Likelihood-based estimation of the regression model with scrambled responses

A significant problem in the collection of responses to potentially sensitive questions, such as relating to illegal, immoral or embarrassing activities, is non-sampling error due to refusal to respond or false responses. Eichhorn & Hayre (1983) suggested the use of scrambled responses to reduce this form of bias. This paper considers a linear regression model in which the dependent variable is unobserved but for which the sum or product with a scrambling random variable of known distribution, is known. The performance of two likelihood-based estimators is investigated, namely of a Bayesian estimator achieved through a Markov chain Monte Carlo (MCMC) sampling scheme, and a classical maximum-likelihood estimator. These two estimators and an estimator suggested by Singh, Joarder & King (1996) are compared. Monte Carlo results show that the Bayesian estimator outperforms the classical estimators in almost all cases, and the relative performance of the Bayesian estimator improves as the responses become more scrambled.

n-fold Weibull multiplicative model

In this paper we study the n-fold multiplicative model involving Weibull distributions and examine some properties of the model. These include the shapes for the density and failure rate functions and the WPP plot. These allow one to decide if a given data set can be adequately modelled by the model. We also discuss the estimation of model parameters based on the WPP plot. (C) 2001 Elsevier Science Ltd. All rights reserved.

Finite mixture regression model with random effects: application to neonatal hospital length of stay

A two-component mixture regression model that allows simultaneously for heterogeneity and dependency among observations is proposed. By specifying random effects explicitly in the linear predictor of the mixture probability and the mixture components, parameter estimation is achieved by maximising the corresponding best linear unbiased prediction type log-likelihood. Approximate residual maximum likelihood estimates are obtained via an EM algorithm in the manner of generalised linear mixed model (GLMM). The method can be extended to a g-component mixture regression model with the component density from the exponential family, leading to the development of the class of finite mixture GLMM. For illustration, the method is applied to analyse neonatal length of stay (LOS). It is shown that identification of pertinent factors that influence hospital LOS can provide important information for health care planning and resource allocation. (C) 2002 Elsevier Science B.V. All rights reserved.

Models involving two inverse Weibull distributions

In this paper, we look at three models (mixture, competing risk and multiplicative) involving two inverse Weibull distributions. We study the shapes of the density and failure-rate functions and discuss graphical methods to determine if a given data set can be modelled by one of these models. (C) 2001 Elsevier Science Ltd. All rights reserved.

Multi-level zero-inflated Poisson regression modelling of correlated count data with excess zeros

Count data with excess zeros relative to a Poisson distribution are common in many biomedical applications. A popular approach to the analysis of such data is to use a zero-inflated Poisson (ZIP) regression model. Often, because of the hierarchical Study design or the data collection procedure, zero-inflation and lack of independence may occur simultaneously, which tender the standard ZIP model inadequate. To account for the preponderance of zero counts and the inherent correlation of observations, a class of multi-level ZIP regression model with random effects is presented. Model fitting is facilitated using an expectation-maximization algorithm, whereas variance components are estimated via residual maximum likelihood estimating equations. A score test for zero-inflation is also presented. The multi-level ZIP model is then generalized to cope with a more complex correlation structure. Application to the analysis of correlated count data from a longitudinal infant feeding study illustrates the usefulness of the approach.

Optimal crossover designs for logistic regression models in pharmacodynamics

Pharmacodynamics (PD) is the study of the biochemical and physiological effects of drugs. The construction of optimal designs for dose-ranging trials with multiple periods is considered in this paper, where the outcome of the trial (the effect of the drug) is considered to be a binary response: the success or failure of a drug to bring about a particular change in the subject after a given amount of time. The carryover effect of each dose from one period to the next is assumed to be proportional to the direct effect. It is shown for a logistic regression model that the efficiency of optimal parallel (single-period) or crossover (two-period) design is substantially greater than a balanced design. The optimal designs are also shown to be robust to misspecification of the value of the parameters. Finally, the parallel and crossover designs are combined to provide the experimenter with greater flexibility.

Who fails to complete tuberculosis treatment? Temporal trends and risk factors for treatment interruption in a community-based directly observed therapy programme in a rural district of South Africa

