SEARCH · PubMed Health

Results for “Normal Distribution”

Explore indexed PubMed citations for clinical trials, systematic reviews and public health research. Read source abstracts and follow each citation to its original PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 469 records · Page 26Linked to original sources

PubMed2003

Dependence of fluence errors in dynamic IMRT on leaf-positional errors varying with time and leaf number.

In d-MLC based IMRT, leaves move along a trajectory that lies within a user-defined tolerance (TOL) about the ideal trajectory specified in a d-MLC sequence file. The MLC controller measures leaf positions multiple times per second and corrects them if they deviate from ideal positions by a value greater than TOL. The magnitude of leaf-positional errors resulting from finite mechanical precision depends on the performance of the MLC motors executing leaf motions and is generally larger if leaves are forced to move at higher speeds. The maximum value of leaf-positional errors can be limited by decreasing TOL. However, due to the inherent time delay in the MLC controller, this may not happen at all times. Furthermore, decreasing the leaf tolerance results in a larger number of beam hold-offs, which, in turn leads, to a longer delivery time and, paradoxically, to higher chances of leaf-positional errors (< or = TOL). On the other end, the magnitude of leaf-positional errors depends on the complexity of the fluence map to be delivered. Recently, it has been shown that it is possible to determine the actual distribution of leaf-positional errors either by the imaging of moving MLC apertures with a digital imager or by analysis of a MLC log file saved by a MLC controller. This leads next to an important question: What is the relation between the distribution of leaf-positional errors and fluence errors. In this work, we introduce an analytical method to determine this relation in dynamic IMRT delivery. We model MLC errors as Random-Leaf Positional (RLP) errors described by a truncated normal distribution defined by two characteristic parameters: a standard deviation sigma and a cut-off value deltax0 (deltaxo approximately TOL). We quantify fluence errors for two cases: (i) deltax0 >> sigma (unrestricted normal distribution) and (ii) deltax0 << sigma (deltax0--limited normal distribution). We show that an average fluence error of an IMRT field is proportional to (i) sigma/ALPO and (ii) deltax0/ALPO, respectively, where ALPO is an Average Leaf Pair Opening (the concept of ALPO was previously introduced by us in Med. Phys. 28, 2220-2226 (2001). Therefore, dose errors associated with RLP errors are larger for fields requiring small leaf gaps. For an N-field IMRT plan, we demonstrate that the total fluence error (if we neglect inhomogeneities and scatter) is proportional to 1/square root of N, where N is the number of fields, which slightly reduces the impact of RLP errors of individual fields on the total fluence error. We tested and applied the analytical apparatus in the context of commercial inverse treatment planning systems used in our clinics (Helios and BrainScan). We determined the actual distribution of leaf-positional errors by studying MLC controller (Varian Mark II and Brainlab Novalis MLCs) log files created by the controller after each field delivery. The analytically derived relationship between fluence error and RLP errors was confirmed by numerical simulations. The equivalence of relative fluence error to relative dose error was verified by a direct dose calculation. We also experimentally verified the truthfulness of fluences derived from the log file data by comparing them to film data.

Humans↗

PubMed1997

The effect of different sampling intervals on the measurement of intrapartum fetal heart rate variability.

