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PubMed2005

A penalized maximum likelihood method for estimating epistatic effects of QTL.

Although epistasis is an important phenomenon in the genetics and evolution of complex traits, epistatic effects are hard to estimate. The main problem is due to the overparameterized epistatic genetic models. An epistatic genetic model should include potential pair-wise interaction effects of all loci. However, the model is saturated quickly as the number of loci increases. Therefore, a variable selection technique is usually considered to exclude those interactions with negligible effects. With such techniques, we may run a high risk of missing some important interaction effects by not fully exploring the extremely large parameter space of models. We develop a penalized maximum likelihood method. The method developed here adopts a penalty that depends on the values of the parameters. The penalized likelihood method allows spurious QTL effects to be shrunk towards zero, while QTL with large effects are estimated with virtually no shrinkage. A simulation study shows that the new method can handle a model with a number of effects 15 times larger than the sample size. Simulation studies also show that results of the penalized likelihood method are comparable to the Bayesian shrinkage analysis, but the computational speed of the penalized method is orders of magnitude faster.

Bayes Theorem↗

PubMed2006

Association between residence location and likelihood of kidney transplantation in Aboriginal patients treated with dialysis in Canada.

For reasons that are not well understood, Aboriginal people with end-stage renal disease (ESRD) have lower rates of kidney transplantation. We hypothesized that distance between residence location and the closest transplant center was greater in Aboriginal dialysis patients and would partially explain the lower rate of transplantation in this population. We studied a random sample of 9905 patients initiating dialysis in Canada between 1990 and 2000. We calculated the distance between residence location at dialysis inception and the closest transplant center. Cox proportional hazards models were used to examine the relation between residence location and the likelihood of transplantation over a median period of 2.3 years. The proportion of Aboriginal participants living 300 km from the closest transplant center was 25, 18, 18, and 39% respectively, compared with 55, 19, 11, and 15% among white subjects. The relative likelihood of transplantation was significantly lower for Aboriginal compared to white participants across all four distance strata, with no apparent effect of residence location. For example, the relative likelihood of transplantation was hazard ratio (HR) 0.47, 95% confidence interval (CI) (0.31-0.72) in Aboriginal participants residing 300 km from the closest transplant center. Results were similar for transplants from deceased donors and living donors, and in all seven regions studied. In conclusion, remote location of residence does not explain the lower rate of kidney transplantation among Aboriginal people treated for ESRD in Canada.

Aged↗

PubMed2002

Does a rural educational experience influence students' likelihood of rural practice? Impact of student background and gender.

CONTEXT: The family medicine clerkship at the University of Calgary is a 4-week mandatory rotation in the final year of a 3-year programme. Students are given the opportunity to experience rural practice by training at 1 of several rural practices. OBJECTIVE: To determine whether exposure to a rural educational experience changes students' likelihood of doing a rural locum or rural practice and whether student background and gender are related to these practice plans. METHOD: Clinical clerks from the Classes of 1996-2000, who trained at rural sites, responded to questionnaire items both before and after the rural educational experience. Responses to the questionnaire items and discipline of postgraduate training served as dependent variables. Student background and gender were independent variables. RESULTS: As a result of the rural educational experience all students were more likely to do a rural locum. Compared to their urban-raised peers, students from rural backgrounds reported a significantly greater likelihood of doing a rural locum and practising in a rural community, irrespective of gender or participating in a rural educational experience. There was no relationship between background and career choice. CONCLUSION: A rural educational experience at the undergraduate level increases the stated likelihood of students participating in rural locums and helps to solidify existing rural affiliations. Students with rural backgrounds have a more favourable attitude toward rural practice. This pre-post study provides further support for the preferential admission to medical school of students with rural backgrounds to help alleviate the rural physician shortage.

Alberta↗

PubMed1999

Computer software for performing likelihood tests of pedigree relationship using genetic markers.

