Primary variables

Choosing a single primary endpoint is part of a strategy to reduce multiplicity in statistical testing. We will leave discussion of the problems arising with multiplicity until Chapter 10 and focus here on the nature of endpoints both from a statistical and a clinical point of view. 

Generally the primary endpoint should be that endpoint that is the clinically most relevant endpoint from the patients perspective. 

ICH E9 (1998) Note for Guidance on Statistical Principles for Clinical Trials  

7he primary variable ( target variable, primary endpoint) should be that variable capable of providing the most clinically relevant and convincing evidence directly related to the primary objective of the trial.  

This choice should allow, amongst other things, a clear quantitative measure of benefit at the individual patient level. As we will see, identifying new treatments is not just about statistical significance, it is also about clinical importance and the 

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On-line analysis is often more expensive and difficult to set up initially but can be more accurate and rehable if performed properly. On-line analyzers can also be used to provide real-time control of a process through a secondary variable such as severity or conversion, as opposed to controlling a primary variable, such as temperature (36,52). 

Primary Variables. The most obvious variables are those whose effects on performance are to be evaluated directiy these ate the variables that, most likely, created the need for the investigation in the first place. Such variables may be quantitative, such as catalyst concentration, temperature, or pressure, or they may be quaUtative, such as method of preparation, catalyst type, or batch of material. 

An important purpose of a designed experiment is to obtain information about interactions among the primary variables. This is accompbshed by varying factors simultaneously rather than one at a time. Thus in Figure 2, each of the two preparations would be mn at both low and high temperatures using, for example, a full factorial experiment. 

The symmetry of the preceding example is not always found in practice. For example, there may be six tire types under comparison and fifteen available automobiles. Tires are then assigned to automobiles to obtain the most precise comparison among tire types, using a so-called incomplete block design. Similar concepts apply if there are two or more primary variables, rather than tire type alone. 

A main reason for mnning an experiment in blocks is to ensure that the effect of a background variable does not contaminate evaluation of the effects of the primary variables. However, blocking removes the effect of the blocked variables from the experimental error as well, thus allowing more... 

In this plan, the effects of both automobile and wheel position are controlled by blocking. It should, however, be kept in mind that for the Latin square design, as for other blocking plans, it is generally assumed that the blocking variables do not interact with the primary variable to be evaluated. 

Randomization means that the sequence of preparing experimental units, assigning treatments, miming tests, taking measurements, and so forth, is randomly deterrnined, based, for example, on numbers selected from a random number table. The total effect of the uncontrolled variables is thus lumped together into experimental error as unaccounted variabiUty. The more influential the effect of such uncontrolled variables, the larger the resulting experimental error, and the more imprecise the evaluations of the effects of the primary variables. Sometimes, when the uncontrolled variables can be measured, their effect can be removed from experimental error statistically. 

NO removals of 90% are achievable. The primary variable is temperature, which depends on catalyst type (38). The principal components of an SCR... 

Here m < 5, n = 8, p > 3. Choose D, V, i, k, and as the primary variables. By examining the 5x5 matrix associated with those variables, we can see that its determinant is not zero, so the rank of the matrix is m = 5 thus, p = 3. These variables are thus a possible basis set. The dimensions of the other three variables h, p, and Cp must be defined in terms of the primary variables. This can be done by inspection, although linear algebra can be used, too. 

Variables It is possible to identify a large number of variables that influence the design and performance of a chemical reactor with heat transfer, from the vessel size and type catalyst distribution among the beds catalyst type, size, and porosity to the geometry of the heat-transfer surface, such as tube diameter, length, pitch, and so on. Experience has shown, however, that the reactor temperature, and often also the pressure, are the primary variables feed compositions and velocities are of secondary importance and the geometric characteristics of the catalyst and heat-exchange provisions are tertiary factors. Tertiary factors are usually set by standard plant practice. Many of the major optimization studies cited by Westerterp et al. (1984), for instance, are devoted to reactor temperature as a means of optimization. 

Particle diameter is a primary variable important to many chemical engineering calculations, including settling, slurry flow, fluidized beds, packed reactors, and packed distillation towers. Unfortunately, this dimension is usually difficult or impossible to measure, because the particles are small or irregular. Consequently, chemical engineers have become familiar with the notion of equivalent diameter of a partiele, which is the diameter of a sphere that has a volume equal to that of the particle. 