OBJECTIVE: To test the hypothesis that increasing the sampling interval affects the intrapartum fetal heart rate (FHR) variability measurement. METHODS: Fetal electrocardiograms were obtained from women in labor. Using the peak of the fetal R wave, the R-R interval and FHR were calculated on a beat-to-beat basis. Retrospectively, the original data were repartitioned using different intervals (2-900 seconds) to generate a window of measurement (epoch). The mean value for each epoch and the last FHR in that epoch (epochal value) were compared with published animal and human data. Errors were quantified by comparing the epochal and mean values for each epoch. Fetal heart rate variability between epochs and within each epoch was compared. RESULTS: Fetal heart rate and R-R interval were measured in 146 cases. The FHR had a normal distribution (mean 140.1 beats per minute, +/- standard deviation [SD] 15.6, skew -0.07), but its inverse, the R-R interval, was not normally distributed (mean 432 milliseconds, +/- SD 52.4, skew 1.78). Using a single value for an epoch duration of 2 seconds resulted in an error that was similar to the within-epoch variability (+/- SD of 2.2 beats per minute difference between mean and epochal value compared to +/- SD of 2 beats per minute within epoch) but which increased with epoch duration. CONCLUSION: An epoch duration of 2 seconds and a single sampled value within this period may be appropriate for measurement of both medium and long-term variability in any computerized intrapartum FHR interpretation system. Fetal heart rate (not R-R interval, because of its normal distribution) should be used to design such a computerized system.

Adult↗

PubMed1994

Human herpesvirus 6: a survey of presence and variant distribution in normal peripheral lymphocytes and lymphoproliferative disorders.

The presence and distribution of human herpesvirus 6 (HHV-6) variants was investigated by polymerase chain reaction in samples from healthy donors and biopsies from non-Hodgkin's lymphomas and Hodgkin's disease. HHV-6 DNA was present in peripheral blood lymphocytes of 17% of healthy donors, variant B three times more frequently than A. HHV-6 was not present in 35 non-Hodgkin's lymphomas of B cell origin and was in only 1 of 10 non-Hodgkin's lymphomas in AIDS patients. HHV-6 DNA was present in 29% of Hodgkin's disease samples; variant B was more frequent than A. Epstein-Barr virus DNA was detected in 38% of Hodgkin's disease biopsies and did not correlate with HHV-6. Thus, the two HHV-6 variants are differently distributed in the healthy population, and the virus probably has no direct role in the development of B cell non-Hodgkin's lymphoma. The detection of HHV-6 DNA in about one-third of Hodgkin's disease biopsies suggests that HHV-6 might be associated with a subset of this disorder.

DNA, Viral↗

PubMed2004

Uncertainty analysis of parameters for modeling the transfer and fate of benzo(a)pyrene in Tianjin wastewater irrigated areas.

A Monte Carlo simulation for uncertainty analysis of three key parameters (local coal consumption rate Q(1L), dry deposition velocity of aerosol particulate Kp and biodegradation rate of benzo(a)pyrene in soil and sediment K(R3)) was conducted in this study. Results of the simulation indicate that the three parameters were influenced by uncertainty and that all equilibrium concentrations in the four bulk compartments and various sub-compartments were log-normally distributed. However, the results also indicated that among the six primary transfer fluxes, erosion associated with solids in soil and deposition associated with solids in water, along with output from sewers were also log-normally distributed, while deposition from air to soil and biodegradation in soil and sediment followed normal distributions. The effect of uncertainty on the model results of the three key parameters was derived using a comparison of upper and lower of confidence interval boundaries at the 95% level of confidence. The results reveal that uncertainty in the key parameters had a more significant influence on equilibrium concentrations of the chemical in the bulk compartments of soil and sediment than on concentrations in the other two bulk compartments, various sub-compartments and the six predominant transfer fluxes.

Benzo(a)pyrene↗

PubMed1992

Height and age adjustment for cross sectional studies of lung function in children aged 6-11 years.

