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Results for “Likelihood Functions”

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PubMed1994

A stable, multivariate extension of the log-normal survival model.

When applied to survival data from a population of cancer patients, the log-normal model provides estimates of three important parameters: cured fraction, mean log survival time, and standard deviation log survival time. In the original model, however, these parameters are unrelated to prognostic covariates. Furthermore, the original algorithm is computationally unstable and highly dependent on initial parameter estimates. We have developed an extension of the log-normal model that stabilizes computation and expresses survival parameters as functions of prognostic covariates. We have also developed an ancillary algorithm that provides reliable initial estimates.

Algorithms↗

PubMed2026

Statistical test to compare the linkage model and the admixture model based on central limit results.

In the Admixture Model, the probability that an individual carries a certain allele at a specific marker depends on the allele frequencies in K ancestral populations and the proportion of the individual's genome originating from these populations. The markers are assumed to be independent. The Linkage Model is a Hidden Markov Model that extends the Admixture Model by incorporating linkage between neighboring loci. We prove consistency and asymptotic normality of maximum likelihood estimators for the ancestry of individuals in the Linkage Model, complementing earlier results by (Pfaff et al., 2004; Pfaffelhuber and Rohde, 2022; Heinzel, 2025) for the Admixture Model. These results are used to prove that a statistical test that allows for model selection between the Admixture Model and the Linkage Model is an asymptotic level-α-test. Finally, we demonstrate the practical relevance of our results by applying the test to real-world data from The 1000 Genomes Project Consortium (2015).

Genetic Linkage↗

PubMed1996

Confidence intervals for median survival times under a piecewise exponential model with proportional hazards covariate effects.

Brookmeyer and Crowley derived a non-parametric confidence interval for the median survival time of a homogeneous population by inverting a generalization of the sign test for censored data. The 1-alpha confidence interval for the median is essentially the set of all values t such that the Kaplan--Meier estimate of the survival function at time t does not differ significantly from one-half at significance level alpha. Here I extend the method to incorporate covariates into the analysis by assuming an underlying piecewise exponential model with proportional hazards covariate effects. Maximum likelihood estimates of the model parameters are obtained via iterative techniques, from which the estimated (log) survival curve is easily constructed. The delta method provides asymptotic standard errors. Following Brookmeyer and Crowley, I find the confidence interval for the median survival time at a specified value of the covariate vector by inverting the sign test. I illustrate the methods using data from a clinical trial conducted by the Radiation Therapy Oncology Group in cancer of the mouth and throat. It is seen that the piecewise exponential model provides considerable flexibility in accommodating to the shape of the underlying survival curve and thus offers advantages to other, more restrictive, parametric models. Simulation studies indicate that the method provides reasonably accurate coverage probabilities.

Age Factors↗

PubMed1986

Plicatic acid-specific IgE and nonspecific bronchial hyperresponsiveness in western red-cedar workers.

In a cross-sectional survey of 652 workers in a western red-cedar sawmill, we obtained data on symptoms, pulmonary function, immediate skin reactivity to common allergens, nonspecific bronchial responsiveness, total IgE level, and sensitization to plicatic acid conjugated with human serum albumin as measured by RAST. Dust exposure was estimated by personal and area sampling for total dust during a work shift and cumulative exposure by duration of employment. Seven percent of the workers had an elevated RAST, and 20% had nonspecific bronchial hyperresponsiveness. Elevation in RAST was associated with bronchial hyperresponsiveness. Almost half (46%) of the workers with RAST elevation had bronchial hyperresponsiveness compared to 18% in workers with no RAST elevation. The association was unaffected by total IgE level or by limiting the analysis to workers without respiratory symptoms and was most apparent in younger workers. Bronchial hyperresponsiveness was associated with increased prevalence of respiratory symptoms as well as with lower levels of pulmonary function. The likelihood of bronchial hyperresponsiveness increased with increasing age but was unrelated to the dust-exposure concentration. RAST elevation was unrelated to employment duration or dust exposure and was not associated with an increased prevalence of symptoms or lower levels of pulmonary function independent of bronchial hyperresponsiveness. We conclude that plicatic acid-specific IgE and nonspecific bronchial hyperresponsiveness are associated in western red-cedar workers and that this association may reflect a causal connection.

Adult↗

PubMed1993

Repeated measurement designs with random selections.

