A Comparison of Bayesian and Sampling Theory Inferences in a Probit Model

HE PROBIT MODEL IS A POPULAR DEVICE for explaining binary choice decisions in econometrics. It has been used to describe choices such as labor force participation, travel mode, home ownership, and type of education. These and many more examples can be found in papers by Amemiya (1981) and Maddala (1983). Given the contribution of economics towards explaining such choices, and given the nature of data that are collected, prior information on the relationship between a choice probability and several explanatory variables frequently exists. Bayesian inference is a convenient vehicle for including such prior information. Given the increasing popularity of Bayesian inference it is useful to ask whether inferences from a probit model are sensitive to a choice between Bayesian and sampling theory techniques. Of interest is the sensitivity of inference on coefficients, probabilities, and elasticities. We consider these issues in a model designed to explain choice between fixed and variable interest rate mortgages. Two Bayesian priors are employed: a uniform prior on the coefficients, designed to be noninformative for the coefficients, and an inequality restricted prior on the signs of the coefficients. We often know, a priori, whether increasing the value of a particular explanatory variable will have a positive or negative effect on a choice probability. This knowledge can be captured by using a prior probability density function (pdf) that is truncated to be positive or negative. Thus, three sets of results are compared:those from maximum likelihood (ML) estimation, those from Bayesian estimation with an unrestricted uniform prior on the coefficients, and those from Bayesian estimation with a uniform prior truncated to accommodate inequality restrictions on the coefficients.

Searching for convergence in phylogenetic Markov chain Monte Carlo

Markov chain Monte Carlo (MCMC) is a methodology that is gaining widespread use in the phylogenetics community and is central to phylogenetic software packages such as MrBayes. An important issue for users of MCMC methods is how to select appropriate values for adjustable parameters such as the length of the Markov chain or chains, the sampling density, the proposal mechanism, and, if Metropolis-coupled MCMC is being used, the number of heated chains and their temperatures. Although some parameter settings have been examined in detail in the literature, others are frequently chosen with more regard to computational time or personal experience with other data sets. Such choices may lead to inadequate sampling of tree space or an inefficient use of computational resources. We performed a detailed study of convergence and mixing for 70 randomly selected, putatively orthologous protein sets with different sizes and taxonomic compositions. Replicated runs from multiple random starting points permit a more rigorous assessment of convergence, and we developed two novel statistics, delta and epsilon, for this purpose. Although likelihood values invariably stabilized quickly, adequate sampling of the posterior distribution of tree topologies took considerably longer. Our results suggest that multimodality is common for data sets with 30 or more taxa and that this results in slow convergence and mixing. However, we also found that the pragmatic approach of combining data from several short, replicated runs into a metachain to estimate bipartition posterior probabilities provided good approximations, and that such estimates were no worse in approximating a reference posterior distribution than those obtained using a single long run of the same length as the metachain. Precision appears to be best when heated Markov chains have low temperatures, whereas chains with high temperatures appear to sample trees with high posterior probabilities only rarely. [Bayesian phylogenetic inference; heating parameter; Markov chain Monte Carlo; replicated chains.]

Volumetric and areal bone mineral density measures are associated with cardiovascular disease in older men and women: The health, aging, and body composition study

The associations of volumetric (vBMD) and areal (aBMD) bone mineral density measures with prevalent cardiovascular disease (CVD) and subclinical peripheral arterial disease (PAD) were investigated in a cohort of older men and women enrolled in the Health, Aging, and Body Composition Study. Participants were 3,075 well-functioning white and black men and women (42% black, 51% women), aged 68-80 years. Total hip, femoral neck, and trochanter aBMD were measured using dual-energy X-ray absorptiometry. Quantitative computed tomography was used to evaluate spine trabecular, integral, and cortical vBMD measures in a subgroup (n = 1,489). Logistic regression was performed to examine associations of BMD measures with CVD and PAD. The prevalence of CVD (defined by coronary heart disease, PAD, cerebrovascular disease, or congestive heart failure) was 29.8%. Among participants without CVD, 10% had subclinical PAD (defined as ankle-arm index < 0.9). Spine vBMD measures were inversely associated with CVD in men (odds ratio of integral [ORintegral] = 1.34, 95% confidence interval [CI] 1.10-1.63; ORtrabecular = 1.25, 95% CI 1.02-1.53; ORcortical = 1.36, 95% CI 1.11-1.65). In women, for each standard deviation decrease in integral vBMD, cortical vBMD, or trochanter aBMD, the odds of CVD were significantly increased by 28%, 27%, and 22%, respectively. Total hip aBMD was associated with subclinical PAD in men (OR = 1.39, 95% CI 1.03-1.84) but not in women. All associations were independent of age and shared risk factors between BMD and CVD and were not influenced by inflammatory cytokines (interleukin-6 and tumor necrosis factors-alpha). In conclusion, our results provide further evidence for an inverse association between BMD and CVD in men and women. Future research should investigate common pathophysiological links for osteoporosis and CVD.