BACKGROUND: No standard exists for the adjustment of lung function for height and age in children. Multiple regression should not be used on untransformed data because, for example, forced expiratory volume (FEV1), though normally distributed for height, age, and sex, has increasing standard deviation. A solution to the conflict is proposed. METHODS: Spirometry on representative samples of children aged 6.5 to 11.99 years in primary schools in England. After exclusion of children who did not provide two repeatable blows 910 white English boys and 722 girls had data on FEV1 and height. Means and standard deviations of FEV1 divided by height were plotted to determine whether logarithmic transformation of FEV1 was appropriate. Multiple regression was used to give predicted FEV1 for height and age on the transformed scale; back transformation gave predicted values in litres. Other lung function measures were analysed, and data on inner city children, children from ethnic minority groups, and Scottish children were described. RESULTS: After logarithmic (ln) transformation of FEV1 standard deviation was constant. The ratios of actual and predicted values of FEV1 were normally distributed in boys and girls. From the means and standard deviations of these distributions, and the predicted values, centiles and standard deviation scores can be calculated. CONCLUSION: The method described is valid because the assumption of stable variance for multiple regression was satisfied on the log scale and the variation of ratios of actual to predicted values on the original scale was well described by a normal distribution. The adoption of the method will lead to uniformity and greater ease of comparison of research findings.

Age Factors↗

PubMed1986

Frequency distributions of periodontal attachment loss. Clinical and microbiological features.

The present investigation attempted to determine if the pattern of past periodontal destruction could be concisely summarized, and related to other clinical and microbiological parameters. 61 subjects between the ages of 12 and 61 years with destructive periodontal disease were evaluated at 6 sites per tooth for redness, plaque, suppuration, bleeding on probing, pocket depth, and attachment level. The frequency distribution of baseline attachment level measurements was computed for each individual. A curve fitting algorithm was used to fit the frequency distribution to 1-, 2-, and 3-term normal distributions. The parameters of the fit could be used to summarize concisely all of the frequency distributions. 3 major patterns of attachment loss could be distinguished. Pattern I required a two-term distribution with localized destruction at less than 34% of sites and was further divided into 3 groups, depending on average attachment loss at diseased sites. The means of the second peak for the subgroups were 2.7, 5.3, and 8.6 mm, respectively. Pattern II exhibited more widespread disease (greater than 33% of sites affected) with multiple peaks in the frequency distribution requiring a 3-term distribution for satisfactory fit. However, a significant proportion of sites was not affected. Pattern III exhibited a single-peaked normal distribution in which virtually all sites were affected. Mean attachment levels of the peaks in this group ranged from 2.7 to 8.4 mm. 23 of the 61 subjects showed significant attachment loss at 1 or more sites during the course of bi-monthly monitoring, as determined by the tolerance method of analysis. Subgingival plaque samples were taken from these active sites and matched with control sites prior to therapy. The proportions of Fusobacterium nucleatum, Streptococcus intermedius, and Eikenella corrodens were significantly elevated in active and control sites of subjects in groups II and III combined (the widespread disease groups), and proportions of Actinobacillus actinomycetemcomitans and Propionibacterium acnes were elevated in active and control sites of the more localized disease group I subjects. Group I subjects showed a 13- to 15-fold decrease in hazard rates of periodontal sites after Widman flap surgery and systemic tetracycline, whereas groups II and III subjects showed 2-to 6-fold decreases.

Adolescent↗

PubMedDate not supplied

Toward a stochastic formulation of microbial growth in relation to bioreactor performances: case study of an E. coli fed-batch process.

A stochastic microbial growth model has been elaborated in the case of the culture of E. coli in fed-batch and scale-down reactors. This model is based on the stochastic determination of the generation time of the microbial cells. The determination of generation time is determined by choosing the appropriate value on a log-normal distribution. The appropriateness of such distribution is discussed and growth curves are obtained that show good agreement compared with the experimental results. The mean and the standard deviation of the log-normal distribution can be considered to be constant during the batch phase of the culture, but they vary when the fed-batch mode is started. It has been shown that the parameters related to the log-normal distribution are submitted to an exponential evolution. The aim of this study is to explore the bioreactor hydrodynamic effect on microbial growth. Thus, in a second time, the stochastic growth model has been reinforced by data coming from a previous stochastic bioreactor mixing model (1). The connection of these hydrodynamic data with the actual stochastic growth model has allowed us to explain the scale-down effect associated with the glucose concentration fluctuations. It is important to point out that the scale-down effect is induced differently according to the feeding strategy involved in the fed-batch experiments.

