Data censoring

This construction of p-boxes is general enough to incorporate the uncertainty arising from data censoring. Suppose the laboratory that produced the data sample tells us that 4 of the 15 measurements were below detection limit. This means that, because of the dilutions they used and the analytical resolution of the devices they employed, they cannot be sure that the true values were not zeros. 

Obviously, this kind of approach to data censoring does not result in a precise distribution, no matter how many data measurements are accumulated. By being conservative about measurement uncertainty, analysts can discern its consequences. If the effect of censoring is small, then the p-box will not be much wider on account of it. 

A prediction model must define all of the possible results that may be obtained from the alternative method. This is important since there are many different types of data available from typical alternative methods. Examples of data types include quantitative data, censored data, qualitative data, descriptive data, default values, and nonqualified... 

The mechanical and thermal properties of an in situ toughened silicon nitride material used to make a gas turbine combustor were experimentally measured. The location and nature of failure origins resulting from bend tests were determined with fractographic analysis. The measured Wei bull parameters were used along with thermal and stress analysis to determine failure probabilities of the combustor with the CARES design code. The effects of data censoring and fracture criterion were considered in the analysis. 

When all units have failed, the result is complete data. Singly-censored data result in life testing when testing is terminated before all units fail. And multiply-censored data result from ... 

The following are examples of situations with these reasons for multiply-censored data ... 

Graphical analysis of failure data is most commonly plotted using probability. However, in order to understand the hazard plotting method presented here, is not necessary to understand probability plotting. While it is difficult to utilize probability plotting for multiply-censored data, it is... 

Like all other methods for analyzing censored failure data, the hazard plotting method is also based on a certain assumption that must be satisfied if we are going to rely on the results. The assumption is that if the unfailed units were mn to failure, their failure times would be statistically independent of their censoring times. In other words, there is no relationship or correlation between the censoring time of a unit and the failure time. For example. 

To determine which hazard paper is appropriate to use when plotting a set of multiply censored data, first rely on engineering experience. If that is not an option, try different papers until you find one that is suitable. To save time, it may be a good idea to try plotting the sample cumulative hazard function on exponential hazard paper, since it is just... 

Table 62.5 Randomly censored simulated Weibull data...

The cumulative hazard plotting method and papers presented here provide simple means for statistical analyses of multiply censored failure data to obtain engineering information. The hazard-plotting method is simpler to use for multiply censored data than other plotting methods given in the literature and directly gives failure-rate information not provided by others. 

FIGURE 5.3 The Albumin in Acute Stroke (ALIAS) Phase II Trial. Data represent mean SEM. p-Value according to multiple regression analysis. Dead patients have been censored, (a) Mean change in NIH Stroke Scale score over time since treatment in rt-PA and non-rt-PA cohorts receiving the three lowest doses (Tiers I, 0.34 mg/kg II, 0.68 mg/kg III, 1.03 mg/kg) and three highest doses of albumin (Tiers IV, 1.37 mg/kg V, 1.71 mg/kg VI, 2.03 mg/kg). 

The study termination form data may be used for efficacy or safety analysis purposes. With regard to safety, if patients discontinue a study medication earlier than patients on standard therapy or placebo, then that is important to know. For efficacy analyses, patients who withdraw due to a lack of efficacy or adverse event may be precluded from being considered a treatment responder or success. Also, often the study termination date is used as a censor date in time-to-event analyses for therapy efficacy. Study termination forms play a key role in patient disposition summaries found at the start of a clinical study report. From a CDISC perspective, the study termination form is a finding. 

These methods are essential when there is any significant degree of mortality in a bioassay. They seek to adjust for the differences in periods of risk individual animals undergo. Life table techniques can be used for those data where there are observable or palpable tumors. Specifically, one should use Kaplan-Meier product limit estimates from censored data graphically, Cox-Tarone binary regression (log-rank test), and Gehan-Breslow modification of Kruskal-Wallis tests (Thomas et al., 1977 Portier and Bailer, 1989) on censored data. 

The Kaplan-Meier estimates produce a step function for each group and are plotted over the lifetime of the animals. Planned, accidentally killed, and lost animals are censored. Moribund deaths are considered to be treatment related. A graphical representation of Kaplan-Meier estimates provide excellent interpretation of survival adjusted data except in the cases where the curves cross between two or more groups. When the curves cross and change direction, no meaningful interpretation of the data can be made by any statistical method because proportional odds characteristic is totally lost over time. This would be a rare case where treatment initially produces more tumor or death and then, due to repair or other mechanisms, becomes beneficial. 

The ways in which data are collected in toxicology studies frequently serve to complicate trend analysis, as the length of time for the phenomena underlying a trend to express themselves is frequently artificially censored. 

A statistical technique used to test the significance of differences between the survival curves associated with two different treatments. It is often used to analyze survival (life vs. death) data when there are censored observations (observations that are unknown because a subject has not been in the study long enough for the outcome to be observed) or to analyze the effects of different treatment procedures. ... 

The HR-ICPMS cation analytical results are a robust dataset that is remarkably free of data qualifiers for 32 of the 63 cations analyzed an additional 14 cations have <20% censored data. Further, the low-level data have consistent map distribution patterns that make sense geologically. Described below are patterns for several possible porphyry-related elements. 

In practice, various complications may be encountered for which the simphstic description above will not be adequate. First, still within the realm of ID variabihty modeling, the measurements may be in some sense partially missing, e.g., censored or available only as summary statistics. In addition, methods may be applicable for specifying distributions based on professional judgment, particularly where the probabihties of interest do not represent relative frequencies, or the probabilities of interest do represent relative frequencies, but there are inadequate data to justify particular distributions. 

Finally, Section 3.4 discusses a range of procedures that may be applicable in situations where the information available is less than one would like. The data available may be too few, subject to various kinds of censoring or absence, or available only in summary form. 

Zero-modified distributions may be useful if concentration data contain more nondetections than can be accounted for by censoring at the level of detection. 

The data available may be too few, nonrepresentative, censored, or available only in... 

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