A case-control study of employment status and mortality in a cohort of Australian youth

Recent studies have demonstrated a link in young populations between unemployment and ill health. The purpose of this study is to correlate mortality with employment status in two cohorts of young Australian males, aged 17-25 years, from 1984 to 1988. Two youth cohorts consisting of an initially unemployed sample (n = 1424 males) and a population sample (n = 4573 males), were surveyed annually throughout the study period. Those lost to follow-up during the survey period were matched with death registries across Australia. Employment status was determined from weekly diaries and death certificates and was designated as: employed or student; unemployed; not in the work force (excluding students). Conditional logistic regression, using age- and cohort- matched cases (deaths) and controls (alive), was used to estimate the odds ratio (OR) of dying with regard to employment status, taking into account potential confounders such as ethnicity, aboriginality, educational attainment, pre-existing health problems, socio-economic status of parents, and other factors. Twenty three male survey respondents were positively matched to death registry records. Compared to those employed or students (referent group), significantly elevated ORs were found to be associated with neither being in the workforce nor a student for all cause, external cause, and external cause mortality other than suicide. Odds ratios were adjusted for age, survey cohort, ethnicity, pre-existing physical and mental health status, education level, and socio-economic status of parent(s). A statistically significant increasing linear trend in odds ratios of male mortality for most cause groups was found across the employment categories, from those employed or student (lowest ORs), through those unemployed; to those not in the workforce (highest ORs). Suicide was higher, but not statistically significantly, in those unemployed or not in the workforce. Suicide also was associated, though not significantly, with the respondent not living with their parents when they were 14 years of age. No association was found between mortality and past unemployment experience, as measured by length of time spent unemployed, or the number of spells of unemployment experienced during the survey. The results of this study underscore the elevated risk to survival in young males as a consequence of being neither employed nor a student. (C) 1999 Elsevier Science Ltd. All rights reserved.

High HIV incidence and prevalence among young women in rural South Africa: Developing a cohort for intervention trials

Objective: To measure prevalence and model incidence of HIV infection. Setting: 2013 consecutive pregnant women attending public sector antenatal clinics in 1997 in Hlabisa health district, South Africa. Historical seroprevalence data, 1992-1995. Methods: Serum remaining from syphilis testing was tested anonymously for antibodies to HIV to determine seroprevalence. Two models, allowing for differential mortality between HIV-positive and HIV-negative people, were used. The first used serial seroprevalence data to estimate trends in annual incidence. The second, a maximum likelihood model, took account of changing force of infection and age-dependent risk of infection, to estimate age-specific HIV incidence in 1997. Multiple logistic regression provided adjusted odds ratios (OR) for risk factors for prevalent HIV infection. Results: Estimated annual HIV incidence increased from 4% in 1992/1993 to 10% in 1996/1997. In 1997, highest age-specific incidence was 16% among women aged between 20 and 24 years. in 1997, overall prevalence was 26% (95% confidence interval [CI], 24%-28%) and at 34% was highest among women aged between 20 and 24 years. Young age (<30 years; odds ratio [OR], 2.1; p = .001), unmarried status (OR 2.2; p = .001) and living in less remote parts of the district (OR 1.5; p = .002) were associated with HIV prevalence in univariate analysis. Associations were less strong in multivariate analysis. Partner's migration status was not associated with HIV infection. Substantial heterogeneity of HIV prevalence by clinic was observed (range 17%-31%; test for trend, p = .001). Conclusions: This community is experiencing an explosive HIV epidemic. Young, single women in the more developed parts of the district would form an appropriate cohort to test, and benefit from, interventions such as vaginal microbicides and HIV vaccines.

The advantages of theft over toil: The design inference and arguing from ignorance

Intelligent design theorist William Dembski has proposed an explanatory filter for distinguishing between events due to chance, lawful regularity or design. We show that if Dembski's filter were adopted as a scientific heuristic, some classical developments in science would not be rational, and that Dembski's assertion that the filter reliably identifies rarefied design requires ignoring the state of background knowledge. If background information changes even slightly, the filter's conclusion will vary wildly. Dembski fails to overcome Hume's objections to arguments from design.

