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PubMed1994

Diagnostic tests for deep vein thrombosis. Clinical usefulness depends on probability of disease.

We review the general principles that govern the clinical utility of diagnostic tests, particularly with respect to the diagnosis of deep vein thrombosis (DVT). We stress the importance of clinical probability of disease, which strongly influences the positive predictive value (true-positive rate) and negative predictive value (true-negative rate) of all diagnostic tests. In selecting a diagnostic procedure for DVT, the physician must first consider the clinical probability of disease and then the local accuracy of the test employed and its cost-effectiveness. In 75% to 80% of patients suspected to have DVT, clinical management can be based on the results of noninvasive tests, such as ultrasonography or impedance plethysmography (IPG), rather than venography. Ultrasonography has clear advantages over venography with respect to cost and patient comfort, and it defines the anatomic extent of the thrombus. It should be considered the new diagnostic standard for symptomatic DVT. Despite recent reports of lower sensitivity than previously reported, IPG remains an acceptable alternative to ultrasonography for symptomatic DVT in selected patients. Even if the recently reported lower sensitivity proves to be accurate, the probability of adverse clinical outcomes as a result of overlooked disease is still extremely low in patients with a low probability of DVT. The negative predictive value of IPG under these circumstances approaches 99%. Impedance plethysmography is also useful in patients with a high probability of DVT, in whom the positive predictive value may be as high as 97%. When the findings of IPG (or ultrasonography) are at variance with a strong clinical impression, venography should be considered, especially when there is a high clinical probability of disease and a negative noninvasive test result.

Bias↗

PubMed1993

Evaluation of standard error and confidence interval of estimated multilocus genotype probabilities, and their implications in DNA forensics.

Multilocus genotype probabilities, estimated using the assumption of independent association of alleles within and across loci, are subject to sampling fluctuation, since allele frequencies used in such computations are derived from samples drawn from a population. We derive exact sampling variances of estimated genotype probabilities and provide simple approximation of sampling variances. Computer simulations conducted using real DNA typing data indicate that, while the sampling distribution of estimated genotype probabilities is not symmetric around the point estimate, the confidence interval of estimated (single-locus or multilocus) genotype probabilities can be obtained from the sampling of a logarithmic transformation of the estimated values. This, in turn, allows an examination of heterogeneity of estimators derived from data on different reference populations. Applications of this theory to DNA typing data at VNTR loci suggest that use of different reference population data may yield significantly different estimates. However, significant differences generally occur with rare (less than 1 in 40,000) genotype probabilities. Conservative estimates of five-locus DNA profile probabilities are always less than 1 in 1 million in an individual from the United States, irrespective of the racial/ethnic origin.

Computer Simulation↗

PubMed1996

Evaluation of individual criteria for low probability interpretation of ventilation-perfusion lung scans.

UNLABELLED: The purpose of this investigation was to identify characteristics or combinations of characteristics of the ventilation-perfusion (V/Q) scan in patients with suspected acute pulmonary embolism (PE) can be used for a "very low probability" interpretation ( < 10% positive predictive value). METHODS: Data were culled from individual lungs of 532 patients in the randomized arm of the Prospective Investigation of Pulmonary Embolism Diagnosis (PIOPED) study and 205 patients in the referred arm. All patients had a < 20% consensus probability estimate of PE based on V/Q scan results, and all underwent pulmonary angiography. RESULTS: Nonsegmental perfusion abnormalities, perfusion defects smaller than opacities on the chest radiograph, a combination of these types of perfusion abnormalities, and matched V/Q abnormalities in two or three zones of a single lung had a positive predictive value < 10%. These criteria can therefore be used for a very low probability interpretation. A matched V/Q defect in only one zone of the lung had a positive predictive value greater than 10% and is not a criterion for low probability. Perfusion defects associated with small pleural effusions (obliteration of the costophrenic angle) had a positive predictive value of 25%-33%, depending on the group studied, and are a criterion for intermediate probability. CONCLUSION: Criteria appropriate for a very low probability ( < 10% positive predictive value) interpretation of V/Q scans in patients with suspected acute PE have been identified.

Evaluation Studies as Topic↗

PubMed1995

The 'preclinical phase' of probable Alzheimer's disease. A 13-year prospective study of the Framingham cohort.