Molecular techniques are making ever more genetic markers available for use in parentage assignment, and measures of relatedness. We present a program, Kinship, designed to use likelihood techniques to test for any non-inbred pedigree relationship between pairs of individuals, using single-locus codominant genetic markers. Kinship calculates the likelihood that each pair of individuals in a data set are related by a given pedigree hypothesis, and likelihood ratios for any pair of hypotheses. The program also uses a simulation routine to attach statistical significance to its results.

Journal Article↗

PubMed2003

Modelling autoimmune rheumatic disease: a likelihood rationale.

Immunoglobulins (Igs) and autoantibodies are commonly tested in sera from patients with suspected rheumatic disease. To evaluate the clinical utility of the tests in combination, we investigated sera from 351 patients with autoimmune rheumatic disease (ARD) rheumatoid arthritis (RA), systemic lupus erythematosus (SLE) and Sjögren's syndrome (SS) and 96 patients with nonautoimmune rheumatic disease (NAD) (fibromyalgia, osteoarthritis, etc.). Antinuclear antibodies (ANA), rheumatoid factor (RF), antibodies against DNA and extractable nuclear antigens (anti-ENA), IgG, IgA and IgM were measured for all patients. Logistic regression analysis of test results was used to calculate each patient's probability for belonging to the ARD or NAD group as well as likelihood ratios for disease. Test accuracy was investigated using receiver-operating characteristic (ROC) plots and nonparametric ROC analysis. Neither concentrations of IgG, IgA, IgM, anti-DNA nor anti-ENA gave a significant effect on diagnostic outcome. Probabilities for disease and likelihood ratios calculated by combining RF and ANA performed significantly better at predicting ARD than utilization of the diagnostic tests in isolation (P < 0.001). At a cut-off level of P = 0.73 and likelihood ratio = 1, the logistic model gave a specificity of 93% and a sensitivity of 75% for the differentiation between ARD and NAD. When compared at the same level of specificity, ANA gave a sensitivity of 37% and RF gave a sensitivity of 56.6%. Dichotomizing ANA and RF as positive or negative did not reduce the performance characteristics of the model. Combining results obtained from serological analysis of ANA and RF according to this model will increase the diagnostic utility of the tests in rheumatological practice.

Adolescent↗

PubMed1997

A point score system for predicting the likelihood of blood transfusion after hip or knee arthroplasty.

BACKGROUND: Given the high cost of autologous blood donation for elective surgery, it would be desirable to predict which patients are most likely to benefit from the procedure. The purpose of this study was to develop a point score system for predicting the likelihood of blood transfusion in hip and knee arthroplasty. STUDY DESIGN AND METHODS: A database of 599 patients undergoing elective surgery at a teaching hospital was used for the analysis. Variables were analyzed to determine their univariate association with postoperative blood transfusion. Significant factors were entered into a multiple logistic regression model, and a point score system was developed on the basis of the regression coefficients. Four strata of transfusion risk were constructed. RESULTS: Factors independently associated with blood transfusion included preoperative hemoglobin, type of arthroplasty, primary versus revision surgery, autologous donor status, and patient weight. Four factors were used to create a point score system with four strata. The likelihood of blood transfusion for patients in the four risk strata was 1.7, 11.0, 40.0, and 78.3 percent. The calculated area under the receiver operating characteristic curve was 0.86. CONCLUSION: The likelihood of a postoperative blood transfusion can be predicted by using this simple point score system. Autologous blood donation can subsequently be targeted to the high-risk patients.

Aged↗

PubMed2000

Clinical sign profile likelihood ratios for bovine spongiform encephalopathy suspects.

