594 research outputs found
Comparison of control charts for monitoring clinical performance using binary data.
BACKGROUND: Time series charts are increasingly used by clinical teams to monitor their performance, but statistical control charts are not widely used, partly due to uncertainty about which chart to use. Although there is a large literature on methods, there are few systematic comparisons of charts for detecting changes in rates of binary clinical performance data. METHODS: We compared four control charts for binary data: the Shewhart p-chart; the exponentially weighted moving average (EWMA) chart; the cumulative sum (CUSUM) chart; and the g-chart. Charts were set up to have the same long-term false signal rate. Chart performance was then judged according to the expected number of patients treated until a change in rate was detected. RESULTS: For large absolute increases in rates (>10%), the Shewhart p-chart and EWMA both had good performance, although not quite as good as the CUSUM. For small absolute increases (<10%), the CUSUM detected changes more rapidly. The g-chart is designed to efficiently detect decreases in low event rates, but it again had less good performance than the CUSUM. IMPLICATIONS: The Shewhart p-chart is the simplest chart to implement and interpret, and performs well for detecting large changes, which may be useful for monitoring processes of care. The g-chart is a useful complement for determining the success of initiatives to reduce low-event rates (eg, adverse events). The CUSUM may be particularly useful for faster detection of problems with patient safety leading to increases in adverse event rates.
An Explanatory Study on the Non-Parametric Multivariate T2 Control Chart
Most control charts require the assumption of normal distribution for observations. When distribution is not normal, one can use non-parametric control charts such as sign control chart. A deficiency of such control charts could be the loss of information due to replacing an observation with its sign or rank. Furthermore, because the chart statistics of T2 are correlated, the T2 chart is not a desire performance. Non-parametric bootstrap algorithm could help to calculate control chart parameters using the original observations while no assumption regarding the distribution is needed. In this paper, first, a bootstrap multivariate control chart is presented based on Hotelling’s T2 statistic then the performance of the bootstrap multivariate control chart is compared to a Hotelling’s T2 parametric multivariate control chart, a multivariate sign control chart, and a multivariate Wilcoxon control chart using a simulation study. Ultimately, the bootstrap multivariate control chart is used in an empirical example to study the process of sugar production
Guaranteed Conditional Performance of Control Charts via Bootstrap Methods
To use control charts in practice, the in-control state usually has to be
estimated. This estimation has a detrimental effect on the performance of
control charts, which is often measured for example by the false alarm
probability or the average run length. We suggest an adjustment of the
monitoring schemes to overcome these problems. It guarantees, with a certain
probability, a conditional performance given the estimated in-control state.
The suggested method is based on bootstrapping the data used to estimate the
in-control state. The method applies to different types of control charts, and
also works with charts based on regression models, survival models, etc. If a
nonparametric bootstrap is used, the method is robust to model errors. We show
large sample properties of the adjustment. The usefulness of our approach is
demonstrated through simulation studies.Comment: 21 pages, 5 figure
Some statistical problems in sequential meta-analysis
The objective of meta-analysis is to combine results from several independent studies in
order to make evidence more generalisable and provide evidence base for decision making.
However, recent studies show that the magnitude of effect size estimates reported in many
areas of research have significantly changed over time. These temporal trends can be dramatic
and even lead to the loss or gain of the statistical significance of the cumulative treatment
effect (Kulinskaya and Koricheva, 2010). Standard sequential methods including cumulative
meta-analysis, sequential meta-analysis, the use of quality control charts and penalised z-test
have been proposed for monitoring the trends in meta-analysis. But these methods are only
effective when monitoring in fixed effect model (FEM) of meta-analysis. For random-effects
model (REM), the analysis incorporates the heterogeneity variance, t2 and its estimation
creates complications. This thesis proposes the use of a truncated CUSUM-type test (Gombay
method) for sequential monitoring in REM, and also examines the effect of accumulating
evidence in meta-analysis. Simulations show that the use of Gombay method with critical
values derived from asymptotic theory does not control the Type I error. However, the
test with bootstrap-based critical values (retrospective Gombay sequential bootstrap test
for REM) leads to a reduction of the difference between the true and nominal levels, and
thus constitutes a good approach for monitoring REM. Application of the proposed method
is illustrated using two meta-analytic examples from medicine. Two kinds of bias associated
with accumulating evidence, termed \sequential decision bias" and \sequential design bias" are
identified. It was demonstrated analytically and by simulations that both types of sequential
biases are non negligible. Simulations also show that sequential biases increase with increased
heterogeneity
Nonparametric Predictive Methods for Bootstrap and Test Reproducibility
This thesis investigates a new bootstrap method, this method is called Nonparametric
Predictive Inference Bootstrap (NPI-B). Nonparametric predictive inference
(NPI) is a frequentist statistics approach that makes few assumptions, enabled by
using lower and upper probabilities to quantify uncertainty, and explicitly focuses
on future observations. In the NPI-B method, we use a sample of n observations to
create n + 1 intervals and draw one future value uniformly from one interval. Then
this value is added to the data and the process is repeated, now with n+1 observations.
Repetition of this process leads to the NPI-B sample, which therefore is not
taken from the actual sample, but consists of values in the whole range of possible
observations, also going beyond the range of the actual sample. We explore NPI-B
for data on finite intervals, real line and non negative observations, and compare
it to other bootstrap methods via simulation studies which show that the NPI-B
method works well as a prediction method.
The NPI method is presented for the reproducibility probability (RP) of some
nonparametric tests. Recently, there has been substantial interest in the reproducibility
probability, where not only its estimation but also its actual definition
and interpretation are not uniquely determined in the classical frequentist statistics
framework. The explicitly predictive nature of NPI provides a natural formulation
of inferences on RP. It is used to derive lower and upper bounds of RP values (known
as the NPI-RP method) but if we consider large sample sizes, the computation of
these bounds is difficult. We explore the NPI-B method to predict the RP values
(they are called NPI-B-RP values) of some nonparametric tests. Reproducibility of
tests is an important characteristic of the practical relevance of test outcomes
Probability and Statistics in Aerospace Engineering
This monograph was prepared to give the practicing engineer a clear understanding of probability and statistics with special consideration to problems frequently encountered in aerospace engineering. It is conceived to be both a desktop reference and a refresher for aerospace engineers in government and industry. It could also be used as a supplement to standard texts for in-house training courses on the subject
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