OBJECTIVE: To evaluate the interval between the onset of detectable cognitive impairment and clinical diagnosis in individuals with probable Alzheimer's disease (AD), and to identify the pattern of the earliest changes in cognition in probable AD. DESIGN: Longitudinal follow-up of a community-based cohort sample. In 1976 through 1978, a screening neuropsychological examination was administered to Framingham Study participants. These subjects were then followed up prospectively for development of probable AD for up to 13 years. SETTING: This study was conducted at a community-based center for epidemiologic research. PARTICIPANTS: The surveillance sample consisted of 1045 participants in the Framingham Study aged 65 to 88 years who were free of dementia at the time of the neuropsychological screening examination. MAIN OUTCOME MEASURES: Scores on a group of neuropsychological tests were entered into a series of age- and education-adjusted multiple regression procedures, with the presence or absence of probable AD as the outcome variable. RESULTS: Considered individually, most of the screening neuropsychological measures were significantly related to later AD diagnosis. When stepwise regression procedures were employed, only measures of verbal memory and immediate auditory attention span remained significantly related to AD diagnosis. Of note, subjects later diagnosed with probable AD performed at higher levels than normal subjects on the Digit Span test at initial screening. Regression results were essentially unchanged even when the AD sample was restricted to those individuals for whom the screening examination preceded the clinical onset of dementia by 7 years or more. CONCLUSIONS: These findings support previous contentions that a "preclinical phase" of detectable cognitive deficits can precede the clinical diagnosis of probable AD by many years, and they also support the hypothesis that problems with secondary verbal memory are among the first signs of AD.

Aged↗

PubMed1998

Characteristic analysis of the luxG gene encoding the probable flavin reductase that resides in the lux operon of Photobacterium leiognathi.

Nucleotide sequence of the luxG gene (GenBank Accession No. AF053227) from Photobacterium leiognathi PL741 has been determined, and the encoded probable flavin reductase is deduced. The probable flavin reductase encoded by the luxG gene has a calculated M(r) 26,544 and comprises 235 amino acid residues. The probable flavin reductase like the NAD(P)H-flavin reductase might catalyze the reduction of flavins. Alignment and comparison of the probable flavin reductases from P. leiognathi PL741, ATCC 25521, P. phosphoreum, Vibrio fischeri, and V. harveyi show that they are homologous; there is 66% homologous (29.4% identity and 36.6% similarity). Also, the probable flavin reductase is homologous to the NAD(P)H-flavin reductase; it is perceived that the probable flavin reductase and the NAD(P)H-flavin reductase could be enzyme isoforms encoded by two genes of a multigene family for differential response functions. Functional analysis illustrates that the specific segment sequence lay inside and behind the luxG gene might form the potential hairpin loops omega gI, omega gII, omega o, and omega oT as mRNA stability loop or/and as the attenuator-like loop or the dynamic terminator-like block for sub-regulation in the lux operon. The gene order of the luxG gene in the lux operon and the lum operon is <--ter-lumQ-lumP-R&R-luxC-luxD-luxA-luxB-+ ++luxN-luxE-luxG--> (R&R: regulatory region; ter: transcriptional terminator), whereas the R&R is the regulatory region for the lum operon and the lux operon, and ter is the transcriptional terminator for the lum operon.

Amino Acid Sequence↗

PubMed1998

The global turning probability density function for motile bacteria and its applications.

The angular turning probability density distribution for motile bacteria is usually measured in local coordinates and is therefore inconvenient for global analyses of the chemotactic bacterial migration. In this paper we present analytical derivations that convert the local angular turning probability density distribution into a global one. The explicit expression of a reduced global turning probability density function for motile bacteria was derived and its relevant properties were investigated. Depending on the angle variable being intergrated and the integration range, three types of cosine moments were separately defined and studied. Some statistical indices and parameters such as the directional persistence, persistence number, and one-dimensional reversal probability were found to be embedded in the various moments of the reduced global turning probability density function. Applications of the reduced global turning probability and its integrated moments to a three-dimensional cell balance equation in an axisymmetric system were also discussed.

Bacterial Physiological Phenomena↗

PubMed1991

Radiation risk of tissue late effects, a net consequence of probabilities of various cellular responses.

