Correspondences between Regression Models for Complex Binary Outcomes and Those for Structured Multivariate Survival Analyses

Doksum and Gasko [5] described a one-to-one correspondence between regression models for binary outcomes and those for continuous time survival analyses. This correspondence has been exploited heavily in the analysis of current status data (Jewell and van der Laan [11], Shiboski [18]). Here, we explore similar correspondences for complex survival models and categorical regression models for polytomous data. We include discussion of competing risks and progressive multi-state survival random variables

MAXIMUM LIKELIHOOD ESTIMATION OF ORDERED MULTINOMIAL PARAMETERS

The pool-adjacent violator-algorithm (Ayer et al., 1955) has long been known to give the maximum likelihood estimator of a series of ordered binomial parameters, based on an independent observation from each distribution (see, Barlow et al., 1972). This result has immediate application to estimation of a survival distribution based on current survival status at a set of monitoring times. This paper considers an extended problem of maximum likelihood estimation of a series of ‘ordered’ multinomial parameters pi = (p1i, p2i, . . . , pmi) for 1 \u3c = I \u3c = k, where ordered means that pj1 \u3c = pj2 \u3c = .. . \u3c = pjk for each j with 1 \u3c = j \u3c = m-1. The data consist of k independent observations X1, . . . ,Xk where Xi has a multinomial distribution with probability parameter pi and known index ni \u3e = 1. By making use of variants of the pool adjacent violator algorithm, we obtain a simple algorithm to compute the maximum likelihood estimator of p1, . . . , pk, and demonstrate its convergence. The results are applied to nonparametric maximum likelihood estimation of the sub-distribution functions associated with a survival time random variable with competing risks when only current status data are available. (Jewell et al., 2003

Vertically Shifted Mixture Models for Clustering Longitudinal Data by Shape

Longitudinal studies play a prominent role in health, social and behavioral sciences as well as in the biological sciences, economics, and marketing. By following subjects over time, temporal changes in an outcome of interest can be directly observed and studied. An important question concerns the existence of distinct trajectory patterns. One way to determine these distinct patterns is through cluster analysis, which seeks to separate objects (subjects, patients, observational units) into homogeneous groups. Many methods have been adapted for longitudinal data, but almost all of them fail to explicitly group trajectories according to distinct pattern shapes. To fulfill the need for clustering based explicitly on shape, we propose vertically shifting the data by subtracting the subject-specific mean directly removes the level prior to fitting a mixture modeling. This non-invertible transformation can result in singular covariance matrixes, which makes mixture model estimation difficult. Despite the challenges, this method outperforms existing clustering methods in a simulation study

Temporal Stability and Geographic Variation in Cumulative Case Fatality Rates and Average Doubling Times of SARS Epidemics

We analyze temporal stability and geographic trends in cumulative case fatality rates and average doubling times of severe acute respiratory syndrome (SARS). In part, we account for correlations between case fatality rates and doubling times through differences in control measures. We discuss factors that may alter future estimates of case fatality rates. We also discuss reasons for heterogeneity in doubling times among countries and the implications for the control of SARS in different countries and parameterization of epidemic models

Severe Acute Respiratory Syndrome: Temporal Stability and Geographic Variation in Death Rates and Doubling Times

We analyzed temporal stability and geographic trends in cumulative case-fatality rates and average doubling times of severe acute respiratory syndrome (SARS). In part, we account for correlations between case-fatality rates and doubling times through differences in control measures. Factors that may alter future estimates of case-fatality rates, reasons for heterogeneity in doubling times among countries, and implications for the control of SARS are discussed

Case-Control Current Status Data

Current status observation on survival times has recently been widely studied. An extreme form of interval censoring, this data structure refers to situations where the only available information on a survival random variable, T, is whether or not T exceeds a random independent monitoring time C, a binary random variable, Y. To date, nonparametric analyses of current status data have assumed the availability of i.i.d. random samples of the random variable (Y, C), or a similar random sample at each of a set of fixed monitoring times. In many situations, it is useful to consider a case-control sampling scheme. Here, cases refer to a random sample of observations on C from the sub-population where T is less than or equal to C. On the other hand, controls provide a random sample of observations from the sub-population where T is greater than C. In this paper, we examine the identifiability of the distribution function F of T from such case-control current status data, showing that F is identified up to a one parameter family of distribution functions. With supplementary information on the relative population frequency of cases/controls, a simple weighted version of the nonparametric maximum likelihood estimator for prospective current status data provides a natural estimate for case-control samples. Following the parametric results of Scott and Wild (1997), we show that this estimator is, in fact, nonparametric maximum likelihood

Accelerated Hazards Model: Method, Theory and Applications

In an accelerated hazards model, the hazard functions of a failure time are related through the time scale-change, which is often a function of covariates and associated parameters. When the hazard functions have special properties, such as monotonicity in time, the parameters may be clinically meaningful in measuring a treatment effect. This paper reviews methodological and theoretical development of this model. Applications of the accelerated hazards model including sample size calculation in clinical trials, are also explored