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PubMed2005

Free knot splines for logistic models and threshold selection.

The logistic regression model has been in use in statistical analysis for many years. The paper introduces a spline model to remove the linear restriction on logit function. By considering knot locations as free variables, spline approximation of data is improved. The number of knots and the degree of the spline functions can still be determined by using a model selection procedure. Moreover, a knot, seen as a free parameter for a piecewise linear spline, represents a break point in the logit function which may be interpreted as a threshold value. This method is applied to a clinical trial for an in vitro fertilization program.

Clinical Trials as Topic↗

PubMed2004

Analysis of the threshold liability model provides new understanding of causation in autoimmune diseases.

Autoimmune diseases include a heterogeneous group of complex traits, the causes of which are essentially unknown. The threshold liability model is a hypothesis that has a significant influence on thinking about causation in these diseases. Here, I analyze this model and assess its utility in understanding causation in autoimmunity. According to the model, members of a population have a normal distribution of genetic liability for a particular autoimmune disease. Further, a threshold value exists for each autoimmune disease such that an individual develops disease when his/her liability exceeds the threshold value; environmental and stochastic factors and epistatic gene interactions may increase or decrease an individual's disease liability. There are, however, two main problems with the threshold liability model. First, for a particular autoimmune disease, the threshold value divides a population into two distinct groups that consist either of affected or of healthy individuals. I show that this dichotomous division is inaccurate and misleading. Second, the threshold value corresponds to the occurrence of a component-cause of disease, i.e. when an appropriate collection of causative factors for a particular autoimmune disease is present, the disease must inevitably occur. I argue, however, that the disease contribution of essentially unknown random or stochastic factors to causation is at least similar in importance to the contributions of genetic and environmental factors. These stochastic factors add a significant element of unpredictability to the effects of genetic and environmental factors. Consequently causes in autoimmunity do not act deterministically, which is implied by the component-cause concept. Instead, the role of causative factors is to alter disease risk. I therefore reject the threshold liability model and conclude that a probabilistic approach provides the only reasonable way to understand causation in autoimmune diseases. This conclusion has important implications for other deterministic hypotheses in autoimmunity including other component-cause hypotheses.

Autoimmune Diseases↗

PubMedDate not supplied

Measures of the value of a diagnostic test derived from stochastic thresholds.

Previous indices for measuring the potential impact of a diagnostic test on a physician's management of a given patient were derived based on a fixed threshold model. The authors adapted these indices to a stochastic threshold model. In the stochastic threshold model the physician's probability of treating the patient is a function of the patient's probability of disease. From this model the authors derived the management value index (the expected effect that the test has on the physician's probability for treating the patient) and the utility value index (the expected benefit to the patient if the diagnostic test is used). Graphs of the indices versus the patient's probability of disease may be useful in teaching appropriate use of diagnostic tests.

Diagnosis↗

PubMed1990

Comodulation detection differences with multiple signal bands.

Detection thresholds were determined for signals consisting of one, two, or five noise bands embedded in eight "cue" bands. All of the noise bands were 100 Hz wide. The center frequencies of the signal bands ranged from 1250-3250 Hz in 500-Hz steps, and those of the cue bands ranged from 500-4000 Hz in 500-Hz steps. The multiple-band signals either all had the same temporal envelope, or all had different temporal envelopes. Similarly, the cue bands either all had the same temporal envelope or all had different temporal envelopes. In separate listening conditions, signal thresholds were determined for various combinations of the temporal envelope patterns of the signal and cue bands. The results were analyzed both in terms of differences in threshold across listening conditions, and in terms of changes in threshold within a listening condition, as the number of signal bands was increased. For both the single- and multiple-band signals, performance was best when the signal band(s) had a different envelope from the common envelope of the cue bands, and performance was worst when either the cue bands all had different envelopes, or the signal and cue bands all shared the same envelope. The thresholds of the multiple-band signals were better fitted by an independent-thresholds model than by a statistical-summation model. However, neither model predicted thresholds uniformly well in all listening conditions. The results are discussed in terms of both "within-channel" and "across-channel" models.

