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.

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.

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.

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.

Modelling the effect of fibropapilloma disease on the somatic growth dynamics of Hawaiian green sea turtles

The effect of the tumour-forming disease, fibropapillomatosis, on the somatic growth dynamics of green turtles resident in the Pala'au foraging grounds (Moloka'i, Hawai'i) was evaluated using a Bayesian generalised additive mixed modelling approach. This regression model enabled us to account for fixed effects (fibropapilloma tumour severity), nonlinear covariate functional form (carapace size, sampling year) as well as random effects due to individual heterogeneity and correlation between repeated growth measurements on some turtles. Somatic growth rates were found to be nonlinear functions of carapace size and sampling year but were not a function of low-to-moderate tumour severity. On the other hand, growth rates were significantly lower for turtles with advanced fibropapillomatosis, which suggests a limited or threshold-specific disease effect. However, tumour severity was an increasing function of carapace size-larger turtles tended to have higher tumour severity scores, presumably due to longer exposure of larger (older) turtles to the factors that cause the disease. Hence turtles with advanced fibropapillomatosis tended to be the larger turtles, which confounds size and tumour severity in this study. But somatic growth rates for the Pala'au population have also declined since the mid-1980s (sampling year effect) while disease prevalence and severity increased from the mid-1980s before levelling off by the mid-1990s. It is unlikely that this decline was related to the increasing tumour severity because growth rates have also declined over the last 10-20 years for other green turtle populations resident in Hawaiian waters that have low or no disease prevalence. The declining somatic growth rate trends evident in the Hawaiian stock are more likely a density-dependent effect caused by a dramatic increase in abundance by this once-seriously-depleted stock since the mid-1980s. So despite increasing fibropapillomatosis risk over the last 20 years, only a limited effect on somatic growth dynamics was apparent and the Hawaiian green turtle stock continues to increase in abundance.

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.

Review of recent results on excursion set models

Many images consist of two or more 'phases', where a phase is a collection of homogeneous zones. For example, the phases may represent the presence of different sulphides in an ore sample. Frequently, these phases exhibit very little structure, though all connected components of a given phase may be similar in some sense. As a consequence, random set models are commonly used to model such images. The Boolean model and models derived from the Boolean model are often chosen. An alternative approach to modelling such images is to use the excursion sets of random fields to model each phase. In this paper, the properties of excursion sets will be firstly discussed in terms of modelling binary images. Ways of extending these models to multi-phase images will then be explored. A desirable feature of any model is to be able to fit it to data reasonably well. Different methods for fitting random set models based on excursion sets will be presented and some of the difficulties with these methods will be discussed.

Effect of disorder on quantum phase transitions in anisotropic XY spin chains in a transverse field

We present some exact results for the effect of disorder on the critical properties of an anisotropic XY spin chain in a transverse held. The continuum limit of the corresponding fermion model is taken and in various cases results in a Dirac equation with a random mass. Exact analytic techniques can then be used to evaluate the density of states and the localization length. In the presence of disorder the ferromagnetic-paramagnetic or Ising transition of the model is in the same universality class as the random transverse field Ising model solved by Fisher using a real-space renormalization-group decimation technique (RSRGDT). If there is only randomness in the anisotropy of the magnetic exchange then the anisotropy transition (from a ferromagnet in the x direction to a ferromagnet in the y direction) is also in this universality class. However, if there is randomness in the isotropic part of the exchange or in the transverse held then in a nonzero transverse field the anisotropy transition is destroyed by the disorder. We show that in the Griffiths' phase near the Ising transition that the ground-state energy has an essential singularity. The results obtained for the dynamical critical exponent, typical correlation length, and for the temperature dependence of the specific heat near the Ising transition agree with the results of the RSRODT and numerical work. [S0163-1829(99)07125-8].

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.

An fMRI study indicating increased cortical recruitment during a cognitive interference task in Huntington's disease patients

We used an event related fMRI design to study the BOLD response in Huntington’s disease (HD) patients during performance of a Simon interference task. We hypothesised that HD patients will demonstrate significantly slower RTs than controls, and that there will be significant differences in the pattern of brain activation between groups. Seventeen HD patients and 15 age and sex matched controls were scanned using 3T GE scanner (FOV = 24 cm2; TE = 40 ms; TR = 3 s; FA = 60°; slice thickness = 6 mm; in-plane resolution = 1.88x1.88 mm2). The task involved two activation conditions, namely congruent (for example, left pointing arrow appearing on the left side of the screen) and incongruent (for example, left pointing arrow appearing on the right side of the screen), and a baseline condition. Each stimulus was presented for 2500 ms followed by a blank screen for 500 ms. Subjects were instructed to press a button using the same hand as indicated by the direction of the arrow head and were given 3000 ms to respond. Data analysis was performed using SPM2 with a random effects analysis model. For each subject parameter estimates for combined task conditions (congruent and incongruent combined) were calculated. Comparisons such as these, based on block designs, have superior statistical power for detecting subtle changes in the BOLD response anywhere in the brain. The activations reported are significant at PFDR_corr

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.