Late effects from the exposure to low doses of ionizing radiation are hardly or not at all observed in man probably due to the low values of risk coefficients that preclude statistical analyses of data from populations that are exposed to doses less than 0.2 Gy. In order to arrive at an assessment of potential risk from radiation exposure in the low dose range, the microdosimetry approach is essential. In the low dose range, ionizing radiation generates particle tracks, mainly electrons, which are distributed rather heterogenously within the exposed tissue. Taking the individual cell as the elemental unit of life, observations and calculations of cellular responses to being hit by energy deposition events from low LET type are analysed. It emerges that besides the probability of a hit cell to sustain a detrimental effect with the consequence of malignant transformation there are probabilities of various adaptive responses that equip the hit cell with a benefit. On the one hand, an improvement of cellular radical detoxification was observed in mouse bone marrow cells; another adaptive response pertaining to improved DNA repair, was reported for human lymphocytes. The improved radical detoxification in mouse bone marrow cells lasts for a period of 5-10 hours and improved DNA repair in human lymphocytes was seen for some 60 hours following acute irradiation. It is speculated that improved radical detoxification and improved DNA repair may reduce the probability of spontaneous carcinogenesis. Thus it is proposed to weigh the probability of detriment for a hit cell within a multicellular system against the probability of benefit through adaptive responses in other hit cells in the same system per radiation exposure. In doing this, the net effect of low doses of low LET radiation in tissue with individual cells being hit by energy deposition events could be zero or even beneficial. Since there was no simple additivity of equal effects from repeated exposures to equal doses and because of the potential effect of adaptive cell responses on the spontaneous evolution of malignancy in tissue, the extrapolation of risk with absorbed dose reaching down to zero, does not appear to be generally valid.

Cell Survival↗

PubMed1984

Fibroblast feeder layers inhibit differentiation of retinoic acid-treated embryonal carcinoma cells by increasing the probability of stem cell renewal.

The appearance of differentiated cells in embryonal carcinoma (EC) cultures can be inhibited by culturing the cells on fibroblast feeder layers. To determine whether or not feeder layers act by increasing the probability of stem cell renewal, growth and differentiation were monitored in cultures of F9 (subclone OTF9 -63) EC cells exposed to retinoic acid (RA) in either the presence or absence of feeder layers. By measuring the fraction of laminin-positive TROMA 1-positive or alkaline phosphatase-negative cells, it was determined that the frequency of differentiated cells in RA-treated F9 cultures was reduced by 70-80% when cells were cultured on fibroblast feeder layers instead of gelatin-coated dishes. Experiments in which EC cells were cultured in close proximity to a feeder layer demonstrated that cell-cell contact was required for maximal inhibition of differentiation. The probability of stem cell renewal was determined by measuring the number of colony-forming cells in RA-treated cultures as a function of time. Analysis of the data demonstrated that the probabilities of stem cell renewal were 0.5 and 0.25 during the first and second 48 h periods, respectively, following addition of RA for cells cultured without feeder layers. Cultures maintained on feeder layers exhibited a stem cell renewal probability of 0.72. Thus, feeder layers reduce the frequency of differentiated cells in RA-treated cultures by increasing the probability of stem cell renewal. Determining the mechanism by which feeder layers counteract the effect of a chemically defined differentiation inducer should help to uncover the processes that regulate the probability of stem cell renewal.

Animals↗

PubMedDate not supplied

ERPs to stimuli requiring response production and inhibition: effects of age, probability and visual noise.

Sixty-six normal adults ranging in age from 20 to 85 years were presented with stimuli containing explicit instructions to initiate or to inhibit a motor response (the words 'push' or 'wait'). In one task, the effect of stimulus probability was investigated by varying probability between 0.25 and 0.75 for both Go and No-go stimuli. In another task, the effect of visual noise was investigated by degrading the stimuli with ampersands on half of the trials. Regression analysis was used to examine the effects of age on P3 amplitude and latency for each stimulus type. The effects of stimulus variables on P3, independent of age, were examined by standardizing each subject's data to those expected for a 20 year old. P3 latency to all stimuli and RT to Go stimuli increased with age. The latency of P3s to No-go stimuli was less sensitive to age than Go stimuli. P3 amplitude at Cz and Pz (but not Fz) diminished with age. P3s to Go stimuli were maximal at Pz and earlier than P3s to No-go stimuli. P3s to No-go stimuli were maximal at Cz. These differences between Go and No-go stimuli remained true under visual noise and probability manipulations. Visual noise prolonged the latency of Go and No-go P3. Less probable Go and No-go stimuli elicited larger and later P3s than more probable stimuli. Decreasing the probability of the No-go stimulus enhanced its central distribution.