We consider repeated measurement designs with a single group as well as with multiple groups. Conventionally, the repeated measurements are made at fixed, often evenly spaced times. The first and second moment conditions needed for an exact F test are not satisfied in general, but with random permutation of the times, a probability measure results that does satisfy these moment conditions, unconditionally. As a consequence, unfortunately, we lose the asymptotic normality that is also essential to justify an F test. We introduce a class of designs and estimators for which both the moment conditions and asymptotic normality are satisfied. The times are the same for all subjects and they are chosen in such a way that they are mutually independent and identically distributed. It is important to understand that our conditions are satisfied only unconditionally--that is, if we do not condition by the randomly chosen times. There is a small probability that the randomly sampled times could be very unevenly allocated. Since we are not conditioning by the times, strictly speaking, this does not matter. It is possible to impose a mild condition of "spread," as we show, at small cost in terms of the P-value. Our method of design makes it possible to do regression analysis, interval estimation, and hypothesis testing on the mean response as a function of time. Because we have mutual independence and identical distributions of times we can form confidence bands.

Animals↗

PubMed1976

Prognosis for recovery of function in acute renal failure. Value of the renal image obtained using iodohippurate sodium I 131.

Twenty-four survivors of acute, nonobstructive, nonnephritic renal failure had a renal scan using iodohippurate sodium I 131 performed early in the acute illness. Scans were judged according to whether the renal images were prominent, faint, or absent during the first 30 minutes after intravenous injection of 100 to 250 microcuries of iodohippurate sodium I 131. All ten patients with prominent renal images attained life-sustaining renal function with an average postrecovery creatinine clearance of 80 ml/min. Of the seven patients with faint renal images, six recovered life-sustaining renal function (average creatinine clearance of 39 ml/min), and one required chronic hemodialysis. Seven patients had no renal image initially; four recovered life-sustaining renal function with an average creatinine clearance of 25 ml/min; three required chronic hemodialysis. We conclude that, for patients with acute renal failure, the appearance of the renal image obtained using this substance is an important indicator of renal viability and of the likelihood for functional recovery.

Acute Kidney Injury↗

PubMed1992

On identifying a positive dose-response surface for combination agents.

This article concerns construction of a confidence surface for tangential slopes of the dose-response surface of a combination therapy to identify where response increases as a function of drug dosage. This approach extends to the assessment of the effectiveness of the combination therapy.

Dose-Response Relationship, Drug↗

PubMed1994

Dust exposure indices and lung function changes in longshoremen and dock workers.

A group of Dutch harbor workers involved in loading and unloading bulk products from sea vessels such as coal, cokes, and some other products like alumina, borax, phosphate ore, and vermiculite was studied. Exposures were characterized by personal and environmental monitoring. This information was subsequently used to estimate several dust exposure indices and to study relationships with lung function variables and respiratory symptoms. Average respirable dust exposure levels ranged from 0.3-4.0 mg/m3. Workers involved in unloading products from sea vessels were exposed to the highest dust levels. Supervisors and workers with tasks in the dock had an intermediate to low exposure. Office workers had the lowest exposure to respirable dust. Inhalable dust levels were considerably higher and average exposures ranged from 0.3-80 mg/m3. The ranking of occupational titles by inhalable dust exposure was almost identical to the rank order of respirable dust levels. Workers with higher current and cumulative dust exposures tended to have a lower lung function, and only shortness of breath had a statistically significant relationship with current and cumulative inhalable dust exposure. In general, relationships between lung function and inhalable dust levels tended to be somewhat stronger in terms of statistical significance, because inhalable dust is an estimate of dust deposition in the upper airways and lung function is a measurable parameter of airway obstruction in that region. However, the differences with respirable dust were minimal, and variability in dust exposure levels was extremely large for this population. It was concluded that harbor workers involved in unloading ships containing coal and various kinds of ore can be exposed to high dust levels. Relationships between dust exposure and lung function illustrate that these exposures are a respiratory hazard. Our finding that inhalable dust levels have a somewhat stronger relationship with lung function level than respirable dust levels deserves further attention.

Adult↗

PubMed1992

A random dipole model for spontaneous brain activity.

The statistical properties of the EEG and the MEG are described mathematically as the result of randomly distributed dipoles. These dipoles represent the interactions of cortical neurons. For certain dipole distributions, the first- and second-order moments of the electric and magnetic fields are derived analytically. If the dipoles are in a spherical volume conductor and have no preference for any direction, the variance of a differentially measured EEG-signal is only a function of the electrode distance. In this paper, the theoretically derived variance function will be compared with EEG- and MEG-measurements. It is shown that a dipole with a fixed position and a randomly fluctuating amplitude is an adequate model for the alpha-rhythm. An expression for the covariance between the magnetic field and a differentially measured EEG-signal is derived. This covariance is considered as a function of the magnetometer position, and is compared with the measurements of Chapman et al. [23]. The theory can be used to obtain a (spatial) covariance matrix of the background noise, which occurs in evoked potential measurements. Such a covariance matrix can be used to obtain a maximum likelihood estimator of the dipole parameters in evoked potential studies, to evaluate the merits of the so-called "Laplacian derivation," and for the interpolation of electromagnetic data.