Unfortunately, neither the computer nor the potentiometric recorder measures the primary variable, volume of mobile phase, but does measure the secondary variable, time. This places stringent demands on the LC pump as the necessary accurate and proportional relationship between time and volume flow depends on a constant flow rate. Thus, peak area measurements should never be made unless a good quality pump is used to control the mobile phase flow rate. Furthermore, the pump must be a constant flow pump and not a constant pressure pump. 

Once the primary variables were obtained, numerous secondary variables were also calculated such as overall conversion, monomer A and B conversions, polymer composition from the moles of A and B in the copolymer, and number average molecular weight. The latter was obtained by dividing the mass of monomers A and B in the polymer by the moles of polymer. 

The basic SFC system comprises a mobile phase delivery system, an injector (as in HPLC), oven, restrictor, detector and a control/data system. In SFC the mobile phase is supplied to the LC pump where the pressure of the fluid is raised above the critical pressure. Pressure control is the primary variable in SFC. In SFC temperature is also important, but more as a supplementary parameter to pressure programming. Samples are introduced into the fluid stream via an LC injection valve and separated on a column placed in a GC oven thermostatted above the critical temperature of the mobile phase. A postcolumn restrictor ensures that the fluid is maintained above its critical pressure throughout the separation process. Detectors positioned either before or after the postcolumn restrictor monitor analytes eluting from the column. The key feature differentiating SFC from conventional techniques is the use of the significantly elevated pressure at the column outlet. This allows not only to use mobile phases that are either impossible or impractical under conventional LC and GC conditions but also to use more ordinary... 

In the analysis of experimental rate data taken in variable volume systems it is possible to develop another expression for the rate of formation of species i that is more convenient to use than equation 3.1.39. This alternative approach has been popularized by Levenspiel (2). It involves the use of fraction conversion rather than concentration as a primary variable and is applicable only to systems in which the volume varies linearly with the fraction conversion. 

These four dimensionless groups can now be used as the primary variables to define the system behavior in place of the original seven variables. 

Because the chemical structure of a molecule encodes its biological properties, structure has long served as the primary variable and determinant for the discovery of new drugs by medicinal chemists. For this reason, systematic structural modification has been the primary tool of choice to isolate and enhance a desired biologic activity. Moreover, with the relatively recent development of in vitro receptor-binding assays, combinatorial methods of chemical synthesis, and computer graphics, the overall approach to structural modification has become increasingly sophisticated. 

We will also talk in Chap. 11 about the two types of cascade control series cascade and parallel cascade. The two examples discussed above are both series cascade systems because the manipulated variable affects the secondary controlled variable, which then affects the primary variable. In a parallel cascade system the manipulated variable affects both the primary and the secondary controlled variables directly. Thus the two processes are basically different and result in different dynamic characteristics. We will quantify these ideas later. 

Retention theory from the work of Lanin and Nikitin [55] (Equation 1.6) was adapted to describe the dependency of retention factors k) as a function of the mobile phase composition [53]. The concentration of the polar modifier is, besides the type, the primary variable for the optimization of the separation and can be described by competitive adsorption reactions of solute (i.e., sorbate) and polar modifier for which the following relationship can be applied (Equation 1.6)... 

Equation 9.5 shows that for an acceptable retention factor, the diffusion coefficient and particle size of the packing are the primary variables that can be varied to affect the N/tf An increase in the diffusion coefficient or a decrease in the particle size causes an increase in N/tf If the diffusion coefficient can be increased without impacting the retention factor significantly, then significant increases in separation speed will result. To minimally impact the retention factor the solvent strength of the mobile phase must be maintained. 

The primary variables influencing hydrotreating are hydrogen partial pressure, process temperature, and contact time. Higher hydrogen pressure gives a better removal of undesirable... 

Is one variable more important than others Redefinition of the primary variable after... 

Sample sizes for clinical trials are discussed more fully elsewhere in this book and should be established in discussion with a statistician. Sample sizes should, however, be sufficient to be 90% certain of detecting a statistically significant difference between treatments, based on a set of predetermined primary variables. This means that trials utilising an active control will generally be considerably larger than placebo-controlled studies, in order to exclude a Type II statistical error (i.e. the failure to demonstrate a difference where one exists). Thus, in areas where a substantial safety database is required, for example, hypertension, it may be appropriate to have in the programme a preponderance of studies using a positive control. 

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