Adult↗

PubMed1985

Relationship between lymph nodal status and primary tumor control probability in tumors of the supraglottic larynx.

A retrospective review of 248 patients with squamous cell carcinoma of the supraglottic larynx was undertaken to determine the relationship between the probability of control of the primary lesion, the extent of neck nodal disease at initial presentation, and its ultimate control. All patients were treated at the U.T. M. D. Anderson Hospital between 1960 and 1980, and had a minimum of 3 years follow-up. The primary lesion was staged T1 in 38 patients, T2 in 132, T3 in 50 and T4 in 28. The initial volume of neck nodal disease was scored on a scale of 0 (no palpable nodes) to 9 (bilateral neck nodes greater than 6 cm in diameter). All primary lesions were treated definitively with megavoltage radiation therapy. Treatment to the neck varied according to the extent of lymph node involvement. There was no significant difference in the range of total radiation doses delivered to the primary lesion, stage for stage, in patients who presented with clinically negative or positive nodes, or in those with controlled versus uncontrolled neck disease. Analysis of the probability of primary tumor control was made by life table methods because of the poorer survival expectation in node positive patients. For T1 and T2 primary lesions, any positive node decreased the probability of primary tumor control (p = 0.06). For T3 and T4 lesions, a single node less than 3 cm in diameter did not worsen the chance of primary tumor control, but any greater degree of lymph node involvement did (p = 0.03). For both T stage groupings, the probability of primary tumor control at 5 years decreased progressively with increasing neck nodal disease. Primary tumor control probability was also significantly associated with control of the neck disease, independent of the modality of neck treatment. No correlation could be demonstrated between the histological grade of the primary tumor and initial lymph node status or tumor control probability. Possible interpretations of this manifestation of biological heterogeneity are discussed.

Biopsy↗

PubMed1998

Predicting probabilities of pregnancy and multiple gestation from in vitro fertilization--a new model.

OBJECTIVE: To develop a statistical model that adjusts for variation between patients and adequately predicts the observed distribution of pregnancies among singletons and multiple gestations of various orders. METHODS: All in vitro fertilization (IVF) cycles from the inception of the IVF program at Women and Infants' Hospital on May 26, 1988, until December 31, 1993, were evaluated using logistic regression in selected subsets. RESULTS: A new cycle-one specific model uses three different probabilities: P1, the probability of pregnancy (predicted by age and total embryo score); P2/P1, the conditional probability of finding a second implantation in those who had become pregnant with at least one (predicted by total embryo score); and P3/P2, the conditional probability of finding a third implantation in those who had become pregnant with at least two (with no significant predictors). This is the first model to use these three adjusted probabilities. CONCLUSION: P1 increases with increasing total embryo score but decreases with increasing age. P2/P1 increases with increasing total embryo score but does not depend on age. Embryo scoring is useful because the total embryo score is a better predictor of P1 and P2/P1 than the number of embryos alone. By using patient-specific information (age and total embryo score) and cycle-specific tables, an estimate of the probability of pregnancy and multiple gestation can be provided before embryo transfer.

Adult↗

PubMed1997

Survival chance in papillary thyroid cancer in Hungary: individual survival probability estimation using the Markov method.

PURPOSE: The typically benign, but occasionally rapidly fatal clinical course of papillary thyroid cancer has raised the need for individual survival probability estimation, to tailor the treatment strategy exclusively to a given patient. MATERIALS AND METHODS: A retrospective study was performed on 400 papillary thyroid cancer patients with a median follow-up time of 7.1 years to establish a clinical database for uni- and multivariate analysis of the prognostic factors related to survival (Kaplan-Meier product limit method and Cox regression). For a more precise prognosis estimation, the effect of the most important clinical events were then investigated on the basis of a Markov renewal model. The basic concept of this approach is that each patient has an individual disease course which (besides the initial clinical categories) is affected by special events, e.g. internal covariates (local/regional/distant relapses). On the supposition that these events and the cause-specific death are influenced by the same biological processes, the parameters of transient survival probability characterizing the speed of the course of the disease for each clinical event and their sequence were determined. The individual survival curves for each patient were calculated by using these parameters and the independent significant clinical variables selected from multivariate studies, summation of which resulted in a mean cause-specific survival function valid for the entire group. On the basis of this Markov model, prediction of the cause-specific survival probability is possible for extrastudy cases, if it is supposed that the clinical events occur within new patients in the same manner and with the similar probability as within the study population. RESULTS: The patient's age, a distant metastasis at presentation, the extent of the surgical intervention, the primary tumor size and extent (pT), the external irradiation dosage and the degree of TSH suppression proved to be statistically significant and independent prognostic factors with regard to cause-specific survival in multivariate studies. During follow-up, 14, 14, 9 and 12% of the patients underwent local/regional/distant relapses or thyroid cancer-related death, respectively. Through use of the above six independent clinical variables and the parameters relating to the four clinical events and their interrelations, mean cause-specific survival probabilities of 88, 83 and 78% were determined at 10, 20 and 30 years, respectively. The survival-predicting software (PATHYPRE) written on the basis of the biostatistical model is available through Internet connections on the home page of the National Institute of Oncology, Budapest (www.oncol.hu). CONCLUSION: Prediction of the individual survival probability for extrastudy cases affords a rationale for individualization of the treatment of papillary thyroid cancer patients.

