sensitizer moiety. The polarized resonances of these products are assigned in the spectra. Reprinted from [21].

To overcome the primary weakness of GTO fimetions (i.e. their radial derivatives vanish at the nucleus whereas the derivatives of STOs are non-zero), it is coimnon to combine two, tliree, or more GTOs, with combination coefficients which are fixed and not treated as LCAO-MO parameters, into new functions called contracted GTOs or CGTOs. Typically, a series of tight, medium, and loose GTOs are multiplied by contraction coefficients and suimned to produce a CGTO, which approximates the proper cusp at the nuclear centre. 

To solve the Kohn-Sham equations a number of different approaches and strategies have been proposed. One important way in which these can differ is in the choice of basis set for expanding the Kohn-Sham orbitals. In most (but not all) DPT programs for calculating the properties of molecular systems (rather than for solid-state materials) the Kohn-Sham orbitals are expressed as a linear combination of atomic-centred basis functions ... 

Fig. 12.27 The generation of 3-centre pharmacophore keys, illustrated using benperidol. Two different conformations are shown, together with two different combinations of three pharmacophore points.

A major trend in organic synthesis, however, is the move towards complex systems. It may happen that one needs to combine a steroid and a sugar molecule, a porphyrin and a carotenoid, a penicillin and a peptide. Also the specialists in a field have developed reactions and concepts that may, with or without modifications, be applied in other fields. If one needs to protect an amino group in a steroid, it is advisable not only to search the steroid literature but also to look into publications on peptide synthesis. In the synthesis of corrin chromophores with chiral centres, special knowledge of steroid, porphyrin, and alkaloid chemistry has been very helpful (R.B. Woodward, 1967 A. Eschenmoser, 1970). 

When there is only one process line and one MCC alone is adequate to control the entire process, it is possible to combine the PCC and the MCC into one unit to save on space and cost. The assembly may now be called a PMCC (power-cum-motor control centre). 

From an FMEA of the system design, a Severity Rating S) = 1 was allocated, relating to a safety critical failure in service. It is required to find the optimum unequal angle section size from the standard sizes available. It is assumed that the load is carried at the section s centre of gravity, G, and only stresses due to bending of the section are considered, that is, the torsional effects are minimal. The combined weight of the beam and tie rod are not to be taken into account. 

Overview of combined modeling of heat transport and air movement, AIVC Technical Note TN 40. Coventry Air Infiltration and Ventilation Centre, 1993. 

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