Bioreactors↗

PubMed1983

A, B, O(H) blood group antigen distribution in normal skin and squamous cell carcinoma of the penis.

The distribution of A, B, O(H) blood group antigens was studied in paraffin sections of 4 and 11 specimens, respectively, of normal skin and squamous cell carcinoma of the penis using specific red cell adherence (SRCA) test. In the normal skin of the penis the antigens appeared on the uppermost cornifying layers, while basal and malpighian layers were devoid of antigens. In squamous cell carcinoma of the penis the antigens were either absent or confined only to the epithelial pearl formations. Each of the 4 normal skins and 3 of the 11 carcinomas were antigen positive. As the blood group antigens were frequently absent in patients with carcinoma of the penis regardless of the tumor grade and stage as well as patient's condition, they lack the power to discriminate invasive potential.

ABO Blood-Group System↗

PubMed2005

Testing models of parental investment strategy and offspring size in ants.

Parental investment strategies can be fixed or flexible. A fixed strategy predicts making all offspring a single 'optimal' size. Dynamic models predict flexible strategies with more than one optimal size of offspring. Patterns in the distribution of offspring sizes may thus reveal the investment strategy. Static strategies should produce normal distributions. Dynamic strategies should often result in non-normal distributions. Furthermore, variance in morphological traits should be positively correlated with the length of developmental time the traits are exposed to environmental influences. Finally, the type of deviation from normality (i.e., skewed left or right, or platykurtic) should be correlated with the average offspring size. To test the latter prediction, we used simulations to detect significant departures from normality and categorize distribution types. Data from three species of ants strongly support the predicted patterns for dynamic parental investment. Offspring size distributions are often significantly non-normal. Traits fixed earlier in development, such as head width, are less variable than final body weight. The type of distribution observed correlates with mean female dry weight. The overall support for a dynamic parental investment model has implications for life history theory. Predicted conflicts over parental effort, sex investment ratios, and reproductive skew in cooperative breeders follow from assumptions of static parental investment strategies and omnipresent resource limitations. By contrast, with flexible investment strategies such conflicts can be either absent or maladaptive.

Animals↗

PubMed1991

Performance of Vitalograph wedge-bellows spirometer--comparison with a rolling seal spirometer.

The performance of a Vitalograph spirometer has been compared with a rolling seal spirometer (Ohio) to determine whether (i) spirometric measurements are normally distributed, (ii) fatigue occurs with repeated attempts, and (iii) how many tests are required. Twenty forced expiratory manoeuvres were performed on both spirometers at minute intervals, on ten normal subjects. To determine how many tests were required, the first five manoeuvres for each subject were analysed using eleven algorithms. The Vitalograph had a smaller volume, a shorter timing duration and a combined inertia and resistance greater than the European standards. The Ohio complied with the standards for volume and timing duration and had a much lower combined inertia and resistance. For each device, the spirometric indices were normally distributed, there were no fatigue effects, and no significant difference between any two algorithms. We conclude that (1) the performance of repeated forced expiratory manoeuvres using the Vitalograph spirometer does not result in fatigue, (2) spirometric indices are normally distributed, (3) estimation of forced expiratory flows between 25-50% of vital capacity from a Vitalograph may not be appropriate, and (4) the best of a number of technically satisfactory attempts, measured at one minute intervals, may be reported.

Algorithms↗

PubMedDate not supplied

Social cognitive theory in an after-school nutrition intervention for urban Native American youth.