Acoustic Stimulation↗

PubMed1998

The effect of white and filtered noise on contrast detection thresholds.

Models of the dipper effect seen in contrast discrimination experiments predict that small amounts of noise should facilitate detection of a subthreshold sinusoidal grating. Although facilitation of chromatic sine waves has been measured with chromatic or luminance noise, a facilitory effect of luminance sinusoidal gratings has not been measured, most likely because the stimulus characteristics were not tuned for revealing facilitation. The present study measures contrast detection thresholds (CDTs) of sinusoidal gratings in two-dimensional, static, band-limited white noise and low-pass and high-pass filtered noise using a two-interval forced-choice paradigm. The results show facilitation in near threshold white noise of middle frequency sinusoidal gratings, and facilitation in filtered noise of sinusoidal gratings whose frequency is far outside the pass band of the noise. Based on these results, a model of contrast detection thresholds is modified such that the facilitation is attributed to reduced observer uncertainty caused by small amounts of noise.

Contrast Sensitivity↗

PubMed2005

Clinical multiple sclerosis occurs at one end of a spectrum of CNS pathology: a modified threshold liability model leads to new ways of thinking about the cause of clinical multiple sclerosis.

Multiple sclerosis (MS) is a complex trait, the causes of which are elusive. A threshold liability model influences thinking about the causes of this disorder. According to this model, a population has a normal distribution of genetic liability to MS. In addition, a threshold exists, so that MS begins when an individual's liability exceeds the MS threshold; environmental and other causative factors may increase or decrease an individual's MS liability. It is argued here, however, that this model is misleading, as it is based on the incorrect assumption that MS is a disorder that one either has or does not have. This paper hypothesizes, instead, that patients with a diagnosis of MS share identical CNS pathology, termed MS pathology, with some individuals who have a diagnosis of possible MS and with some apparently healthy individuals, who may never have a diagnosis of MS. In order to accommodate this hypothesis, the current threshold liability model is modified as follows. (1) In addition to a normal distribution of MS liability within a population, a spectrum of MS pathology occurs in some who have a high MS liability. (2) A clinical MS threshold exists at a point on this liability distribution, where the burden and distribution of MS pathology permits a diagnosis of clinical MS. (3) Additional thresholds exist that correspond to a lower MS liability and a lesser burden of MS pathology than occur at the clinical MS threshold. This modified threshold model leads to the postulate that causes act at various time points to increase MS liability and induce MS pathology. The accumulation of MS pathology sometimes leads to a diagnosis of clinical MS. One implication of this model is that the MS pathology in clinical MS and in some with possible MS differs only in the extent but not in the type of CNS injury. Thus, it may be possible to obtain insight into the causative environmental factors that increase MS liability and induce MS pathology by focusing on patients who have clinical MS; some environmental factors that induce new lesions in patients with clinical MS may be identical to those that induce MS pathology in genetically susceptible individuals who do not have clinical MS. Identification of these causative factors has importance, as specific treatment may prevent the accumulation of MS pathology that leads to the significant CNS damage associated with clinical MS.

Central Nervous System Diseases↗

PubMed1995

Modeling and optimization of populations subject to time-dependent mutation.

It has become clear that many organisms possess the ability to regulate their mutation rate in response to environmental conditions. So the question of finding an optimal mutation rate must be replaced by that of finding an optimal mutation schedule. We show that this task cannot be accomplished with standard population-dynamic models. We then develop a "hybrid" model for populations experiencing time-dependent mutation that treats population growth as deterministic but the time of first appearance of new variants as stochastic. We show that the hybrid model agrees well with a Monte Carlo simulation. From this model, we derive a deterministic approximation, a "threshold" model, that is similar to standard population dynamic models but differs in the initial rate of generation of new mutants. We use these techniques to model antibody affinity maturation by somatic hypermutation. We had previously shown that the optimal mutation schedule for the deterministic threshold model is phasic, with periods of mutation between intervals of mutation-free growth. To establish the validity of this schedule, we now show that the phasic schedule that optimizes the deterministic threshold model significantly improves upon the best constant-rate schedule for the hybrid and Monte Carlo models.