SETTING: Hlabisa Tuberculosis Programme, Hlabisa, South Africa. OBJECTIVE: To determine trends in and risk factors for interruption of tuberculosis treatment. METHODS: Data were extracted from the control programme database starting in 1991. Temporal trends in treatment interruption are described; independent risk factors for treatment interruption were determined with a multiple logistic regression model, and Kaplan-Meier survival curves for treatment interruption were constructed for patients treated in 1994-1995. RESULTS: Overall 629 of 3610 surviving patients (17%) failed to complete treatment; this proportion increased from 11% (n = 79) in 1991/1992 to 22% (n = 201) in 1996. Independent risk factors for treatment interruption were diagnosis between 1994-1996 compared with 1991-1393 (odds ratio [OR] 1.9, 95% confidence interval [CT] 1.6-2.4); human immunodeficiency virus (HIV) positivity compared with HIV negativity (OR 1.8, 95% CI 1.4-2.4); supervised by village clinic compared with community health worker (OR 1.9, 95% CI 1.4-2.6); and male versus female sex (OR 1.3, 95% CI 1.1-1.6). Few patients interrupted treatment during the first 2 weeks, and the treatment interruption rate thereafter was constant at 1% per 14 days. CONCLUSIONS: Frequency of treatment interruption from this programme has increased recently. The strongest risk factor was year of diagnosis, perhaps reflecting the impact of an increased caseload on programme performance. Ensuring adherence to therapy in communities with a high level of migration remains a challenge even within community-based directly observed therapy programmes.

Variation in mortality rates in Australia: correlation with Indigenous status, remoteness and socio-economic deprivation

Background The aim of this study was to study ecological correlations between age-adjusted all-cause mortality rates in Australian statistical divisions and (1) the proportion of residents that self-identify as Indigenous, (2) remoteness, and (3) socio-economic deprivation. Methods All-cause mortality rates for 57 statistical divisions were calculated and directly standardized to the 1997 Australian population in 5-year age groups using Australian Bureau of Statistics (ABS) data. The proportion of residents who self-identified as Indigenous was obtained from the 1996 Census. Remoteness was measured using ARIA (Accessibility and Remoteness Index for Australia) values. Socioeconomic deprivation was measured using SEIFA (Socio-Economic index for Australia) values from the ABS. Results Age-standardized all-cause mortality varies twofold from 5.7 to 11.3 per 1000 across Australian statistical divisions. Strongest correlation was between Indigenous status and mortality (r = 0.69, p < 0.001). correlation between remoteness and mortality was modest (r = 0.39, p = 0.002) as was correlation between socio-economic deprivation and mortality (r = -0.42, p = 0.001). Excluding the three divisions with the highest mortality, a multiple regression model using the logarithm of the adjusted mortality rate as the dependent variable showed that the partial correlation (and hence proportion of the variance explained) for Indigenous status was 0.03 (9 per cent; p = 0.03), for SEIFA score was -0.17 (3 per cent; p = 0.22); and for remoteness was -0.22 (5 per cent; p = 0.13). Collectively, the three variables studied explain 13 per cent of the variability in mortality. Conclusions Ecological correlation exists between all-cause mortality, Indigenous status, remoteness and disadvantage across Australia. The strongest correlation is with indigenous status, and correlation with all three characteristics is weak when the three statistical divisions with the highest mortality rates are excluded. intervention targeted at these three statistical divisions could reduce much of the variability in mortality in Australia.

Stochastic structure and individual-tree growth models

The majority of past and current individual-tree growth modelling methodologies have failed to characterise and incorporate structured stochastic components. Rather, they have relied on deterministic predictions or have added an unstructured random component to predictions. In particular, spatial stochastic structure has been neglected, despite being present in most applications of individual-tree growth models. Spatial stochastic structure (also called spatial dependence or spatial autocorrelation) eventuates when spatial influences such as competition and micro-site effects are not fully captured in models. Temporal stochastic structure (also called temporal dependence or temporal autocorrelation) eventuates when a sequence of measurements is taken on an individual-tree over time, and variables explaining temporal variation in these measurements are not included in the model. Nested stochastic structure eventuates when measurements are combined across sampling units and differences among the sampling units are not fully captured in the model. This review examines spatial, temporal, and nested stochastic structure and instances where each has been characterised in the forest biometry and statistical literature. Methodologies for incorporating stochastic structure in growth model estimation and prediction are described. Benefits from incorporation of stochastic structure include valid statistical inference, improved estimation efficiency, and more realistic and theoretically sound predictions. It is proposed in this review that individual-tree modelling methodologies need to characterise and include structured stochasticity. Possibilities for future research are discussed. (C) 2001 Elsevier Science B.V. All rights reserved.

Willingness to pay for conservation of the Asian elephant in Sri Lanka: A contingent valuation study

Results from a CVM survey of willingness to pay for the conservation of the Asian elephant of a sample of urban residents in three selected housing schemes in Colombo, the capital of Sri Lanka, are reported. Face– to–face surveys were conducted using an interview schedule. A non-linear logit regression model was constructed to analyse the respondents’ responses for the payment principle questions and to identify the factors that influence their responses. We investigate whether urban residents’ WTP for the conservation of elephants is sufficient to compensate farmers for the damage caused by elephants, and consequently to raise farmers’ tolerance of the presence of elephants on the farming fields. We find that beneficiaries (the urban residents) could compensate losers (the farmers in the HEC affected areas) and be better off than in the absence of elephants in Sri Lanka. This suggests that there is a strong economic case for the conservation of the wild elephant population in Sri Lanka. However, we have insufficient data to determine Sri Lanka’s optimal elephant population in the Kaldor-Hicks sense.

