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

spcadjust: an R package for adjusting for estimation error in control charts

In practical applications of control charts the in-control state and the corresponding chart parameters are usually estimated based on some past in-control data. The estimation error then needs to be accounted for. In this paper we present an R package, spcadjust , which implements a bootstrap based method for adjusting monitoring schemes to take into account the estimation error. By bootstrapping the past data this method guarantees, with a certain probability, a conditional performance of the chart. In spcadjust the method is implement for various types of Shewhart, CUSUM and EWMA charts, various performance criteria, and both parametric and non-parametric bootstrap schemes. In addition to the basic charts, charts based on linear and logistic regression models for risk adjusted monitoring are included, and it is easy for the user to add further charts. Use of the package is demonstrated by examples

A weighted cumulative sum (WCUSUM) to monitor medical outcomes with dependent censoring

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/108011/1/sim6139.pd

Risk-adjusted CUSUM control charts for shared frailty survival models with application to hip replacement outcomes: a study using the NJR dataset

Background:  Continuous monitoring of surgical outcomes after joint replacement is needed to detect which brands’ components have a higher than expected failure rate and are therefore no longer recommended to be used in surgical practice. We developed a monitoring method based on cumulative sum (CUSUM) chart specifically for this application.  Methods:  Our method entails the use of the competing risks model with the Weibull and the Gompertz hazard functions adjusted for observed covariates to approximate the baseline time-to-revision and time-to-death distributions, respectively. The correlated shared frailty terms for competing risks, corresponding to the operating unit, are also included in the model. A bootstrap-based boundary adjustment is then required for risk-adjusted CUSUM charts to guarantee a given probability of the false alarm rates. We propose a method to evaluate the CUSUM scores and the adjusted boundary for a survival model with the shared frailty terms. We also introduce a unit performance quality score based on the posterior frailty distribution. This method is illustrated using the 2003-2012 hip replacement data from the UK National Joint Registry (NJR). Results:  We found that the best model included the shared frailty for revision but not for death. This means that the competing risks of revision and death are independent in NJR data. Our method was superior to the standard NJR methodology. For one of the two monitored components, it produced alarms four years before the increased failure rate came to the attention of the UK regulatory authorities. The hazard ratios of revision across the units varied from 0.38 to 2.28. Conclusions:  An earlier detection of failure signal by our method in comparison to the standard method used by the NJR may be explained by proper risk-adjustment and the ability to accommodate time-dependent hazards. The continuous monitoring of hip replacement outcomes should include risk adjustment at both the individual and unit level

Pseudo Observations in Multi-State Models and CUSUM Charts for Monitoring Outcomes of Multi-Center Studies.

This dissertation looks at two different problems essentially. In recent years, pseudo observations have found application in multi-state survival models, models for mean lifetime and competing risks to name a few. We have investigated the performance of estimates and confidence intervals based on pseudo observations in the context of a multi-state model with independent right censoring. This has been compared to estimates from a Cox proportional hazards model with confidence intervals obtained from the bootstrap. While simulations show that the bootstrap is doing well, it becomes evident from simulations and some theory that the pseudo observations method presents difficulty with implementation and may lead to inconsistent estimates, particularly with covariate-dependent censoring. The cumulative sum (CUSUM) procedure has been used for quite some time as a graphical sequential monitoring scheme for detecting small persistent shifts in the mean of observations generated from a manufacturing process. In recent years, it has also found application in the medical literature in the context of monitoring performances of participating centers for quality improvement in a multi-center study involving an ongoing intervention. In this dissertation, we develop and implement risk-adjusted CUSUM charts defined as a process in continuous time when the reports of outcomes are immediate as well as when there is a random delay or lag involved. Approximate theoretical results on the Average Run Length (ARL) of the CUSUM are also provided. A discussion on how to choose a control limit for the CUSUM and some relevant issues that come into play in doing so are also discussed in some detail. Simulation studies show that the new proposal is able to detect changes quicker than other methods in practice. The method is also illustrated on kidney transplant data from the Scientific Registry of Transplant Recipients (SRTR).Ph.D.BiostatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/57629/2/pbiswas_1.pd

Relative Survival Methods – Theory, Applications and Extensions to Monitoring

In cancer research, one is often interested in the part of the hazard which corresponds to the disease. If the cause of death is unknown as in cancer registry data, the standard methods in survival analysis do not distinguish between the mortality due to disease and other causes. This issue becomes the main motivation for the development of relative survival methods. First, the main concepts in relative survival are presented. Both non-parametric estimators and models of the excess hazard are studied and discussed. Simulation studies show that even if the Pohar-Perme method is an unbiased estimator of the so-called net survival, the traditional Ederer 2 estimator might still be preferable in certain situations due to its lower variance. When informative censoring is present, the degree of bias looks to be the same on average for both estimators. When it comes to modelling of the excess hazard, we cover two different types of models. The first group corresponds to parametric models where the baseline excess hazard is a piecewise constant function. For real-life data, this is usually not the case and a more flexible and semi-parametric model based on the EM-algorithm is therefore considered. By simulation, the piecewise constant models still perform decent if the gradient of the baseline excess hazard is not large and there are enough data such that a finer splitting of the follow-up interval can be used in the estimation procedure. In some situations, one might also want to monitor the excess hazard over time in order to detect a change. An approach based on methods from relative survival and statistical process control is proposed for this intention. Different simulation setups are used in order to illustrate the purpose of the method. Finally, most of the methods presented are applied to colon and rectum cancer data from the Norwegian Cancer Registry. Interesting results are obtained from the analysis. For instance, the effect of tumour location seems to vary between age groups. Similar arguments are observed related to cancer stage as well. The CUSUM charts show a clear improvement in the excess hazard over time, which agree with the results from non-parametric methods when stratified by diagnosis year period

Sequential change detection and monitoring of temporal trends in random-effects meta-analysis

Temporal changes in magnitude of effect sizes reported in many areas of research are a threat to the credibility of the results and conclusions of meta-analysis. Numerous sequential methods for meta-analysis have been proposed to detect changes and monitor trends in effect sizes so that meta-analysis can be updated when necessary and interpreted based on the time it was conducted. The difficulties of sequential meta-analysis under the random-effects model are caused by dependencies in increments introduced by the estimation of the heterogeneity parameter τ2. In this paper we propose the use of a retrospective CUSUM-type test with bootstrap critical values. This method allows retrospective analysis of the past trajectory of cumulative effects in random-effects meta-analysis, and its visualisation on a chart similar to CUSUM chart. Simulation results show that the new method demonstrates good control of Type I error regardless of the number or size of the studies and the amount of heterogeneity. Application of the new method is illustrated on two examples of medical meta-analyses

Risk Adjustment in clinical procedures

Ph.DDOCTOR OF PHILOSOPH