Artifacts↗

PubMed1993

Construct validation and the Rasch model: functional ability of healthy elderly people.

The purpose of this study was to test the construct validity of a measure of functional ability, developed with the intention of achieving a high degree of variability and capacity for discriminating among a group of healthy elderly people. Data were collected from 734 70-year-old people in Denmark in the county of Copenhagen. Functional ability was measured with the traditional activities of daily living and with a classification system developed specially for healthy elderly people. Construct validity was tested by the Rasch model for item analysis, addressing specifically the internal validity by assessing the homogeneity of items under different conditions. The results show that the proposed measure of functional ability is a combination of six different dimensions, divided into 3 types: mobility function, lower limb function and upper limb function. With regard to these three types decreased functional ability can appear by either tiredness or reduced speed.

Activities of Daily Living↗

PubMed1989

Determination of characteristic parameters of human postural dynamics.

Posture control performance was quantified in three variables (swiftness, stiffness, damping). Subjects were tested with a force platform recording body sway induced by vibrators attached to the calf muscles. Parameter estimation was made with identification of a transfer function representing the stabilized inverted pendulum. It is conjectured that the state feedback parameters identified are suitable for use in assessing ability to maintain posture.

Adult↗

PubMed1993

The value of the forced expiratory time in the physical diagnosis of obstructive airways disease.

OBJECTIVE: To evaluate the test characteristics of the forced expiratory time (FET) in the diagnosis of obstructive airways disease. DESIGN: A cross-sectional diagnostic test study. The FET of 400 subjects was measured by a physician examiner and was compared with the criterion standard of spirometry. In a second sample of 100 subjects, the FET was measured by pairs of physician examiners to evaluate interexaminer agreement. SETTING: A pulmonary function test laboratory at a tertiary care hospital that receives referrals for preoperative evaluations, acute and chronic pulmonary disease, and occupational lung disease. SUBJECTS: A consecutive sample of patients who were referred to the pulmonary function laboratory from primary care internists, pulmonary physicians, and surgeons. INTERVENTIONS: None. MAIN OUTCOME MEASURES: The sensitivity and specificity of the FET in the diagnosis of obstructive airways disease at cutoff values ranging from 2 to 14 seconds. A receiver operating characteristic curve was used to evaluate the diagnostic performance of the FET. Likelihood ratio lines were determined using a logistic regression model adjusting for the subjects age. Interexaminer agreement was evaluated with a kappa statistic. RESULTS: Using the FET maneuver with a cutoff value of 6 seconds will correctly diagnose the greatest number of subjects with obstructive airways disease. The FET maneuver is more discriminating for subjects 60 years or older compared with younger subjects. The positive likelihood ratio for a subject aged 60 years or older with an FET of 4 to 6 seconds is 0.42 (95% confidence interval [CI], 0.24 to 0.73); of 6 to 8 seconds, 2.19 (95% CI, 1.02 to 4.80); and of greater than 8 seconds, 4.08 (95% CI, 2.54 to 6.79). The kappa statistic for interexaminer agreement is 0.70. CONCLUSIONS: The FET demonstrates moderately good performance as a diagnostic test for obstructive airways disease. The value of the test will depend on the pretest probability of disease and the clinical circumstances in which it is used.

Adult↗

PubMed1995

A QALY-based societal health statistic for Canada, 1985.

This paper assesses the appropriateness of QALYs (quality adjusted life years) as a foundation for an index of societal health, and the feasibility of using such an index to guide health care policy. Results of this paper suggest that the standard aggregate QALY index imposes an ethical position on policy makers which may promote inequality in well-being associated with health. It is possible to rectify this problem in theory, but current data are insufficient to estimate such corrected indices. A QALY-based index, constructed using the best available data, indicates morbidity has a significant effect on Canadian health status (e.g. life expectancy figures alone overstate community health by about 10%), that the impact of morbidity is unequal across regions and gender, and that role (the ability to fulfil social functions) and mobility dysfunction are important determinants of ill-health in this population.

Adolescent↗

PubMed1996

Testing of hypotheses about altitude decompression sickness by statistical analyses.

This communication extends a statistical analysis of forced-descent decompression sickness at altitude in exercising subjects (J Appl Physiol 1994; 76:2726-2734) with a data subset having an additional explanatory variable, rate of ascent. The original explanatory variables for risk-function analysis were environmental pressure of the altitude, duration of exposure, and duration of pure-O2 breathing before exposure; the best fit was consistent with the idea that instantaneous risk increases linearly as altitude exposure continues. Use of the new explanatory variable improved the fit of the smaller data subset, as indicated by log likelihood. Also, with ascent rate accounted for, replacement of the term for linear accrual of instantaneous risk by a term for rise and then decay made a highly significant improvement upon the original model (log likelihood increased by 37 log units). The authors conclude that a more representative data set and removal of the variability attributable to ascent rate allowed the rise-and-decay mechanism, which is expected from theory and observations, to become manifest.