OBJECTIVE: To improve dietary self-efficacy through a 7-month nutrition intervention for Native American children (5 to 10 years) and adolescents (11 to 18 years). DESIGN: Single-group pretest, posttest design. SETTING: An after-school program in a local community center for urban Native American youth. PARTICIPANTS: 104 urban Native American youth (65 children and 39 adolescents). INTERVENTION(S): A 9-month project with pre-post evaluation and a 7-month intervention. MAIN OUTCOMES MEASURE(S): Dietary self-efficacy and 24-hour recalls. ANALYSIS: Descriptive statistics were computed for comparability analysis of dietary self-efficacy and diet at baseline. For the normally distributed data, independent t tests were used for gender comparisons, whereas 1-way analysis of variance with post hoc Tukey adjustment was used to compare responses among body mass index (BMI) categories. Non-normally distributed data were analyzed with Kruskal-Wallis tests with post hoc pairwise Mann-Whitney analyses. For non-normally distributed data, the Bonferroni correction was used, and the P values were set at .025 for gender comparisons and .016 for BMI comparisons. Wilcoxon signed rank tests determined whether fat and sugar intake changed significantly between pre- and postintervention time points among adolescents. RESULTS: Both children and adolescents exhibited moderate levels of dietary self-efficacy at baseline, with no variation by BMI. The nutrition intervention significantly improved the self-efficacy of children. Overweight children significantly improved their dietary self-efficacy. The intervention was not successful among adolescents. CONCLUSIONS AND IMPLICATIONS: Social Cognitive Theory is an effective model from which to explore influential constructs of health behavior. This project demonstrates that a nutrition intervention provided at monthly intervals is an effective way to significantly improve dietary self-efficacy among urban Native American children. The lack of intervention effect among adolescents reiterates the need for greater comprehension of personal, environmental, and behavioral constraints, influencing dietary self-efficacy and behavior.

Adolescent↗

PubMed1996

Bootstrap method of interior-branch test for phylogenetic trees.

Statistical properties of the bootstrap test of interior branch lengths of phylogenetic trees have been studied and compared with those of the standard interior-branch test in computer simulations. Examination of the properties of the tests under the null hypothesis showed that both tests for an interior branch of a predetermined topology are quite reliable when the distribution of the branch length estimate approaches a normal distribution. Unlike the standard interior-branch test, the bootstrap test appears to retain this property even when the substitution rate varies among sites. In this case, the distribution of the branch length estimate deviates from a normal distribution, and the standard interior-branch test gives conservative confidence probability values. A simple correction method was developed for both interior-branch tests to be applied for testing the reliability of tree topologies estimated from sequence data. This correction for the standard interior-branch test appears to be as effective as that obtained in our previous study, though it is much simpler. The bootstrap and standard interior-branch tests for estimated topologies become conservative as the number of sequence groups in a star-like tree increases.

Animals↗

PubMed1994

Folate binding protein distribution in normal tissues and biological fluids from ovarian carcinoma patients as detected by the monoclonal antibodies MOv18 and MOv19.

Folate-binding proteins (FBP), which are molecules relevant in folate metabolism, are overexpressed in ovarian carcinomas, as detected by the monoclonal antibodies (MAb) MOv18 and MOv19, which recognise two different epitopes of the gp38/FBP. In this paper, features of the FBP such as the distribution on normal tissues and the release in biological fluids of normal and tumour origin have been investigated. Immunohistochemical analyses on frozen sections of normal tissues showed the presence of the gp38/FBP on some epithelia. The reactivity of both the MAb on Fallopian tubes was intense and comparable to that observed on ovary carcinoma sections. The kidney, bronchial glands, alveolar epithelium of the lung, oesophagus, stomach, pancreas, breast and thyroid showed different levels of staining. By MOv18/MOv19 double-determinant immunoradiometric assay (DDIRMA), the gp38/FBP was found in soluble form in ascitic fluid, serum and urine of nude mice in which the human ovary carcinoma cell line IGROV1 grew as ascitic carcinomatosis. In human biological fluids, the gp38/FBP was detected in ascites of 60% of ovarian carcinoma patients, and in 29% of those with other carcinomas, but not in patients with non-epithelial tumours or with other non-tumoral pathologies. The mean serum arbitrary units (a.u.)/ml values of ovary carcinoma patients were significantly different to those of healthy donors or patients with endometriosis (P < 0.005 and P < 0.01, respectively), but not when compared to the sera of lung carcinoma patients. In addition, the sensitivity of DDIRMA was poor, since only 24% of the ovary carcinoma patients were positive with this assay. When a restricted number of cases selected for the presence of tumour cells in the ascites was examined, the percentage of DDIRMA-positive sera and ascites rose to 41 and 94%, respectively. In the urine, a strong reactivity was observed in the samples of both normal and tumour origin.