The net benefit of saving the Asian Elephant: A policy and contingent valuation Study

Reports results from a contingent valuation survey of willingness to pay for the conservation of the Asian elephant of a sample of urban residents living in three selected housing schemes in Colombo, the capital of Sri Lanka. Face–to–face surveys were conducted using an interview schedule. A non-linear logit regression model is used to analyse the respondents’ responses for the payment principle questions and to identify the factors that influence their responses. We investigate whether urban residents’ willingness to pay for the conservation of elephants is sufficient to compensate farmers for the damage caused by elephants. We find that the beneficiaries (the urban residents) could compensate losers (the farmers in the areas affected by human–elephant conflict) and be better off than in the absence of elephants in Sri Lanka. Therefore, there is a strong economic case for the conservation of the wild elephant population in Sri Lanka. However, we have insufficient data to determine the optimal level of this elephant population in the Kaldor-Hicks sense. Nevertheless, the current population of elephant in Sri Lanka is Kaldor-Hicks preferable to having none.

Genetic and environmental contributions to educational attainment in Australia

The genetic and environmental contributions to educational attainment in Australia are examined using a multiple regression model drawn from the medical research literature. Data from a large sample of Australian twins are analysed. The findings indicate that at least as much as 50 percent and perhaps as much as 65 percent of the variance in educational attainments can be attributed to genetic endowments. It is suggested that only around 25 percent of the variance in educational attainments may be due to environmental factors, though this contribution is shown to be around 40 percent when adjustments for measurement error and assortative mating are made. The high fraction of the observed variation in educational attainments due to genetic differences is consistent with results reported by Heath et al. (Heath, A.C., Berg, K., Eaves, L.J., Solaas, M.H., Corey, L.A., Sundet, J., Magnus, P., Nance, W.E., 1985. Education policy and the heritability of educational attainment. Nature 314(6013), 734-736.), Tambs et al. (Tambs, K., Sundet, J.M., Magnus, P., Berg, K., 1989. Genetic and environmental contributions to the covariance between occupational status, educational attainment and IQ: a study of twins. Behavior Genetics 19(2), 209-222.), Vogler and Fulker (Vogler, G.P., Fulker, D.W., 1983. Familial resemblance for educational attainment. Behavior Generics 13(4), 341-354.) and Behrman and Taubman (Behrman, J., Taubman, P., 1989. Is schooling mostly in the genes? Nature-nurture decomposition using data on relatives. Journal of Political Economy 97(6), 1425-1446.), suggesting that the finding is robust. (C) 2001 Elsevier Science Ltd. All rights reserved.

Trade relationships between the Gulf Cooperation Council and the European Union

This paper examines the trade relationship between the Gulf Cooperation Council (GCC) and the European Union (EU). A simultaneous equation regression model is developed and estimated to assist with the analysis. The regression results, using both the two stage least squares (2SLS) and ordinary least squares (OLS) estimation methods, reveal the existence of feedback effects between the two economic integrations. The results also show that during times of slack in oil prices, the GCC income from its investments overseas helped to finance its imports from the EU.

Geographical variation in the penetrance of CDKN2A mutations for melanoma

Background: Germline mutations in the CDKN2A gene, which encodes two proteins (p16INK4A and p14ARF), are the most common cause of inherited susceptibility to melanoma. We examined the penetrance of such mutations using data from eight groups from Europe, Australia and the United States that are part of The Melanoma Genetics Consortium Methods: We analyzed 80 families with documented CDKN2A mutations and multiple cases of cutaneous melanoma. We modeled penetrance for melanoma using a logistic regression model incorporating survival analysis. Hypothesis testing was based on likelihood ratio tests. Covariates included gender, alterations in p14APF protein, and population melanoma incidence rates. All statistical tests were two-sided. Results: The 80 analyzed families contained 402 melanoma patients, 320 of whom were tested for mutations and 291 were mutation carriers. We also tested 713 unaffected family members for mutations and 194 were carriers. Overall, CDKN2A mutation penetrance was estimated to be 0.30 (95% confidence interval (CI) = 0.12 to 0.62) by age 50 years and 0.67 (95% CI = 0.31 to 0.96) by age 80 years. Penetrance was not statistically significantly modified by gender or by whether the CDKN2A mutation altered p14ARF protein. However, there was a statistically significant effect of residing in a location with a high population incidence rate of melanoma (P = .003). By age 50 years CDKN2A mutation penetrance reached 0.13 in Europe, 0.50 in the United States, and 0.32 in Australia; by age 80 years it was 0.58 in Europe, 0.76 in the United States, and 0.91 in Australia. Conclusions: This study, which gives the most informed estimates of CDKN2A mutation penetrance available, indicates that the penetrance varies with melanoma population incidence rates. Thus, the same factors that affect population incidence of melanoma may also mediate CDKN2A penetrance.