Altitude↗

PubMed1993

A bivariate survival model with modified gamma frailty for assessing the impact of interventions.

Bivariate survival analysis models that incorporate random effects or 'frailty' provide a useful framework for determining the effectiveness of interventions. These models are based on the notion that two paired survival times are correlated because they share a common unobserved value of a random variate from a frailty distribution. In some applications, however, investigators may have some information that characterizes pairs and thus provides information about their frailty. Alternatively, there may be an interest in assessing whether the correlation within certain types of pairs is different from the correlation within other types of pairs. In this paper, we present a method to incorporate 'pair-wise' covariate information into the dependence parameter of the bivariate survival function. We provide an example using data from the Framingham Heart Study to investigate the times until the occurrence of two events within an individual: the first detection of hypertension and the first cardiovascular disease event. We model the dependence between these two events as a function of the age of the individual at the time of enrollment into the Framingham Study.

Adult↗

PubMed1995

Cognitive function and assessment of lung function in the elderly.

The feasibility of spirometry or respiratory impedance measurements for assessing lung function in the elderly was compared in 208 institutionalized patients with various degrees of cognitive function impairment. Respiratory impedance was determined by the forced oscillation technique. Cognitive function was assessed by the score for the mini-mental state (MMS) examination. Of the 208 patients, 126 had severe cognitive impairment (MMS < or = 17), 36 had mild impairment (18 < or = MMS < or = 23), and 46 had no impairment (MMS > or = 24). Of the 208 patients, respiratory impedance measurements were possible in 159, whereas in only 85 was spirometry possible. The overall difference between the feasibility rates for the spirometric and respiratory impedance measurements was highly significant (chi 2 = 71.4; p < 10(-6)). The difference between the feasibility rates for the two techniques was higher in the group of subjects with severe cognitive impairment than in the groups with mild impairment and no impairment, respectively. Among the 84 patients able to complete both tests, significant correlations were found between the spirometric and respiratory impedance measurements. These results indicate that respiratory impedance measurement seems a more useful tool than spirometry for assessing lung function in elderly patients whenever cognitive function is impaired.

Aged↗

PubMed2025

Penalized likelihood optimization for censored missing value imputation in proteomics.

Label-free bottom-up proteomics using mass spectrometry and liquid chromatography has long been established as one of the most popular high-throughput analysis workflows for proteome characterization. However, it produces data hindered by complex and heterogeneous missing values, which imputation has long remained problematic. To cope with this, we introduce Pirat, an algorithm that harnesses this challenge using an original likelihood maximization strategy. Notably, it models the instrument limit by learning a global censoring mechanism from the data available. Moreover, it estimates the covariance matrix between enzymatic cleavage products (ie peptides or precursor ions), while offering a natural way to integrate complementary transcriptomic information when multi-omic assays are available. Our benchmarking on several datasets covering a variety of experimental designs (number of samples, acquisition mode, missingness patterns, etc.) and using a variety of metrics (differential analysis ground truth or imputation errors) shows that Pirat outperforms all pre-existing imputation methods. Beyond the interest of Pirat as an imputation tool, these results pinpoint the need for a paradigm change in proteomics imputation, as most pre-existing strategies could be boosted by incorporating similar models to account for the instrument censorship or for the correlation structures, either grounded to the analytical pipeline or arising from a multi-omic approach.

Proteomics↗

PubMed1993

Robustness of some estimators for the analysis of covariance structures.

A sampling experiment was designed to evaluate the robustness of some estimators used in the analysis of covariance structures to misspecification of the discrepancy function in finite samples. The estimators were studied under four distribution (a multivariate normal, an elliptical, a non-elliptically symmetric, and an asymmetric multivariate distribution, and eight sample size (75, 150, 300, 600, 1200, 2400, 4800, 9600) conditions. Parameters of the composite direct product model for a 6-variable MTMM matrix were estimated using the Maximum Wishart Likelihood (MWL), generalized least squares (GLS), asymptotically distribution free (ADF), and approximate ADF (DADF) estimators. Browne's elliptical correction (CMWL) to the test statistic and standard errors for scale-invariant models was also made for each sample. Each of the 32 distribution-sample size conditions was replicated 300 times. The accuracy of the parameter estimates and estimated standard errors and the distribution of the test statistic were studied. The theoretically predicted importance of information contained in higher-order moments of arbitrary distributions was confirmed. Robustness of the MWL and normal theory GLS estimators cannot be taken for granted. Elliptical corrections may be a practical solution to some data analytic problems.

Female↗