Animals↗

PubMed1978

Gastrin cell distribution in normal human stomachs and in patients with Zollinger-Ellison syndrome.

Quantitative distribution of gastrin cells was evaluated in three normal human stomachs and in four stomachs from patients with Zollinger-Ellison syndrome. Cells identified by the immunoperoxidase method were counted along the entire length of five mucosal strips parallel to the axis of the lesser curvature and sampled from the posterior to the anterior walls. The number of cells per unit area (2300 microns2) decreased from the pylorus to the borderline of the gastric body from (mean +/- SEM) 50.9 +/- 12.0 to 24.2 +/- 13.0 and from 29.6 +/- 5.6 to 10.4 +/- 2.6 for control and Zollinger-Ellison syndrome, respectively, with large interindividual variations. From factorial analysis no statistical difference was found between the two groups. It is therefore suggested that the number of gastrin cell in antral mucosa may not be a significant criteria in the diagnosis of Zollinger-Ellison syndrome.

Aged↗

PubMed1999

Valid inference in random effects meta-analysis.

The standard approach to inference for random effects meta-analysis relies on approximating the null distribution of a test statistic by a standard normal distribution. This approximation is asymptotic on k, the number of studies, and can be substantially in error in medical meta-analyses, which often have only a few studies. This paper proposes permutation and ad hoc methods for testing with the random effects model. Under the group permutation method, we randomly switch the treatment and control group labels in each trial. This idea is similar to using a permutation distribution for a community intervention trial where communities are randomized in pairs. The permutation method theoretically controls the type I error rate for typical meta-analyses scenarios. We also suggest two ad hoc procedures. Our first suggestion is to use a t-reference distribution with k-1 degrees of freedom rather than a standard normal distribution for the usual random effects test statistic. We also investigate the use of a simple t-statistic on the reported treatment effects.

Anticholesteremic Agents↗

PubMed2000

Detecting failed WBC-reduction processes: a quality assurance program introduced in a blood center.

BACKGROUND: Pragmatic yet statistically valid quality assurance (QA) programs are necessary so that blood centers can select, validate, and monitor their WBC-reduction processes. A QA system for WBC-reduction processes based on the practical application of statistical theory within a large blood center was developed. The system identifies parameters for procedure and component evaluation and provides sample size and formatting suggestions. STUDY DESIGN AND METHODS: Analyses of both procedure and component performance were undertaken during the purchase, validation, and control of filtration and apheresis WBC-reduction processes at Blood Centers of the Pacific from 1997 through 1999. QA analysis was categorized on the basis of whether the process was new to the organization or was a modification of a previously validated system. The numbers of samples necessary to consistently detect failure in platelet yield, unit volume, pH, and WBC count was statistically determined by parametric and nonparametric techniques. RESULTS: Parametric analysis (power analysis) of the mean +/- SD of smaller numbers of samples was highly sensitive to shifted distributions, but only if the shift was normally distributed. Nonparametric analysis, necessary when the nature of the underlying distribution is unknown, suggested a minimal sample of 40 was required to achieve high confidence that significant bimodal failure (a secondary population with WBCs 5% above the cutoff) would be detected. CONCLUSION: A QA system, developed for the evaluation of new or revised WBC-reduction processes, was based on statistical analysis of normally and non-normally distributed process failure. The number of samples was determined that allowed the achievement of confidence and tolerance levels considered appropriate within the blood center. Suggestions for outlier evaluation and a format for performance documentation have also been developed. To better define blood center quality goals, further research is necessary on donor and component biologic variability and the most significant modes of WBC-reduction process failure.