Adolescent↗

PubMed1990

Exact computation of pattern probabilities in random sequences generated by Markov chains.

Observed patterns in macromolecular sequences are often considered as words and compared with their probabilities of occurring in random sequences. Calculation of these probabilities, however, often lacks rigour. We have developed an algorithm for exact computation of such probabilities for stochastic sequences that follow a Markov chain model. The method is applicable to the case that a random sequence contains one out of two given patterns P and Q, or both simultaneously. Another application yields the probability function P(x) that a sequence contains pattern P exactly x times. An application to patterns that include wild-card characters yields probabilities for homonucleotide clusters of a given length. We prove the probability of multiple runs of single nucleotides in the SV40 genome to be in accordance with the dinucleotide composition of the sequence, although it is in conflict with mononucleotide composition.

Algorithms↗

PubMed1989

The probability of quantal secretion at release sites in different calcium concentrations in toad (Bufo marinus) muscle.

1. The number of quanta secreted from visualized release sites along terminal branches at toad (Bufo marinus) neuromuscular junctions in different extracellular concentrations of calcium ions. [Ca2+]o, and during facilitation was determined. Terminal branches were visualized by prior staining with the fluorescent dye, 3-3 diethyloxardicarbocyanine iodide (DiOC2(5)). 2. Increasing [Ca2+]o between 0.25 and 0.4 mM gave a similar proportional increase in the mean quantal content of the end-plate potential recorded with an extracellular electrode (me) at all sites along terminal branches. Thus the length constant for the experimental decline in me along terminal branches (the quantal length constant) remained constant with an increase in [Ca2+]o. The increase in m with [Ca2+]o followed a fourth power relation at both proximal and distal release sites. 3. The increase in me with [Ca2+]o was almost entirely due to an increase in the binomial probability for secretion, pe, which increased as the third to fourth power of [Ca2+]o. However, at higher [Ca2+]o there was an increasing tendency for the binomial parameter ne to increase. It is shown that when ne increases by about 1 there is very little change in pe, suggesting that the new release site recruited at high [Ca2+]o has a relatively low probability for secretion. 4. Test impulses gave a similar proportional increase in me following a conditioning impulse at all sites along terminal branches. The quantal length constant remained constant for both conditioning and test values of me. The increase in me for the test impulse increased linearly with an increase in me for the conditioning impulse at all release sites. 5. Facilitation of me declined exponentially with an increase in the test-conditioning interval. The time constant for this decline (30-40 ms) was similar at both proximal and distal release sites. Changes in facilitation of me were almost entirely due to changes in pe except at very short test-conditioning intervals of about 10 ms. At these intervals ne frequently increased by about 1 and there was very little change in pe. Again, this suggests that additional release sites recruited at short intervals have relatively low probability for secretion. 6. The results indicate that relatively low probability release sites exist in close juxtaposition to relatively high probability release sites which themselves decline in probability along the length of terminal branches.

Animals↗

PubMedDate not supplied

Relation of physicians' predicted probabilities of pneumonia to their utilities for ordering chest x-rays to detect pneumonia.