B-Lymphocytes↗

PubMed2006

The failure of dose-response models to predict low dose effects: a major challenge for biomedical, toxicological and aging research.

Recent detailed evaluations of the pharmacological, toxicological, and biogerontological literature indicate that the hormetic dose-response is quite common and highly generalizable by biological model, endpoint, and chemical class. Head-to-head comparisons of the hormetic model with the traditional threshold model have revealed the hormetic model to occur with considerably greater frequency in the biomedical literature. Despite these developments, the history of both pharmacology and toxicology reflects a strong acceptance and centralizing of the threshold model concept while profoundly marginalizing of the hormetic dose-response. This commentary will address why the biomedical community especially those in the areas of pharmacology and toxicology made an incorrect judgment that the most fundamental nature of the dose-response was threshold rather than hormetic and why this conclusion has continued to dominate these fields and their numerous applications despite convincing evidence to the contrary. These findings have particular relevance to the area of biogerontology since this discipline often resides at the pharmacological-toxicological interface.

Aging↗

PubMed1993

Have animal data been used inappropriately to estimate risks to humans from environmental trichloroethylene?

Trichloroethylene (TCE) is widely viewed as an environmental hazard. Its major metabolite, chloral hydrate, is a currently used medicine. Regulation of TCE is based on a linear extrapolation from effects of high doses in rodents to risks for humans at low doses. However, metabolic, toxicologic, and epidemiologic data on trichloroethylene and chloral hydrate as well as water chlorination studies call this approach into question. The mechanism of carcinogenesis of TCE and chloral hydrate in rodents is nonlinear: very high doses, sufficient to cause cellular necrosis, are necessary. Malignancy arises from repeated cycles of necrosis and regeneration with the ultimate emergence of hyperplasia and then neoplasia. Metabolites of TCE, trichloroacetic acid and dichloroacetic acid, mediate this toxic effect of TCE. These chloroacetic acids also induce similar lesions in rodents given high doses of the medicine, chloral hydrate. Human epidemiologic data show no increase in mortality or malignancy from substantial chronic exposure to trichloroethylene. Chlorination of drinking water produces much higher levels of chloroacetic acids than could be obtained from metabolizing TCE under current regulations. We conclude that the assumptions underlying current regulations are not applicable to TCE. Instead of a straight-line extrapolation model, a threshold model may be more appropriate. The data suggest that it is possible to increase substantially the allowable trichloroethylene in drinking water without increasing health hazards.

Animals↗

PubMed2005

Number of inseminations to conception in Holstein cows using censored records and time-dependent covariates.

Three methodologies that accommodate censoring or time-dependent covariates were used to estimate variance components for number of inseminations to conception. Data included 80,071 lactation records and 143,927 artificial inseminations in 47,509 Spanish Holstein cows. Up to 4 inseminations to conception, along with their respective censoring information, were analyzed. An ordinal-censored threshold model (CTM), a sequential threshold model (STM), and a grouped survival analysis via a discrete proportional hazards model (DPH) were implemented. Sire variance estimates on the liability scale were 0.016 and 0.010 for CTM and STM, respectively, and 0.012 for DPH on the logarithmic scale. Heritability estimates on the liability scale were 0.050 and 0.038 with CTM and STM, respectively. All models led to similar rankings of sires, and the strong correlations (0.97 to 0.98) between methodologies suggested robustness in ranking of sires of cows. Service sire variance estimates were 0.021 for both CTM and STM; DPH led to an approximate service sire variance of 0.020. Rankings for service sires between methodologies ranged from 0.76 to 0.90. These lower values are most likely due to differences in the treatment of time-dependent covariates. The STM had greater predictive ability of daughter fertility at first insemination than the other methodologies. However, the CTM predicted daughter fertility more accurately in subsequent inseminations. The DPH and STM had a similar predictive ability of daughter fertility in second and subsequent inseminations.

Algorithms↗

PubMed1992

EUROMAC. A European concerted action: maternal alcohol consumption and its relation to the outcome of pregnancy and child development at 18 months. Results--strategy of analysis and analysis of pregnancy outcome.

