Overcoming biases and misconceptions in ecological studies

The aggregate data study design provides an alternative group level analysis to ecological studies in the estimation of individual level health risks. An aggregate model is derived by aggregating a plausible individual level relative rate model within groups, such that population-based disease rates are modelled as functions of individual level covariate data. We apply an aggregate data method to a series of fictitious examples from a review paper by Greenland and Robins which illustrated the problems that can arise when using the results of ecological studies to make inference about individual health risks. We use simulated data based on their examples to demonstrate that the aggregate data approach can address many of the sources of bias that are inherent in typical ecological analyses, even though the limited between-region covariate variation in these examples reduces the efficiency of the aggregate study. The aggregate method has the potential to estimate exposure effects of interest in the presence of non-linearity, confounding at individual and group levels, effect modification, classical measurement error in the exposure and non-differential misclassification in the confounder.     

Flexible regression modeling

The author proposes a new method for flexible regression modeling of multi‐dimensional data, where the regression function is approximated by a linear combination of logistic basis functions. The method is adaptive, selecting simple or more complex models as appropriate. The number, location, and (to some extent) shape of the basis functions are automatically determined from the data. The method is also affine invariant, so accuracy of the fit is not affected by rotation or scaling of the covariates. Squared error and absolute error criteria are both available for estimation. The latter provides a robust estimator of the conditional median function. Computation is relatively fast, particularly for large data sets, so the method is well suited for data mining applications.     

Bootstrapping Malmquist Indices for Danish Seiners in the North Sea and Skagerrak

In connection with assessing how an ongoing development in fisheries management may change fishing activity, evaluation of Total Factor Productivity (TFP) change over a period, including efficiency, scale and technology changes, is an important tool. The Malmquist index, based on distance functions evaluated with Data Envelopment Analysis (DEA), is often employed to estimate TFP changes. DEA is generally gaining attention for evaluating efficiency and capacity in fisheries. One main criticism of DEA is that it does not have any statistical foundation, i.e. that it is not possible to make inference about DEA scores or related parameters. The bootstrap method for estimating confidence intervals of deterministic parameters can however be applied to estimate confidence intervals for DEA scores. This method is applied in the present paper for assessing TFP changes between 1987 and 1999 for the fleet of Danish seiners operating in the North Sea and the Skagerrak.     

A flexible semiparametric transformation model for survival data

I suggest an extension of the semiparametric transformation model that specifies a time-varying regression structure for the transformation, and thus allows time-varying structure in the data. Special cases include a stratified version of the usual semiparametric transformation model. The model can be thought of as specifying a first order Taylor expansion of a completely flexible baseline. Large sample properties are derived and estimators of the asymptotic variances of the regression coefficients are given. The method is illustrated by a worked example and a small simulation study. A goodness of fit procedure for testing if the regression effects lead to a satisfactory fit is also suggested.     

A unified approach to regression analysis under double-sampling designs

We propose a unified approach to the estimation of regression parameters under double-sampling designs, in which a primary sample consisting of data on the rough or proxy measures for the response and/or explanatory variables as well as a validation subsample consisting of data on the exact measurements are available. We assume that the validation sample is a simple random subsample from the primary sample. Our proposal utilizes a specific parametric model to extract the partial information contained in the primary sample. The resulting estimator is consistent even if such a model is misspecified, and it achieves higher asymptotic efficiency than the estimator based only on the validation data. Specific cases are discussed to illustrate the application of the estimator proposed.     

Confidence intervals for secondary parameters following a sequential test

In sequential studies, formal interim analyses are usually restricted to a consideration of a single null hypothesis concerning a single parameter of interest. Valid frequentist methods of hypothesis testing and of point and interval estimation for the primary parameter have already been devised for use at the end of such a study. However, the completed data set may warrant a more detailed analysis, involving the estimation of parameters corresponding to effects that were not used to determine when to stop, and yet correlated with those that were. This paper describes methods for setting confidence intervals for secondary parameters in a way which provides the correct coverage probability in repeated frequentist realizations of the sequential design used. The method assumes that information accumulates on the primary and secondary parameters at proportional rates. This requirement will be valid in many potential applications, but only in limited situations in survival analysis.     

Estimation of long-run inefficiency levels: a dynamic frontier approach

Cornwell, Schmidt, and Sickles (1990) and Kumbhakar (1990), among others, developed stochasticfrontier production models which allow firm specific inefficiency levels to change over time. These studies assumed arbitrary restrictions on the short-run dynamics of efficiency levels which have little theoretical justification. Further, the models are inappropriate for estimation of long-run efficiencies. We consider estimation of an alternative frontier model in which firmspecific technical inefficiency levels are autoregressive. This model is particularly useful to examine a potential dynamic link between technical innovations and production inefficiency levels. We apply our methodology to a panel of US airlines.     

GMM Estimation with persistent panel data: an application to production functions

This paper considers the estimation of Cobb-Douglas production functions using panel data covering a large sample of companies observed for a small number of time periods. GMM estimatorshave been found to produce large finite-sample biases when using the standard first-differenced estimator. These biases can be dramatically reduced by exploiting reasonable stationarity restrictions on the initial conditions process. Using data for a panel of R&Dperforming US manufacturing companies we find that the additional instruments used in our extended GMM estimator yield much more reasonable parameter estimates.     

Estimation of Distribution Functions Using Data from Different Environments

Suppose that when a unit operatesin a certain environment, its lifetime has distribution G,and when the unit operates in another environment, its lifetimehas a different distribution, say F. Moreover, supposethe unit is operated for a certain period of time in the firstenvironment and is then transferred to the second environment.Thus we observe a censored lifetime in the first environmentand a failure time of a ``used' unit in the second environment.We propose an EM algorithm approach for obtaining a self-consistentestimator of F. Moreover, suppose using observations from both environments.The case where failure times are subject to right censoring isconsidered as well. We also establish the maximum likelihoodestimator of F. Moreover, suppose when the unit is repairable. Applicationand simulation studies are presented to illustrate the methodsderived.     

Random regression models for human immunodeficiency virus ribonucleic acid data subject to left censoring and informative drop-outs

Objectives in many longitudinal studies of individuals infected with the human immunodeficiency virus (HIV) include the estimation of population average trajectories of HIV ribonucleic acid (RNA) over time and tests for differences in trajectory across subgroups. Special features that are often inherent in the underlying data include a tendency for some HIV RNA levels to be below an assay detection limit, and for individuals with high initial levels or high ranges of change to drop out of the study early because of illness or death. We develop a likelihood for the observed data that incorporates both of these features. Informative drop-outs are handled by means of an approach previously published by Schluchter. Using data from the HIV Epidemiology Research Study, we implement a maximum likelihood procedure to estimate initial HIV RNA levels and slopes within a population, compare these parameters across subgroups of HIV-infected women and illustrate the importance of appropriate treatment of left censoring and informative drop-outs. We also assess model assumptions and consider the prediction of random intercepts and slopes in this setting. The results suggest that marked bias in estimates of fixed effects, variance components and standard errors in the analysis of HIV RNA data might be avoided by the use of methods like those illustrated.