To investigate the relation between physicians' predicted probabilities of pneumonia and their utilities for ordering chest x-rays to detect pneumonia, the authors studied 52 physicians who ordered chest x-rays of 886 patients presenting to an emergency department with fever or respiratory complaints. Physicians estimated the probability of pneumonia prior to obtaining the results of the chest x-ray. Utilities were assessed by asking physicians to consider a hypothetical patient presenting with acute respiratory symptoms, with unknown chest x-ray status, and to rank on a scale from +50 ("best thing I could do") to -50 ("worst thing I could do") their rating scale utilities for not diagnosing pneumonia and not ordering a chest x-ray when the patient had pneumonia (i.e., missing a pneumonia), and for diagnosing pneumonia and ordering a chest x-ray when the patient did not have pneumonia (i.e., ordering an unnecessary x-ray). The utility for ordering an unnecessary x-ray was negatively correlated with average predicted probability (r = -0.1495, p = 0.29), whereas the utility for missing a pneumonia was positively correlated with average predicted probability (r = 0.2254, p = 0.11), although the correlations were not statistically significant. Relative chagrin, defined as the difference in these utilities, was significantly inversely correlated with average predicted probability (r = -0.2992, p less than 0.035), even after adjusting for the prevalence of pneumonia seen by each physician (partial r = -0.42, p less than 0.0027). It is concluded that physicians who experienced greater regret over missing a pneumonia than over ordering an unnecessary x-ray estimated lower probabilities of pneumonia for patients for whom they ordered x-rays.(ABSTRACT TRUNCATED AT 250 WORDS)

Cost-Benefit Analysis↗

PubMed1998

Effects of signal probability on individual differences in vigilance.

Decrements in the proportion of signals detected over time on task and large individual differences in performance are typical findings in studies of vigilance. This study investigates the effects of signal probability on individual differences in vigilance performance. Participants monitored stimulus events on computer displays over 2-h periods at three signal probability levels (.01, .04, & .12). Results were analyzed between groups, within groups, and within subjects. Detection decrements were found to be inversely related to signal probability levels across groups. High signal probabilities generated consistent within-group and within-subject performance, whereas low probabilities generated both lower performance and larger within-subject variance. This relationship between signal probability and within-group and within-subject variance has not been previously demonstrated. Future investigations should focus on the sources of both between-subjects and within-subject variation in vigilance performance in order to identify optimal interventions. Actual or potential applications include designing work to minimize vigilance decrement and maximize human performance under conditions that require sustained attention.

Analysis of Variance↗

PubMed1989

Intuitive reasoning about probability: theoretical and experimental analyses of the "problem of three prisoners".

Among various Bayesian problems of probability, the "problem of three prisoners" (Lindley, 1971; Mosteller, 1965) is an especially good example which illustrates the drastic discrepancy between intuitive reasoning and mathematical formal reasoning about probability. In particular, it raises intriguing questions concerning the mathematical and cognitive relevance of factors such as prior probabilities and the context in which certain information is given. In the current paper, we report a new version of the problem which turned out to be even more counterintuitive. This new version was also designed so that different inferential schemes would lead to separate estimates of posterior probability. The data obtained from questionnaires and theoretical analyses of the original and modified problems suggest that: (1) The psychological processes of intuitive reasoning are qualitatively different from mathematical reasoning. (2) The tendency to neglect prior probabilities (Tversky & Kahneman, 1974, 1982) is not always the critical factor for illusory judgments. (3) Intuitive judgments can be categorized by several, distinctive propositional beliefs from which the judgments are apparently derived. We call these prototypical, crude beliefs "subjective theorems," and discuss their nature and roles in the current paper.

Adult↗

PubMed1994

Root probabilities for intraspecific gene trees under neutral coalescent theory.

The rooting of intraspecific gene or haplotype trees has proven to be difficult using the traditional techniques of rooting species trees such as outgroups. As an alternative, we apply neutral coalescent theory to the problems of determining the root of an intraspecific gene tree and the relative ages of the haplotypes. By using a recursive equation, exact root probabilities can be calculated for small cladograms and sample sizes. These exact probabilities indicate that root probabilities are not very sensitive to the parameter theta, which is four times the mutation rate times the inbreeding effective size. The exact probabilities also indicate that root probabilities are not very sensitive to the absolute numbers of each haplotype (allele) class, only their relative proportions. The exact method, unfortunately, is not feasible for implementation with larger data sets with present algorithms and computers. However, the exact results suggested a simple heuristic for determining outgroup weights; that is, finding the haplotype that is the oldest in the sample and that can serve as an outgroup for the remainder of the haplotype tree. Computer simulations revealed that these outgroup weights are strongly correlated with actual age and are much better indicators of haplotype age than is the haplotype frequency, another commonly used indicator of relative age.

Gene Frequency↗