Discussion on “Time‐dynamic profiling with application to hospital readmission among patients on dialysis,” by Jason P. Estes, Danh V. Nguyen, Yanjun Chen, Lorien S. Dalrymple, Connie M. Rhee, Kamyar Kalantar‐Zadeh, and Damla Senturk

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/147781/1/biom12906_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/147781/2/biom12906.pd

Aspects of the analysis of multivariative failure time data

Multivariate failure time data arise in various forms including recurrent event data when individuals are followed to observe the sequence of occurrences of a certain type of event; correlated failure time when an individual is followed for the occurrence of two or more types of events for which the individual is simultaneously at risk, or when distinct individuals have dependent event times; or more complicated multistate processes when individuals may move among a number of discrete states over the course of a follow-up study and the states and associated sojourn times are recorded. Here we provide a critical review of statistical models and data analysis methods for the analysis of recurrent event data and correlated failure time data. This review suggests a valuable role for partially marginalized intensity models for the analysis of recurrent event data, and points to the usefulness of marginal hazard rate models and nonparametric estimates of pairwise dependencies for the analysis of correlated failure times. Areas in need of further methodology development are indicated

A Risk‐Adjusted O–E CUSUM with Monitoring Bands for Monitoring Medical Outcomes

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/97491/1/biom1822.pd

Discussions

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/111979/1/j.1751-5823.2011.00145.x.pd

Statistical Analysis of Illness–Death Processes and Semicompeting Risks Data

In many instances, a subject can experience both a nonterminal and terminal event where the terminal event (e.g., death) censors the nonterminal event (e.g., relapse) but not vice versa. Typically, the two events are correlated. This situation has been termed semicompeting risks (e.g., Fine, Jiang, and Chappell, 2001 ,  Biometrika   88, 907–939; Wang, 2003 ,  Journal of the Royal Statistical Society, Series B   65, 257–273), and analysis has been based on a joint survival function of two event times over the positive quadrant but with observation restricted to the upper wedge. Implicitly, this approach entertains the idea of latent failure times and leads to discussion of a marginal distribution of the nonterminal event that is not grounded in reality. We argue that, similar to models for competing risks, latent failure times should generally be avoided in modeling such data. We note that semicompeting risks have more classically been described as an illness–death model and this formulation avoids any reference to latent times. We consider an illness–death model with shared frailty, which in its most restrictive form is identical to the semicompeting risks model that has been proposed and analyzed, but that allows for many generalizations and the simple incorporation of covariates. Nonparametric maximum likelihood estimation is used for inference and resulting estimates for the correlation parameter are compared with other proposed approaches. Asymptotic properties, simulations studies, and application to a randomized clinical trial in nasopharyngeal cancer evaluate and illustrate the methods. A simple and fast algorithm is developed for its numerical implementation.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/78705/1/j.1541-0420.2009.01340.x.pd

Block-Conditional Missing at Random Models for Missing Data

Two major ideas in the analysis of missing data are (a) the EM algorithm [Dempster, Laird and Rubin, J. Roy. Statist. Soc. Ser. B 39 (1977) 1--38] for maximum likelihood (ML) estimation, and (b) the formulation of models for the joint distribution of the data ${Z}$ and missing data indicators ${M}$, and associated "missing at random"; (MAR) condition under which a model for ${M}$ is unnecessary [Rubin, Biometrika 63 (1976) 581--592]. Most previous work has treated ${Z}$ and ${M}$ as single blocks, yielding selection or pattern-mixture models depending on how their joint distribution is factorized. This paper explores "block-sequential"; models that interleave subsets of the variables and their missing data indicators, and then make parameter restrictions based on assumptions in each block. These include models that are not MAR. We examine a subclass of block-sequential models we call block-conditional MAR (BCMAR) models, and an associated block-monotone reduced likelihood strategy that typically yields consistent estimates by selectively discarding some data. Alternatively, full ML estimation can often be achieved via the EM algorithm. We examine in some detail BCMAR models for the case of two multinomially distributed categorical variables, and a two block structure where the first block is categorical and the second block arises from a (possibly multivariate) exponential family distribution.Comment: Published in at http://dx.doi.org/10.1214/10-STS344 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

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

The profile inter‐unit reliability

To assess the quality of health care, patient outcomes associated with medical providers (eg, dialysis facilities) are routinely monitored in order to identify poor (or excellent) provider performance. Given the high stakes of such evaluations for payment as well as public reporting of quality, it is important to assess the reliability of quality measures. A commonly used metric is the inter‐unit reliability (IUR), which is the proportion of variation in the measure that comes from inter‐provider differences. Despite its wide use, however, the size of the IUR has little to do with the usefulness of the measure for profiling extreme outcomes. A large IUR can signal the need for further risk adjustment to account for differences between patients treated by different providers, while even measures with an IUR close to zero can be useful for identifying extreme providers. To address these limitations, we propose an alternative measure of reliability, which assesses more directly the value of a quality measure in identifying (or profiling) providers with extreme outcomes. The resulting metric reflects the extent to which the profiling status is consistent over repeated measurements. We use national dialysis data to examine this approach on various measures of dialysis facilities.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/155899/1/biom13167_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/155899/2/biom13161-sup-0001-BiomarkerDesign_supplementary_pub.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/155899/3/biom13167.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/155899/4/biom13161-sup-0003-supmat.pd

Mixed Discrete and Continuous Cox Regression Model

The Cox (1972) regression model is extended to include discrete and mixed continuous/discrete failure time data by retaining the multiplicative hazard rate form of the absolutely continuous model. Application of martingale arguments to the regression parameter estimating function show the Breslow (1974) estimator to be consistent and asymptotically Gaussian under this model. A computationally convenient estimator of the variance of the score function can be developed, again using martingale arguments. This estimator reduces to the usual hypergeometric form in the special case of testing equality of several survival curves, and it leads more generally to a convenient consistent variance estimator for the regression parameter. A small simulation study is carried out to study the regression parameter estimator and its variance estimator under the discrete Cox model special case and an application to a bladder cancer recurrence dataset is provided.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46860/1/10985_2004_Article_5119440.pd