Use of the regression of mean crowding on mean density for estimating sample size and the transformation of data for the analysis of variance

An approximate method for estimating the sample size in simple random sampling and a systematic way of transformation of sample data are derived by using the parameters α and β of the regression of mean crowding on mean density in the spatial distribution per quadrat of animal populations (Iwao , 1968). If the values of α and β have been known for the species concerned, the sample size needed to attain a desired precision can be estimated by simply knowing the approximate level of mean density of the population to be sampled. Also, an appropriate variance stabilizing transformation of sample data can be obtained by the method given here without restrictions on the distribution pattern of the frequency counts.     

Semiparametric regression estimation in the presence of dependent censoring

We propose a semiparametric estimation procedure for estimatingthe regression of an outcome Y, measured at the end of a fixedfollow-up period, on baseline explanatory variables X, measuredprior to start of follow-up, in the presence of dependent censoringgiven X. The proposed estimators are consistent when the dataare ‘missing at random’ but not ‘missing completelyat random’ (Rubin, 1976), and do not require full specificationof the complete data likelihood. Specifically, we assume thatthe probability of censoring at time t is independent of theoutcome Y conditional on the recorded history up to t of a vectorof time-dependent covariates that are correlated with Y. Ourestimators can be used to adjust for dependent censoring andnonrandom noncompliance in randomised trials studying the effectof a treatment on the mean of a response variable of interest.Even with independent censoring, our methods allow the investigatorto increase efficiency by exploiting the correlation of theoutcome with a vector of time-dependent covariates.     

Correcting for regression to the mean in behavior and ecology

If two successive trait measurements have a less-than-perfect correlation, individuals or populations will, on average, tend to be closer to the mean on the second measurement (the so-called regression effect). Thus, there is a negative correlation between an individual's state at time 1 and the change in state from time 1 to time 2. In addition, whenever groups differ in their initial mean values, the expected change in the mean value from time 1 to time 2 will differ among the groups. For example, birds feeding nestlings lose weight, but initially heavier birds lose more weight than lighter birds, a result expected from the regression effect. In sexual selection, males who remain unmated in the first year are, on average, less attractive than mated males. The regression effect predicts that these males will increase their attractiveness in the second year more than mated males. In well-designed experiments, changes in the experimental and control groups would be compared. In observational studies, however, no such comparison is available, and expected differential effects must be accounted for before they can be attributed to external causes. We describe methods to correct for the regression effect and assess alternative causal explanations.     

Attributable risk estimation from case-control data via logistic regression.

By fitting an unconditional logistic regression model to unmatched case-control data, an estimate of the joint population attributable risk for the factor included is obtained. This estimate and its asymptotic variance can easily be computed from the intercept parameter and its asymptotic variance. A generalization to the analysis of stratified data with large strata enables the calculation of stratum-specific attributable risks and their variances via stratum-specific intercept parameters. If sampling of cases is independent of strata, an estimate of the summary attributable risk and its asymptotic variance may be obtained as a weighted sum of the stratum-specific attributable risks.     

A note on regression to the mean

Sex‐related Cognitive Differences: By Julia A. Sherman. Charles C Thomas, Springfield, Illinois, 1978. 262 pp. Cloth, $16.25; paper, $12.25.

Kinometrics: Determinants of So‐cioeconomic Success Within and Between Families. Edited by Paul Taubman. North‐Holland Publishing Company, Amsterdam, 1977. $28.25

Nutrition and Human Reproduction: Edited by W. Henry Mosley. Plenum Publishing Corporation, New York, 1978. 526 pp. $42.50.

Manual of the International Statistical Classification of Diseases, Injuries, and Causes of Death, Volume 1: World Health Organization, 1977. 777 pp. $12.00 (hardbound). (Also to be published in French, Spanish, and Russian.)

Women in Jamaica: Patterns of Reproduction and Family: By George W. Roberts and Sonja A. Sinclair. KTO Press, New York, 1978. $16.00.     

A regression-based method for estimating mean treatment cost in the presence of right-censoring

In many clinical trials and evaluations using medical care administrative databases it is of interest to estimate not only the survival time of a given treatment modality but also the total associated cost. The most widely used estimator for data subject to censoring is the Kaplan-Meier (KM) or product-limit (PL) estimator. The optimality properties of this estimator applied to time-to-event data (consistency, etc.) under the assumptions of random censorship have been established. However, whenever the relationship between cost and survival time includes an error term to account for random differences among patients' costs, the dependency between cumulative treatment cost at the time of censoring and at the survival time results in KM giving biased estimates. A similar phenomenon has previously been noted in the context of estimating quality-adjusted survival time. We propose an estimator for mean cost which exploits the underlying relationship between total treatment cost and survival time. The proposed method utilizes either parametric or nonparametric regression to estimate this relationship and is consistent when this relationship is consistently estimated. We then present simulation results which illustrate the gain in finite-sample efficiency when compared with another recently proposed estimator. The methods are then applied to the estimation of mean cost for two studies where right-censoring was present. The first is the heart failure clinical trial Studies of Left Ventricular Dysfunction (SOLVD). The second is a Health Maintenance Organization (HMO) database study of the cost of ulcer treatment.     