Analyses were made of the relation between maternal alcohol consumption before and in early pregnancy and five infant outcome variables: birthweight, crown-heel length, occipitofrontal circumference and the Apgar scores at 1 and 5 minutes. The data were analysed for all centres combined and separately. From tabulation of the mean values of the outcome variables by alcohol consumption, it appeared that a poorer outcome was related to consumption of 120 g/week absolute alcohol or more. Multiple regression analysis was used to allow for possible confounding by the child's gestational age at birth and sex, the mother's age, parity and smoking habit, and survey centre. Two threshold models were applied to the combined data, taking the confounders into account. The offset threshold model (assuming no effect of alcohol up to a threshold value, and then a constant multiplicative effect at higher levels) suggested a negative effect on birthweight at about 60 g/week absolute alcohol, but with a wide 85% confidence interval of 5-130 g/week. A step function threshold model, which assumes a constant effect above the threshold value, behaved erratically. Similar analyses for crown-heel length and occipitofrontal circumference provided only a very poor fit to the data. Data on reported congenital anomalies are presented by survey centre and maternal alcohol consumption, but due to the unstandardized method of collection they were not analysed further.

Alcohol Drinking↗

PubMed1985

Resolving genetic models for the transmission of schizophrenia.

Although family studies have consistently reported elevated rates of schizophrenia among the relatives of schizophrenics, the exact nature of the transmission of the disorder remains uncertain. Genetic models hypothesized to explain the transmission of schizophrenia include the generalized single locus and multifactorial threshold models. Here we briefly describe these models and test their goodness-of-fit to a single data set on the pooled morbid risks of schizophrenia among the relatives of schizophrenic probands in nine different classes of relatives with five different degrees of genetic relatedness. The generalized single locus model is rejected, while a pure polygenic threshold model does fit the observed risks. Allowance for environmental sources of familial resemblance under the multifactorial threshold model significantly improved the fit of the model to the data. An application of the multifactorial model to family data on tuberculosis is also reported. For tuberculosis, a strong familial environmental but not genetic effect was found, consistent with the known infectious etiology of this condition, showing that the finding of a strong genetic effect upon schizophrenia is not a necessary bias of these methods of analysis. The implications of these results for the search for major gene effects in schizophrenia are discussed.

Alleles↗

PubMedDate not supplied

A simulation study for the analysis of uncertain binary responses: application to first insemination success in beef cattle.

A simulation was carried out to investigate the methods of analyzing uncertain binary responses for success or failure at first insemination. A linear mixed model that included, herd, year, and month of mating as fixed effects; and unrelated service sire, sire and residual as random effects was used to generate binary data. Binary responses were assigned using the difference between days to calving and average gestation length. Females deviating from average gestation length lead to uncertain binary responses. Thus, the methods investigated were the following: (1) a threshold model fitted to certain (no uncertainty) binary data (M1); (2) a threshold model fitted to uncertain binary data ignoring uncertainty (M2); and (3) analysis of uncertain binary data, accounting for uncertainty from day 16 to 26 (M3) or from day 14 to 28 (M4) after introduction of the bull, using a threshold model with fuzzy logic classification. There was virtually no difference between point estimates obtained from M1, M3, and M4 with true values. When uncertain binary data were analyzed ignoring uncertainty (M2), sire variance and heritability were underestimated by 22 and 24%, respectively. Thus, for noisy binary data, a threshold model contemplating uncertainty is needed to avoid bias when estimating genetic parameters.

Analysis of Variance↗

PubMedDate not supplied

An alternative perspective: a critical evaluation of the Waddell threshold extrapolation model in chemical carcinogenesis.

In a recent Perspective article (Toxicologic Pathology 31: 260-262, 2003) Waddell asserts that he has developed a log linear extrapolation model that can demonstrate a threshold and resolve for once and for all the uncertainies associated with low dose cancer risk extrapolation. However, his method essentially forces, rather than demonstrates, a threshold, and has many serious flaws that result in significant under-estimation of low dose risk. It would be a serious mistake for the scientific community to adopt Waddell's log linear extrapolation model for chemical carcinogenesis risk assessment.