Factors associated with rural practice among Australian-trained general practitioners

Objective: To determine the factors associated with general practitioners' current practice location, with particular emphasis on rural location. Design: Observational, retrospective, case-control study using a self-administered questionnaire. Setting: Australian general practices in December 2000. Participants: 2414 Australian-trained rural and urban GPs. Main outcome measure: Current urban or rural practice location. Results: For Australia as a whole, rural GPs were more likely to be male (odds ratio [OR], 1.42; 95% CI, 1.17-1.73), Australian-born (OR, 1.95; 95% CI, 1.55-2.45), and to report attending a rural primary school for some (OR, 2.21; 95% CI, 1.69-2.89) or all (OR, 2.79; 95% CI, 1.94-4.00) of their primary schooling. Rural GPs' partners or spouses were also more likely to report some (OR, 2.75; 95% CI, 2.07-3.66) or all (OR, 2.86; 95% CI, 2.02-4.05) rural primary schooling. A rural background in both GP and partner produced the highest likelihood of rural practice (OR, 6.28; 95% CI, 4.26-9.25). For individual jurisdictions, a trend towards more rural GPs being men was only significant in Tasmania. In all jurisdictions except Tasmania and the Northern Territory, rural GPs were more likely to be Australian-born. Conclusions: GPs' and their partners' rural background (residence and primary and secondary schooling) influences choice of practice location, with partners' background appearing to exert more influence.

Fitting genetic models to twin data with binary and ordered categorical responses: A comparison of structural equation modelling and Bayesian hierarchical models

We compare Bayesian methodology utilizing free-ware BUGS (Bayesian Inference Using Gibbs Sampling) with the traditional structural equation modelling approach based on another free-ware package, Mx. Dichotomous and ordinal (three category) twin data were simulated according to different additive genetic and common environment models for phenotypic variation. Practical issues are discussed in using Gibbs sampling as implemented by BUGS to fit subject-specific Bayesian generalized linear models, where the components of variation may be estimated directly. The simulation study (based on 2000 twin pairs) indicated that there is a consistent advantage in using the Bayesian method to detect a correct model under certain specifications of additive genetics and common environmental effects. For binary data, both methods had difficulty in detecting the correct model when the additive genetic effect was low (between 10 and 20%) or of moderate range (between 20 and 40%). Furthermore, neither method could adequately detect a correct model that included a modest common environmental effect (20%) even when the additive genetic effect was large (50%). Power was significantly improved with ordinal data for most scenarios, except for the case of low heritability under a true ACE model. We illustrate and compare both methods using data from 1239 twin pairs over the age of 50 years, who were registered with the Australian National Health and Medical Research Council Twin Registry (ATR) and presented symptoms associated with osteoarthritis occurring in joints of the hand.

Host-dependent Anopheles flavirostris larval distribution reinforces the risk of malaria near water

Malaria control strategies are more likely to be successful if groups at high risk can be accurately predicted. Given that mosquitoes have an obligate aquatic phase we were interested in determining how vector larval abundance relates to the spatial distribution of human malaria infection. We examined the relationship between malaria parasite prevalence and distance from vector larval habitat, and vector larval abundance and distance from human habitation, in separate studies in rural, low-endemic areas of the Philippines. Parasite prevalence among symptomatic patients was significantly higher among those living in proximity ( less than or equal to 50 m) to potential larval habitats of the major vector, Anopheles flavirostris (adjusted odds ratio [AOR] 2.64, P = 0.02 and AOR 3.43, P = 0.04). A larval survey of A. flavirostris revealed a higher density of early and late instars near human habitation (adjusted P < 0.05). The results suggest that larvae are associated with human habitation, thereby reinforcing malaria risk in people living close to larval habitats. This has implications for understanding the interaction between vectors, hosts, and parasites, and the potential for success of localized malaria control measures.