Semiparametric estimation of proportional mean residual life model in presence of censoring

A mean residual life function is the average remaining life of a surviving subject, as it varies with time. The proportional mean residual life model was proposed by Oakes and Dasu (1990, Biometrika77, 409-410) in regression analysis to study its association with related covariates in absence of censoring. In this article, we develop some semiparametric estimation procedures to take censoring into account. The proposed methodology is evaluated via simulation studies, and further applied to a clinical trial of chemotherapy in postoperative radiotherapy of lung cancer patients.     

The estimation of mean duration from stage frequency data

Summary A simple method of estimating duration from stage frequency data is derived. A simulation model of the passage of individuals through a particular stage in the life-cycle is presented, together with results from the model on the influence of recruitment, development and mortality on the parameters used in the estimation of stage duration. The application of the method to field data is described and a test example, using simulated data, is given.     

Identifiability of causal effects for binary variables with baseline data missing due to death

We discuss identifiability and estimation of causal effects of a treatment in subgroups defined by a covariate that is sometimes missing due to death, which is different from a problem with outcomes censored by death. Frangakis et al. (2007, Biometrics 63, 641-662) proposed an approach for estimating the causal effects under a strong monotonicity (SM) assumption. In this article, we focus on identifiability of the joint distribution of the covariate, treatment and potential outcomes, show sufficient conditions for identifiability, and relax the SM assumption to monotonicity (M) and no-interaction (NI) assumptions. We derive expectation-maximization algorithms for finding the maximum likelihood estimates of parameters of the joint distribution under different assumptions. Further we remove the M and NI assumptions, and prove that signs of the causal effects of a treatment in the subgroups are identifiable, which means that their bounds do not cover zero. We perform simulations and a sensitivity analysis to evaluate our approaches. Finally, we apply the approaches to the National Study on the Costs and Outcomes of Trauma Centers data, which are also analyzed by Frangakis et al. (2007) and Xie and Murphy (2007, Biometrics 63, 655-658).     

Evaluating pedigree data. I. The estimation of pedigree error in the presence of marker mistyping

Pedigrees used in the analysis of genetic or medical data are usually ascertained from sources subject to a variety of errors including misidentification of individuals, faults in historical documents or record linkage, nonpaternity, and unidentified adoption. Genetic markers can be used to verify putative family and pedigree data through the search for inconsistencies, or genetic exclusions, between putative parents and offspring. The probability of observing an exclusion given the occurrence of an error depends upon the gene frequencies at the loci under study and the forms of error. In addition, inconsistencies can arise from laboratory errors in marker determination. Together, these problems make the proper statistical analysis of such data desirable. Here we give a model that specifies the combined effects of various kinds of pedigree error along with genetic marker error. This model allows the maximum-likelihood estimation of the rates of various forms of pedigree error and laboratory error from genetic marker data collected on putative families. The method is illustrated by applying it to data obtained from a South Pacific island population, Tokelau. From the observed distribution of genetic marker inconsistencies between the parents and offspring of putative families, derived from the extensive genealogy of this population, we are able to estimate that the error of a paternal link is 4%, the error of a maternal link is zero, and the overall system typing error is 1%.     

Haplotype frequency estimation error analysis in the presence of missing genotype data

Background  

Increasingly researchers are turning to the use of haplotype analysis as a tool in population studies, the investigation of linkage disequilibrium, and candidate gene analysis. When the phase of the data is unknown, computational methods, in particular those employing the Expectation-Maximisation (EM) algorithm, are frequently used for estimating the phase and frequency of the underlying haplotypes. These methods have proved very successful, predicting the phase-known frequencies from data for which the phase is unknown with a high degree of accuracy. Recently there has been much speculation as to the effect of unknown, or missing allelic data – a common phenomenon even with modern automated DNA analysis techniques – on the performance of EM-based methods. To this end an EM-based program, modified to accommodate missing data, has been developed, incorporating non-parametric bootstrapping for the calculation of accurate confidence intervals.     

Empirical Bayes estimation of random effects parameters in mixed effects logistic regression models

We extend an approach for estimating random effects parameters under a random intercept and slope logistic regression model to include standard errors, thereby including confidence intervals. The procedure entails numerical integration to yield posterior empirical Bayes (EB) estimates of random effects parameters and their corresponding posterior standard errors. We incorporate an adjustment of the standard error due to Kass and Steffey (KS; 1989, Journal of the American Statistical Association 84, 717-726) to account for the variability in estimating the variance component of the random effects distribution. In assessing health care providers with respect to adult pneumonia mortality, comparisons are made with the penalized quasi-likelihood (PQL) approximation approach of Breslow and Clayton (1993, Journal of the American Statistical Association 88, 9-25) and a Bayesian approach. To make comparisons with an EB method previously reported in the literature, we apply these approaches to crossover trials data previously analyzed with the estimating equations EB approach of Waclawiw and Liang (1994, Statistics in Medicine 13, 541-551). We also perform simulations to compare the proposed KS and PQL approaches. These two approaches lead to EB estimates of random effects parameters with similar asymptotic bias. However, for many clusters with small cluster size, the proposed KS approach does better than the PQL procedures in terms of coverage of nominal 95% confidence intervals for random effects estimates. For large cluster sizes and a few clusters, the PQL approach performs better than the KS adjustment. These simulation results agree somewhat with those of the data analyses.