Animals↗

PubMed1992

Temporomandibular-related pressure thresholds: a model for establishing baselines.

The use of pressure threshold measurement to quantify tender spots and trigger points in muscles is well established. Its application to the field of temporomandibular disorders, however, has been more recent and less widely published. Pressure threshold measurement may be useful to define values for dysfunctional muscles or structures so that changes in muscle condition through a course of treatment can be quantified. Normal values for many muscles in the body have been established, but studies of this type in the masticatory system are limited and have often used a fixed, pre-determined pressure cutoff, rather than measuring thresholds across a number of patients. This pilot study seeks to determine whether normal values exist for the anterior temporalis muscles, the masseter muscles, and the lateral capsules of the temporomandibular joints. Intrarater and interrater reliability in measuring thresholds was also studied with the aim of contributing toward a methodological model for further study.

Adolescent↗

PubMed1982

Genetic models of schizophrenia.

Multiple threshold models of inheritance are applied to a large sample of Franz Kallmann's (1938) pedigree data on schizophrenia. Paranoid and nonparanoid subtypes are represented in the models at different thresholds on a continuum of genetic-environmental liability. Single major locus and multifactorial-polygenic inheritance are ruled out as modes of transmission. These findings suggest that the paranoid-non-paranoid dichotomy cannot be used as a genetic threshold determinant in the population studied.

Gene Frequency↗

PubMed1983

Genetic analysis of manic-depressive illness.

Two threshold models, a single locus model, and two combined models are fitted to data on familial incidence of bipolar affective disorder in 194 nuclear families ascertained through a bipolar proband. The relative fit of alternative transmission models is tested by a likelihood ratio chi-square with the degrees of freedom defined by the difference in the number of parameters estimated by each model. All parameters are estimated by the method of maximum likelihood. The simplest threshold model, permitting only a single background familial correlation, is found to provide a statistically poorer fit than any of the alternative models, and may be rejected as a model for the etiology of bipolar affective disorder. The four remaining models are statistically indistinguishable. It is suggested, however, that the involvement of a major locus in the etiology of this disorder deserves further scrutiny since any of the models incorporating a major locus, with or without a multifactorial background, are consistently associated with greater likelihoods than the complex threshold model. It is also noted that diagnostic criteria are critical in the analysis. In the present study, relatives of probands are considered affected if a diagnosis of bipolar or unipolar affective disorder is present. When only bipolar relatives are considered affected, none of the transmission models may be rejected. Finally, the results of these analyses are found to be independent of the ascertainment parameter.

Biometry↗

PubMed2006

Models for the relationship between ambient temperature and daily mortality.

BACKGROUND: Ambient temperature is an important determinant of daily mortality that is of interest both in its own right and as a confounder of other determinants investigated using time-series regressions, in particular, air pollution. The temperature-mortality relationship is often found to be substantially nonlinear and to persist (but change shape) with increasing lag. We review and extend models for such nonlinear multilag forms. DEVELOPMENT: Popular models for mortality by temperature at given lag include polynomial and natural cubic spline curves, and the simple but more easily interpreted linear thresholds model, comprising linear relationships for temperatures below and above thresholds and a flat middle section. Most published analyses that have allowed the relationship to persist over multiple lags have done so by assuming that spline or threshold models apply to mean temperature in several lag strata (e.g., lags 0-1, 2-6, and 7-13). However, more flexible models are possible, and a modeling framework using products of basis functions ("cross-basis" functions) suggests a wide range, some used previously and some new. These allow for stepped or smooth changes in the model coefficients as lags increase. Applying a range of models to data from London suggest evidence for relationships up to at least 2 weeks' lag, with smooth models fitting best but lag-stratified threshold models allowing the most direct interpretation. CONCLUSIONS: A wide range of multilag nonlinear temperature-mortality relationships can be modeled. More awareness of options should improve investigation of these relationships and help control for confounding by them.

Humans↗