Missing at random

Subjects will drop out of trials for either random (ignorable) reasons or perhaps for a reason attributable to their disease, trial conditions, or other nonignorable factor. Both conditions are important to consider for efficacy trial simulation. In the former case, subjects who drop out (are missing) at random will result in a decrease in total sample size and may affect the study power. In the latter case, nonrandom dropout is considered to be nonignorable in that the reason for dropout is informative to the trial outcome and may bias the results. In the seminal paper by Sheiner (25), an example of nonrandom dropout is presented for an analgesic trial, where those subjects not achieving adequate pain relief were more likely to drop out (i.e., to take rescue medication). 

Suppose that patients are due to be measured on two occasions post randomization, yielding values i l, i 2> but that some are missing at random before the second occasion. A last observation carried forward approach is used and the second value is imputed using the first for such patients. We assume that there is no bias in this, so that we have the sort of condition where the effect of treatment is constant over a period of observation. (This might apply approximately, for example, for beta-agonists in asthma.)... 

Initially the calcium ions were placed on the faces of rings as well as at random locations in the cavity. Once many of the distinct minima had been found for specific aluminium configurations, calciums were placed in these positions to verify that no minima had been missed and optimised for all of the aluminium configurations The calcium ion positions were obtained in Cartesian co-ordinates relative to the centre of region 1, rather than fractional coordinates since ions in a defect model are not replicated periodically. In order to compare with X-ray diffraction data, approximate fractional co-ordinates for the calcium ion were found by assuming that the fractional co-ordinates of the defect centre did not change when the geometry of the defect was relaxed. Positions could then be related to the unit cell of the pure material. 

We observed surprisingly little guessing in our students. To be sure, there was some. A few students appeared to select icons at random and then proceeded immediately to use the calculator, combining all or some of the numbers in a hit or miss fashion, as already demonstrated in the first episode of Table 8.3. These students were, needless to say, among the least successful of the group. Most of the time, when an incorrect icon was accessed, the student eventually discovered this for himself or herself and moved on to the appropriate one. 

Drug development in the past has mostly been a hit or a miss affair with a large number of compounds being synthesized at random. Luck has played a great part, but we can now recognize strategies which have evolved over the years ... 

The importance of the execution model cannot be overemphasized. The execution model describes how the study is carried out and deviations from the protocol. There are deviations from the protocol that are done by the patient such as refusal to enter the study, dropouts, and patient noncompliance. Other deviations are due to practitioner behavior such as missing data, wrong recording of data, or improper preparation of doses. It must be decided whether the deviations are completely at random or if there is some influencing factor that may result in protocol deviations. For example, would patients experiencing adverse events have a greater tendency to drop out of the study ... 

Missing completely at random x2 was missing with probability 0.5 independent of Y or x ... 

The main problem with missing completely at random approaches is that it is hard... 

So vast are the applications of the new materials developed by chemists in collaboration with materials scientists, physicists, biologists, and engineers that I can do no more than stand in this Aladdin s cave of wonders and point around at random, knowing that I will miss a crucial development or example, but hoping to convey through just a few examples the impression that life is being transformed by this collaboration. 

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