This study has described a method for generating the probability of a bovine spongiform encephalopathy (BSE) suspect being a true positive BSE case. A weighting equivalent to the clinical sign frequencies recorded in histopathologically confirmed BSE cases was assigned to 14 clinical observations and a clinical profile score for the case was generated by the summation of the weightings. This method was applied to 50 histopathologically confirmed (true positive cases) BSE suspects and 50 histopathologically unconfirmed (false positive cases) BSE suspects. The profile scores for the true positive BSE suspect cases were statistically significantly higher than the profile scores of the false positive BSE suspect cases (P = 0.0014) using a Mann-Whitney U non-parametric test. The mean profile score for the true positive cases was 944 and for the false positive scores was 879. Likelihood ratios for BSE suspects with different clinical profile scores were computed using different clinical profile score cut off point and ranges. A BSE suspect with profile score of 727 or above (the lowest cut off point) and 1037 or above (the highest cut off point) had likelihood ratios for being BSE of 1. 09 and 4.00 respectively. The likelihood ratios for a BSE suspect being a true positive BSE case in the profile score ranges 627-866, 867-966, 967-1036 and 1037-1067 were 0.35, 1.06, 1.30 and 4.0 respectively. Further investigations or a revisit may be justified in animals with a low probability of being BSE.

Animals↗

PubMed2003

Nodal yield in neck dissection and the likelihood of metastases.

OBJECTIVES: The purpose of this study was to begin investigating the relationship between nodal yield in neck dissection and the likelihood of finding cervical metastases in T1 and T2 head and neck squamous cell carcinoma (HNSCC). No clinical implications are drawn from this preliminary work. STUDY DESIGN AND SETTING: This study was a retrospective analysis of 564 patients with T1 and T2 HNSCC of the oral cavity, oropharynx, or hypopharynx from the National Cancer Institute Surveillance, Epidemiology, and End Results (SEER) Program registry. A multivariate analysis was performed to evaluate the relationship between nodal yield in neck dissection and the discovery of cervical metastases. Other independent factors included in the analysis were gender, age, race, and primary site of tumor. RESULTS: Compared with nodal yield < 13, cervical metastases were more likely to be found for nodal yield 21-28 (P < 0.001, odds ratio [OR] = 3.68), 29-40 (P = 0.021, OR = 1.98), and >40 (P < 0.001, OR = 3.52). Increased age, male sex, and oropharynx and hypopharynx primaries were also associated with a significantly increased likelihood of finding cervical metastases. CONCLUSION: In T1 and T2 cases of HNSCC, nodal yield >20, increased age, male sex, and primary site correspond with an increased likelihood of finding cervical metastases.

Adolescent↗

PubMed1986

Maximum likelihood estimation for stationary point processes.

In this paper we derive the log likelihood function for point processes in terms of their stochastic intensities by using the martingale approach. For practical purposes we work with an approximate log likelihood function that is shown to possess the usual asymptotic properties of a log likelihood function. The resulting estimates are strongly consistent and asymptotically normal (under some regularity conditions). As a by-product, a strong law of large numbers and a central limit theorem for martingales in continuous times are derived.

Journal Article↗

PubMed1995

Transmission maximum-likelihood reconstruction with ordered subsets for cone beam CT.

An iterative algorithm is presented for accelerated reconstruction of cone beam transmission CT data (CBCT). CBCT supplies an attenuation map for SPECT attenuation compensation and anatomical correlation. Iterative algorithms are necessary to reduce truncation artifacts and 3D reconstruction artifacts. An existing transmission maximum-likelihood algorithm (TRML) is accurate but the reconstruction time is too long. The new algorithm is a modified EM algorithm, based on ordered subsets (OSEM). OSEM was evaluated in comparison to TRML using a thorax phantom and a 3D Defrise phantom. A wide range of image measures were evaluated, including spatial resolution, noise, log likelihood, region quantification, truncation artifact removal, and 3D artifact removal. For appropriate subset size, OSEM produced essentially the same image as TRML, but required only one-tenth as many iterations. Thus, adequate images were available in two to four iterations (20-30 min on a SPARC 2 workstation). Further, OSEM still approximately maximizes likelihood: divergence occurs only for very high (and clinically irrelevant) iterations. Ordered subsets are likely to be useful in other geometries (fan and parallel) and for emission CT as well. Therefore, with ordered subsets, high-quality iterative reconstruction is now available in clinically practical reconstructions times.

