Pseudo Maximum Likelihood Approach Research Articles

Semiparametric analysis of short-term and long-term hazard ratios with two-sample survival data

Standard approaches to semiparametric modelling of two-sample survival data are not appropriate when the two survival curves cross. We introduce a two-sample model that accommodates crossing survival curves. The two scalar parameters of the model have the interpretations of being the short-term and long-term hazard ratios respectively. The time-varying hazard ratio is expressed semiparametrically by the two scalar parameters and an unspecified baseline distribution. The new model includes the Cox model and the proportional odds model as submodels. For inference we use a pseudo maximum likelihood approach that can be expressed via some simple estimating equations, analogous to that for the maximum partial likelihood estimator of the Cox model, that provide consistent and asymptotically normal estimators. Simulation studies show that the estimators perform well for moderate sample sizes. We also illustrate the methods with a real-data example. The new model can be extended easily to the regression setting.

Estimation of effective population size of HIV-1 within a host: a pseudomaximum-likelihood approach.

Using pseudomaximum-likelihood approaches to phylogenetic inference and coalescent theory, we develop a computationally tractable method of estimating effective population size from serially sampled viral data. We show that the variance of the maximum-likelihood estimator of effective population size depends on the serial sampling design only because internal node times on a coalescent genealogy can be better estimated with some designs than with others. Given the internal node times and the number of sequences sampled, the variance of the maximum-likelihood estimator is independent of the serial sampling design. We then estimate the effective size of the HIV-1 population within nine hosts. If we assume that the mutation rate is 2.5 x 10(-5) substitutions/generation and is the same in all patients, estimated generation lengths vary from 0.73 to 2.43 days/generation and the mean (1.47) is similar to the generation lengths estimated by other researchers. If we assume that generation length is 1.47 days and is the same in all patients, mutation rate estimates vary from 1.52 x 10(-5) to 5.02 x 10(-5). Our results indicate that effective viral population size and evolutionary rate per year are negatively correlated among HIV-1 patients.

Combining complete multivariate outcomes with incomplete covariate information: a latent class approach.

This work was motivated by the need to combine outcome information from a reference population with risk factor information from a screened subpopulation in a setting where the analytic goal was to study the association between risk factors and multiple binary outcomes. To achieve such an analytic goal, this article proposes a two-stage latent class procedure that first summarizes the commonalities among outcomes using a reference population sample, then analyzes the association between outcomes and risk factors. It develops a pseudo-maximum likelihood approach to estimating model parameters. The performance of the proposed method is evaluated in a simulation study and in an illustrative analysis of data from the Women's Health and Aging Study, a recent investigation of the causes and course of disability in older women. Combining information in the proposed way is found to improve both accuracy and precision in summarizing multiple categorical outcomes, which effectively diminishes ambiguity and bias in making risk factor inferences.

Identification of multivariable stochastic linear systems via spectral analysis given time-domain data

Estimation of the parametric multiple-input-multiple-output (MIMO) infinite impulse response transfer function given time-domain input-output (IO) data is considered. We first propose a frequency-domain solution to the least-squares equation error multivariable system identification problem using the power spectrum and the cross-spectrum of the IO data to estimate the IO parametric transfer function. The proposed approach is shown to yield a unimodal performance surface and consistent identification in colored noise and the sufficient-order case. We then investigate an iterative pseudo-maximum likelihood approach and analyze its consistency under sufficient-order modeling. Finally, a computer simulation example is provided to illustrate the two approaches.

Identification of linear systems via spectral analysis given time-domain data: consistency, reduced-order approximation, and performance analysis

Estimation of a parametric input-output (I/O) infinite impulse response transfer function given time-domain I/O data is considered. Some of the desirable properties of any approach to this problem are: unimodality of the performance surface, consistent identification in the sufficient-order case, and stability of the fitted model under undermodeling. We first consider a frequency-domain solution to the least squares equation error identification problem using the power spectrum and the cross-spectrum of the I/O data to estimate the I/O parametric transfer function. The proposed approach is shown to yield a unimodal performance surface, consistent identification in colored noise and sufficient-order case, and stable fitted models under undermodeling for arbitrary stationary inputs so long as they are persistently exciting of sufficiently high order. Asymptotic performance analysis is carried out for both sufficient-order and reduced-order cases. These asymptotic results are then used to derive statistics on the corresponding estimated transfer function. We also investigate an iterative pseudomaximum likelihood approach and analyze its performance under sufficient-order modeling. Finally, computer simulation examples are provided to illustrate the two approaches.

A likelihood-based method for analysing longitudinal binary responses

SUMMARY In this paper, we discuss a likelihood-based method for analysing correlated binary responses based on a multivariate model. It is related to the pseudo-maximum likelihood approach suggested recently by Zhao & Prentice (1990). Their parameterization results in a simple pairwise model, in which the association between responses is modelled in terms of correlations, while the present paper uses conditional log odds-ratios. With this approach, higher-order associations can be incorporated in a natural way. One important advantage of this parameterization is that the maximum likelihood estimates of the marginal mean parameters are robust to misspecification of the time dependence. We describe an iterative two-stage procedure for obtaining the maximum likelihood estimates. Two examples are presented to illustrate this methodology.