Perceived environment attributes, residential location, and walking for particular purposes

Background: Identifying environmental factors that can influence physical activity is a public health priority. We examined associations of perceived environmental attributes with walking for four different purposes: general neighborhood walking, walking for exercise, walking for pleasure, and walking to get to and from places. Methods: Participants (n =399; 57% women) were surveyed by mail. They reported place of residence, walking behaviors, and perceptions of neighborhood environmental attributes. Results: Men with the most positive perceptions of neighborhood aesthetics were significantly more likely (odds ratio [OR] =7.4) to be in the highest category of neighborhood walking. Men who perceived the weather as not inhibiting their walking were much more likely (OR= 4.7) to be high exercise walkers. Women who perceived the weather as not inhibiting their walking were significantly more likely to be high neighborhood walkers (OR=3.8) and those with moderate perceptions of accessibility were much more likely to do more walking for pleasure (OR=3.5). Conclusions: Different environmental attributes were associated with different types of walking and these differed between men and women. Approaches to increasing physical activity might usefully focus on those attributes of the local environment that might influence particular subsets of walking behavior.

Identifying the energy gap: Magnitude and determinants of 5-year weight gain in midage women

Objective: The aims of this study were to estimate average yearly weight gain in midage women and to identify the determinants of weight gain and gaining weight at double the average rate. Research Methods and Procedures: The study sample comprised 8071 participants (45 to 55 years old) in the Australian Longitudinal Study on Women's Health who completed mailed surveys in 1996, 1998, and 2001. Results: On average, the women gained almost 0.5 kg per year [average 2.42 kg (95% confidence interval, 2.29 to 2.54) over 5 years]. In multivariate analyses, variables associated with energy balance (physical activity, sitting time, and energy intake), as well as quitting smoking, menopause/hysterectomy, and baseline BMI category were significantly associated with weight gain, but other behavioral and demographic characteristics were not. After adjustment for all of the other biological and behavioral variables, the odds of gaining weight at about twice the average rate (> 5 kg over 5 years) were highest for women who quit smoking (odds ratio = 2.94; 95% confidence interval, 2.17, 3.96). There were also independent relationships between the odds of gaining > 5 kg and lower levels of habitual physical activity, more time spent sitting, energy intake (but only in women with BMI > 25 at baseline), menopause transition, and hysterectomy. Discussion: The average weight gain equates with an energy imbalance of only about 10 kcal or 40 kJ per day, which suggests that small sustained changes in the modifiable behavioral variables could prevent further weight gain.

Contribution of the collagen I alpha 1 and vitamin D receptor genes to the risk of hip fracture in elderly women

Context and Objective: Hip fracture is partially genetically determined. The present study was designed to examine the contributions of vitamin D receptor (VDR) and collagen I alpha 1 (COLIA1) genotypes to the liability to hip fracture in postmenopausal women. Design: The study was designed as a prospective population-based cohort investigation. Subjects: Six hundred seventy-seven postmenopausal women of Caucasian background, aged 70 +/- 7 yr (mean +/- SD), have been followed for up to 14 yr. Sixty-nine women had sustained a hip fracture during the period. Main Outcome: Atraumatic hip fractures were prospectively identified through radiologists' reports. Bone mineral density (BMD) at the hip and lumbar spine was measured by dual-energy x-ray absorptiometry. Genotypes: The TaqI and SpI COLIA1 polymorphisms of the VDR and COLIA1 genes were determined. Using the Single Nucleotide Polymorphism database, VDR TT, Tt, and tt genotypes were coded as TT, TC, and CC, whereas COLIA1 SS, Ss, and ss were coded as GG, GT, and TT. Results: Women with VDR CC genotype (16% prevalence) and COLIA1 TT genotype (5% prevalence) had an increased risk of hip fracture [odds ratio (OR) associated with CC, 2.6; 95% confidence interval (CI), 1.2-5.3; OR associated with TT, 3.8; 95% CI, 1.3-10.8] after adjustment for femoral neck BMD (OR, 3.4 per SD; 95% CI, 2.3-5.0) and age (OR, 1.4 per 5 yr; 95% CI, 1.1-1.7). Approximately 20 and 12% of the liability to hip fracture was attributable to the presence of the CC genotype and TT genotype, respectively. Conclusion: The VDR CC genotype and COLIA1 TT genotype were associated with increased hip fracture risk in Caucasian women, and this association was independent of BMD and age.

Reduced between-hospital variation in short term survival after acute myocardial infarction: the result of improved cardiac care?