Algorithms↗

PubMed2002

Likelihood of attending bowel screening after a negative genetic test result: the possible influence of health professionals.

This study was undertaken to determine the extent to which the reported likelihood of attending future bowel screening following negative genetic testing results for familial adenomatous polyposis (FAP) varies between the type of health professional providing care and the country of testing. The study subjects were 103 unaffected adults at risk for FAP who received negative results following predictive DNA testing. Our study indicates that the reported likelihood of attending bowel screening was higher in those given results by nongenetics physicians, rather than by genetics professionals; the reported likelihood of attending bowel screening under these circumstances was also higher in the UK than in Australia. Both of these results were affected by the perceived chances of developing FAP, and, in the case of the country of testing, by the perceived accuracy of the genetic test result and the perceived seriousness of the disease. How and what health professionals communicate with patients about genetic testing may explain the differences between type of health professional and country of testing and attitudes toward bowel screening. If this is the case, training in communication may change patients' perceptions and, in turn, their behavioral intentions and actions following a negative test result.

Adenomatous Polyposis Coli↗

PubMed1987

Predictive value derived from likelihood ratios: a superior technic to interpret quantitative laboratory results.

The predictive value of a quantitative test value calculated from a likelihood ratio is compared with the predictive value of a positive result for computer-simulated laboratory data. A significant loss of information about the magnitude of a quantitative test value occurs when calculating the predictive value of a positive result. This is because of the selection of an arbitrary critical value that classifies the quantitative result as positive or negative. The likelihood ratio (the probability of having disease divided by the probability of not having disease for a given test result) and the prevalence of disease is used to calculate predictive values. Logistic regression is used to predict the likelihood ratio of a test value.

Clinical Laboratory Techniques↗

PubMed1983

Maximum likelihood estimation of the number of nucleotide substitutions from restriction sites data.

A simple method of the maximum likelihood estimation of the number of nucleotide substitutions is presented for the case where restriction sites data from many different restriction enzymes are available. An iteration method, based on nucleotide counting, is also developed. This method is simpler than the maximum likelihood method but gives the same estimate. A formula for computing the variance of a maximum likelihood estimate is also presented.

Animals↗

PubMed1991

A maximum likelihood method for estimating genome length using genetic linkage data.

The genetic length of a genome, in units of Morgans or centimorgans, is a fundamental characteristic of an organism. We propose a maximum likelihood method for estimating this quantity from counts of recombinants and nonrecombinants between marker locus pairs studied from a backcross linkage experiment, assuming no interference and equal chromosome lengths. This method allows the calculation of the standard deviation of the estimate and a confidence interval containing the estimate. Computer simulations have been performed to evaluate and compare the accuracy of the maximum likelihood method and a previously suggested method-of-moments estimator. Specifically, we have investigated the effects of the number of meioses, the number of marker loci, and variation in the genetic lengths of individual chromosomes on the estimate. The effect of missing data, obtained when the results of two separate linkage studies with a fraction of marker loci in common are pooled, is also investigated. The maximum likelihood estimator, in contrast to the method-of-moments estimator, is relatively insensitive to violation of the assumptions made during analysis and is the method of choice. The various methods are compared by application to partial linkage data from Xiphophorus.

Animals↗

PubMed1996

Computation of the full likelihood function for estimating variance at a quantitative trait locus.

The proportion of alleles identical by descent (IBD) determines the genetic covariance between relatives, and thus is crucial in estimating genetic variances of quantitative trait loci (QTL). However, IBD proportions at QTL are unobservable and must be inferred from marker information. The conventional method of QTL variance analysis maximizes the likelihood function by replacing the missing IBDs by their conditional expectations (the expectation method), while in fact the full likelihood function should take into account the conditional distribution of IBDs (the distribution method). The distribution method for families of more than two sibs has not been obvious because there are n(n - 1)/2 IBD variables in a family of size n, forming an n x n symmetrical matrix. In this paper, I use four binary variables, where each indicates the event that an allele from one of the four grandparents has passed to the individual. The IBD proportion between any two sibs is then expressed as a function of the indicators. Subsequently, the joint distribution of the IBD matrix is derived from the distribution of the indicator variables. Given the joint distribution of the unknown IBDs, a method to compute the full likelihood function is developed for families of arbitrary sizes.