Blood Banks↗

PubMed2006

Decomposition analysis of differential dose volume histograms.

Dose volume histograms are a common tool to assess the value of a treatment plan for various forms of radiation therapy treatment. The purpose of this work is to introduce, validate, and apply a set of tools to analyze differential dose volume histograms by decomposing them into physically and clinically meaningful normal distributions. A weighted sum of the decomposed normal distributions (e.g., weighted dose) is proposed as a new measure of target dose, rather than the more unstable point dose. The method and its theory are presented and validated using simulated distributions. Additional validation is performed by analyzing simple four field box techniques encompassing a predefined target, using different treatment energies inside a water phantom. Furthermore, two clinical situations are analyzed using this methodology to illustrate practical usefulness. A comparison of a treatment plan for a breast patient using a tangential field setup with wedges is compared to a comparable geometry using dose compensators. Finally, a normal tissue complication probability (NTCP) calculation is refined using this decomposition. The NTCP calculation is performed on a liver as organ at risk in a treatment of a mesothelioma patient with involvement of the right lung. The comparison of the wedged breast treatment versus the compensator technique yields comparable classical dose parameters (e.g., conformity index approximately = 1 and equal dose at the ICRU dose point). The methodology proposed here shows a 4% difference in weighted dose outlining the difference in treatment using a single parameter instead of at least two in a classical analysis (e.g., mean dose, and maximal dose, or total dose variance). NTCP-calculations for the mesothelioma case are generated automatically and show a 3% decrease with respect to the classical calculation. The decrease is slightly dependant on the fractionation and on the alpha/beta-value utilized. In conclusion, this method is able to distinguish clinically important differences between treatment plans using a single parameter. This methodology shows promise as an objective tool for analyzing NTCP and doses in larger studies, as the only information needed is the dose volume histogram.

Algorithms↗

PubMed2003

A meta-analysis of studies on the association of the platelet PlA polymorphism of glycoprotein IIIa and risk of coronary heart disease.

The Pl(A2) polymorphism of the glycoprotein IIIa subunit of the fibrinogen receptor (GPIIb-IIIa) has been reported by some studies to be associated with an increased risk of coronary thrombosis. Following the first paper on the subject in 1996, a large number of studies have investigated the relationship between this polymorphism and coronary thrombosis, either at the epidemiological or at the cellular and molecular levels. The cellular and molecular studies have shown in a consistent manner that this polymorphism increases platelet responsiveness. In contrast, epidemiological studies have generated inconsistent results regarding the clinical impact of Pl(A2). We consider 12 epidemiological studies that investigate the link between presence/absence of this polymorphism and presence/absence of coronary heart disease. Each is a case-control study that reports an odds ratio. The studies are not directly comparable because they differ greatly in their patient pools and also in the way the data are analysed. We present several meta-analyses of these 12 studies. The simplest one is based on a standard frequentist random effects model with a normal distribution for the study effects (the per-study population log-odds ratios). We also consider a Bayesian version of this model, with a diffuse prior for the mean and variance of the normal distribution of the study effects. The conclusions from both of these analyses is about the same, and is that there is evidence that the Pl(A2) polymorphism is associated with an increased risk of coronary heart disease. A look at the reported log-odds ratios across studies suggests that the study effects do not come from a symmetric distribution. For this reason, we also consider semi-parametric priors for the distribution of the study effects. These priors are specifically designed for this kind of meta-analysis, and are based on a certain class of mixtures of Dirichlet priors. They can be designed to concentrate most of their mass around the family of normal distributions, but still allow for any other distribution. The semi-parametric Bayesian model continues to give evidence of an association between the Pl(A2) polymorphism and the risk of coronary heart disease.

Bayes Theorem↗