Objectives: To re-examine interhospital variation in 30 day survival after acute myocardial infarction ( AMI) 10 years on to see whether the appointment of new cardiologists and their involvement in emergency care has improved outcome after AMI. Design: Retrospective cohort study. Setting: Acute hospitals in Scotland. Participants: 61 484 patients with a first AMI over two time periods: 1988 - 1991; and 1998 - 2001. Main outcome measures: 30 day survival. Results: Between 1988 and 1991, median 30 day survival was 79.2% ( interhospital range 72.1 - 85.1%). The difference between highest and lowest was 13.0 percentage points ( age and sex adjusted, 12.1 percentage points). Between 1998 and 2001, median survival rose to 81.6% ( and range decreased to 78.0 - 85.6%) with a difference of 7.6 ( adjusted 8.8) percentage points. Admission hospital was an independent predictor of outcome at 30 days during the two time periods ( p< 0.001). Over the period 1988 - 1991, the odds ratio for death ranged, between hospitals, from 0.71 ( 95% confidence interval ( CI) 0.58 to 0.88) to 1.50 ( 95% CI 1.19 to 1.89) and for the period 1998 - 2001 from 0.82 ( 95% CI 0.60 to 1.13) to 1.46 ( 95% CI 1.07 to 1.99). The adjusted risk of death was significantly higher than average in nine of 26 hospitals between 1988 and 1991 but in only two hospitals between 1998 and 2001. Conclusions: The average 30 day case fatality rate after admission with an AMI has fallen substantially over the past 10 years in Scotland. Between-hospital variation is also considerably less notable because of better survival in the previously poorly performing hospitals. This suggests that the greater involvement of cardiologists in the management of AMI has paid dividends.

A polymorphism in the agouti signalling protein (ASIP) is associated with decreased levels of mRNA

To date, a role for agouti signalling protein (ASIP) in human pigmentation has not been well characterized. It is known that agouti plays a pivotal role in the pigment switch from the dark eumelanin to the light pheomelanin in the mouse. However, because humans do not have an agouti banded hair pattern, its role in human pigmentation has been questioned. We previously identified a single polymorphism in the 3'-untranslated region (UTR) of ASIP that was found at a higher frequency in African-Americans compared with other population groups. To compare allele frequencies between European-Australians and indigenous Australians, the g.8818A -> G polymorphism was genotyped. Significant differences were seen in allele frequencies between these groups (P < 0.0001) with carriage of the G allele highest in Australian Aborigines. In the Caucasian sample set a strong association was observed between the G allele and dark hair colour (P = 0.004) (odds ratio 4.6; 95% CI 1.4-15.27). The functional consequences of this polymorphism are not known but it was postulated that it might result in message instability and premature degradation of the transcript. To test this hypothesis, ASIP mRNA levels were quantified in melanocytes carrying the variant and non-variant alleles. Using quantitative real-time polymerase chain reaction the mean ASIP mRNA ratio of the AA genotype to the AG genotype was 12 (P < 0.05). This study suggests that the 3'-UTR polymorphism results in decreased levels of ASIP and therefore less pheomelanin production.

Identification of the semaphorin receptor PLXNA2 as a candidate for susceptibility to schizophrenia

The discovery of genetic factors that contribute to schizophrenia susceptibility is a key challenge in understanding the etiology of this disease. Here, we report the identification of a novel schizophrenia candidate gene on chromosome 1q32, plexin A2 (PLXNA2), in a genome-wide association study using 320 patients with schizophrenia of European descent and 325 matched controls. Over 25 000 single-nucleotide polymorphisms (SNPs) located within approximately 14 000 genes were tested. Out of 62 markers found to be associated with disease status, the most consistent finding was observed for a candidate locus on chromosome 1q32. The marker SNP rs752016 showed suggestive association with schizophrenia (odds ratio (OR) = 1.49, P = 0.006). This result was confirmed in an independent case control sample of European Americans (combined OR = 1.38, P = 0.035) and similar genetic effects were observed in smaller subsets of Latin Americans (OR = 1.26) and Asian Americans (OR = 1.37). Supporting evidence was also obtained from two family-based collections, one of which reached statistical significance (OR = 2.2, P = 0.02). High-density SNP mapping showed that the region of association spans approximately 60 kb of the PLXNA2 gene. Eight out of 14 SNPs genotyped showed statistically significant differences between cases and controls. These results are in accordance with previous genetic findings that identified chromosome 1q32 as a candidate region for schizophrenia. PLXNA2 is a member of the transmembrane semaphorin receptor family that is involved in axonal guidance during development and may modulate neuronal plasticity and regeneration. The PLXNA2 ligand semaphorin 3A has been shown to be upregulated in the cerebellum of individuals with schizophrenia. These observations, together with the genetic results, make PLXNA2 a likely candidate for the 1q32 schizophrenia susceptibility locus.