Treatment effects/differences standard error

Effect size. A measure used by meta-analysts to combine information from studies for which the original scales of measurement were different. It is the ratio of the estimated treatment effect from a study to the estimate of the standard deviation (note not the standard error). Since both treatment effect and standard deviation are measured on the same scale it is unit free . Its expected value is more or less independent of the size of the study but it does depend on the study population as well as on the treatment effect. Since sponsors have access to raw data and the ability to plan drug development programmes, they should have little need of this measure. 

Assume that we have decided on the best measure for the treatment effect. If this is expressed as a difference, for example, in the means, then there will be an associated standard error measuring the precision of that difference. If the... 

The answer is analysis of covariance . If we employ analysis of covariance using the baseline as a covariate, it makes absolutely no difference whether our measure is raw outcomes or change scores. Formally, as regards the estimate of the treatment effect and its standard error, exactly the same result is produced (Laird, 1983). Hence, provided analysis of covariance is employed, the whole debate is rendered irrelevant. 

Replication means that the basic experimental measurement is repeated. For example, if one is measuring the CO2 concentration of blood, those measurements would be repeated several times under controlled circumstances. Replication serves several important functions. First, it allows the investigator to estimate the variance of the experimental or random error through the sample standard deviation (s) or sample variance (i ). This estimate becomes a basic unit of measurement for determining whether observed differences in the data are statistically significant. Second, because the sample mean (x) is used to estimate the true population mean (/a), replication enables an investigator to obtain a more precise estimate of the treatment effect s value. If s is the sample variance of the data for n replicates, then the variance of the sample mean is = s /n. 

First, it should be remembered that the basic observation, a rise in plasma factor VIII concentration, depends entirely upon a biological assay, in which the corrective effect of the test plasma is compared to that of a control plasma when both are added to plasma obtained from a severely affected hemophiliac, or to an artificial system containing necessary clotting factors other than factor VIII. In acute experiments it has been usual to assay the subject s pretreatment plasma as well as the plasma obtained after the experiment, or to use the pretreatment plasma as the standard (nominally 100%) for the assay. The second procedure eliminates errors due to differences between subjects, but uncertainty still remains regarding the effects of the experimental treatment upon the assay system, apart from a possible true increase in factor VIII concentration. A number of experiments have therefore been directed to testing the validity of the... 

A significant difference between the effectiveness of semiclassical and optimal treatments is apparent in Fig. 14. The optimal treatment provides an improvement in estimation procedure, and the difference is more than 10 standard deviations beyond the statistical error. High stability and visibility of interference fringes in the optical interferometer along with a high repetition rate of pulsed lasers made the improvement of the NFM phase prediction more evident than in a similar comparison that had been done with thermal neutrons [70] (see Fig. 15). 

In the following section we describe some of these methods and how they may show the different effects of dispersion and systematic error. Then in the remaining two sections of the chapter we will discuss methods for treating heteroscedastic systems. In the first place, we will show how their non-constant standard deviation may be taken into account in estimating models for the kind of treatment we have already described. Then we will describe the detailed study of dispersion within a domain, often employed to reduce variation of a product or process. 

As an example to help understand the effect of equivalence on sample size, consider a case where we wish to show that the difference in FEVi between two treatments is not greater than 200 ml and where the standard deviation is 350 ml for conventional type I and type II errors rates of 0.05 and 0.2. If we assume that the drugs are in fact exactly identical, the sample size needed (using a Normal approximation) is 53. If we allow for a true difference of 50 ml this rises to 69. On the other hand, if we wished to demonstrate superiority of one treatment over another for a clinically relevant difference of 200 ml with the other values as before, a sample size of 48 would suffice. Thus, in the best possible case a rise of about 10% in the sample size is needed (from 48 to 53). This difference arises because we have two one-sided tests each of which must be significant in order to prove efficacy. To have 80% power each must (in the case of exact equality) have approximately 90% power(because 0.9 x 0.9 = 0.8). The relevant sum of z-values for the power calculation is thus 1.2816-1-1.6449 = 2.93 as opposed to for a conventional trial 0.8416 -I-1.9600 = 2.8. The ratio of the square of 2.93 to 2.8 is about 1.1 explaining the 10% Increase in sample size. 

One of the assumptions of one-way (and other) ANOVA calculations is that the uncontrolled variation is truly random. However, in measurements made over a period of time, variation in an uncontrolled factor such as pressure, temperature, deterioration of apparatus, etc., may produce a trend in the results. As a result the errors due to uncontrolled variation are no longer random since the errors in successive measurements are correlated. This can lead to a systematic error in the results. Fortunately this problem is simply overcome by using the technique of randomization. Suppose we wish to compare the effect of a single factor, the concentration of perchloric acid in aqueous solution, at three different levels or treatments (0.1 M, 0.5 M, and 1.0 M) on the fluorescence intensity of quinine (which is widely used as a primary standard in fluorescence spectrometry). Let us suppose that four replicate intensity measurements are made for each treatment, i.e. in each perchloric acid solution. Instead of making the four measurements in 0.1 M acid, followed by the four in 0.5 M acid, then the four in 1 M acid, we make the 12 measurements in a random order, decided by using a table of random numbers. Each treatment is assigned a number for each replication as follows ... 

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