Alleles↗

PubMed1998

Evidence that male smoking affects the likelihood of a pregnancy following IVF treatment: application of the modified cumulative embryo score.

Female cigarette smoking has been implicated as having a detrimental effect on in-vitro fertilization (IVF) outcomes mediated through: (i) a diminished ovarian reserve (DOR), and (ii) an elevated pregnancy loss. Research is sparse regarding the effect of male smoking. The objective of this retrospective cohort study was to investigate the effect of male and female smoking on: (i) the collective quality of embryos selected for uterine transfer, and (ii) the likelihood of achieving an ongoing pregnancy at 12 weeks. A total of 498 consecutive IVF treatment cycles were analysed. Female smokers were significantly younger (P < 0.05) and achieved a better modified cumulative embryo score (mCES) (P < 0.05) than female non-smokers. Female age correlated inversely with the number of oocytes collected (r = -0.42, P < 0.01) and the number of oocytes in turn was important in terms of predicting mCES. The decreasing number of oocytes aspirated with increasing age was of a significantly stronger magnitude for female smokers than for female non-smokers (P < 0.05). Multiple logistic regression was used to determine whether smoking affected the likelihood of achieving a 12-week pregnancy. The mCES, tubal infertility and male smoking were found to be significant. Male smoking interacted with male age (P = 0.0164), indicating for male smokers a decrease of 2.4% in the likelihood of achieving a 12-week pregnancy with every 1-year increase in age. This is the first study to show that male smoking has a deleterious effect on pregnancy outcome among IVF patients. Our study supports the increased risk of DOR but fails to support the elevated incidence of pregnancy loss among female smokers. A reduced pregnancy rate was associated with male smoking possibly through pre-zygotic genetic damage. The growing realization of a paternal component of reproductive impairment suggests that studying the male is necessary.

Cohort Studies↗

PubMed1987

Crossover counts and likelihood in multipoint linkage analysis.

For large numbers of genetic loci, jointly tested to determine their order along a chromosome, likelihood methods become unfeasible owing to the very large numbers of discrete alternative hypotheses (locus orderings) whose likelihoods must be separately evaluated. A method to order loci according to the criterion of minimizing the obligatory crossover count is therefore proposed. A branch-and-bound algorithm implementing this proposal has been programmed; the properties of this algorithm are investigated. The statistical properties of the proposed method are also considered. It is shown to be consistent under wide conditions, including arbitrary locus spacings, variable amounts of information per locus, and some patterns of interference. The relationship between the minimum crossover order and the maximum likelihood order is discussed. For fully informative gametes, and tight linkage, there is a virtual equivalence of the two criteria. For looser linkage, there remains a close relationship.

Algorithms↗

PubMed1989

Epidemiologic programs for computers and calculators. A microcomputer program for multiple logistic regression by unconditional and conditional maximum likelihood methods.

A frequent procedure in matched case-control studies is to report results from the multivariate unmatched analyses if they do not differ substantially from the ones obtained after conditioning on the matching variables. Although conceptually simple, this rule requires that an extensive series of logistic regression models be evaluated by both the conditional and unconditional maximum likelihood methods. Most computer programs for logistic regression employ only one maximum likelihood method, which requires that the analyses be performed in separate steps. This paper describes a Pascal microcomputer (IBM PC) program that performs multiple logistic regression by both maximum likelihood estimation methods, which obviates the need for switching between programs to obtain relative risk estimates from both matched and unmatched analyses. The program calculates most standard statistics and allows factoring of categorical or continuous variables by two distinct methods of contrast. A built-in, descriptive statistics option allows the user to inspect the distribution of cases and controls across categories of any given variable.

Algorithms↗