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Estimation of the day-specific probabilities of conception: current state of the knowledge and the relevance for epidemiological research.

Conception, as defined by the fertilisation of an ovum by a sperm, marks the beginning of human development. Currently, a biomarker of conception is not available; as conception occurs shortly after ovulation, the latter can be used as a proxy for the time of conception. In the absence of serial ultrasound examinations, ovulation cannot be readily visualised leaving researchers to rely on proxy measures of ovulation that are subject to error. The most commonly used proxy measures include: charting basal body temperature, monitoring cervical mucus, and measuring urinary metabolites of oestradiol and luteinising hormone. Establishing the timing of the ovulation and the fertile window has practical utility in that it will assist couples in appropriately timing intercourse to achieve or avoid pregnancy. Identifying the likely day of conception is clinically relevant because it has the potential to facilitate more accurate pregnancy dating, thereby reducing the iatrogenic risks associated with uncertain gestation. Using data from prospective studies of couples attempting to conceive, several researchers have developed models for estimating the day-specific probabilities of conception. Elucidating these will allow researchers to more accurately estimate the day of conception, thus spawning research initiatives that will expand our current limited knowledge about the effect of exposures at critical periconceptional windows. While basal body temperature charting and cervical mucus monitoring have been used with success in field-based studies for many years, recent advances in science and technology have made it possible for women to get instant feedback regarding their daily fertility status by monitoring urinary metabolites of reproductive hormones in the privacy of their own homes. Not only are innovations such as luteinising hormone test kits and digital fertility monitors likely to increase study compliance and participation rates, they provide valuable prospective data that can be used in epidemiological research. Although we have made great strides in estimating the timing and length of the fertile window, more work is needed to elucidate the day-specific probabilities of conception using proxy measures of ovulation that are inherently subject to error. Modelling approaches that incorporate the use of multiple markers of ovulation offer great promise to fill these important data gaps.

Biomarkers↗

The use of probability trees in genetic counselling.

Calculation of genetic risks of persons who may be carriers of X-linked recessive conditions or autosomal dominant diseases with incomplete or delayed penetrance often requires the use of Bayes' theorem. Available methods of computing such risks are often too difficult or too time-consuming for clinicians to use routinely. Probability trees provide a rapid and simple graphical means of estimating genetic risks even in complex clinical situations. The use of probability trees is easily learned because the logic upon which they are based is inherent in their structure.

Adult↗

Determination of the relative probability for prostate cancer to avoid unnecessary biopsy.

BACKGROUND: To investigate whether using a new concept of relative probability for prostate cancer (RPpca) can increase sensitivity and specificity in detecting prostate cancer. METHODS: For 217 patients with total prostate-specific antigen (PSA) level of 4-20 ng/mL, prostate volume and free to total PSA (F/T) ratio were measured. From the fitted curves between positive predictive values for prostate cancer and age, prostate volume, total PSA or the F/T ratio, each function predicting prostate cancer was determined. RPpca defined by the combined functions of age, prostate volume, total PSA and F/T ratio was calculated for each individual patient. The probability of prostate cancer was also calculated, using logistic regression analysis (LRPpca). Receiver-operating characteristic analysis was performed to elucidate the areas under the curve (AUC), sensitivities and specificities and cutoff values of the conventional and new parameters. Finally, we investigated the applicability of the above parameters in the other patient group using a different PSA assay kit (AxSYM). RESULTS: Although RPpca had the largest AUC in the total PSA range of 4-20 ng/mL, it did not reach statistical significance between RPpca and F/T ratio or LRPpca. The cutoff values of F/T ratio, LRPpca and RPpca were determined as 0.15, 0.12 and 0.20, respectively. Using these cutoff values in AxSYM data, RPpca had the highest sensitivity (91%) and specificity (57%). CONCLUSIONS: RPpca can provide more precise information to avoid unnecessary biopsy than LRPpca or F/T ratio. RPpca could be valuable to decide whether to perform prostate biopsy when using various PSA kits.

Adult↗

The use of matrices in calculating mendelian probabilities.

It is shown that the method of calculation of probabilities for genetic counselling developed by Bolling, Chase and Murphy can be generalized to give the relative probabilities for any single individual in any pedigree for any mendelian condition. The calculations only require matrix multiplications (of one kind or another), and the expressions can be written down and evaluated directly, whether by hand or by computer.

Female↗

Recursive descent probabilities for rare recessive lethals.

Recursively computed descent probabilities provide an effective way to evaluate possible ancestries of rare alleles segregating in large and complex genealogies, but they ignore information other than the descent to a small set of current gene copies. We show how descent probability computations can be modified to incorporate the fact that no ancestor can be affected by a lethal recessive trait. This methodology is applied to two rare recessive traits segregating in a complex Hutterite (Lehrerleut) genealogy.

Alleles↗

Probability-independent and -dependent ERPs reflecting visual change detection.

In ERP studies, two posterior components with different polarities have been identified as ERP correlates of visual change detection. To compare these components in terms of sensitivity to the preceding stimulus sequence, two peripheral stimuli of different colors (red and blue) were presented with equal (50:50) or different probabilities (20:80 or 80:20), while 12 participants performed shape discrimination at a central location. A posterior positivity at around 90-140 ms was observed with similar amplitude to all stimuli immediately preceded by a different stimulus. In contrast, a posterior negativity at around 140-180 ms was observed to increase in amplitude with increasing number of preceding different stimuli. These results suggest the existence of probability-independent and -dependent change processing in the human visual system. The functional significance is discussed in terms of memory-based comparison and stimulus-specific refractoriness.

Adult↗

Probability of liver cancer and survival in HCV-related or alcoholic-decompensated cirrhosis. A study of 377 patients.

BACKGROUND: Although chronic alcohol intake and chronic hepatitis C may progress to cirrhosis and hepatocellular carcinoma (HCC), few data are available about survival and probability of developing HCC in decompensated cirrhosis of both aetiologies. METHODS: This study identified factors related with probability of developing HCC and survival in a cohort of 377 consecutive patients with decompensated HCV-related cirrhosis (200 cases) or alcoholic cirrhosis (177 cases) without known HCC, hospitalized for their first hepatic decompensation, as well as to evaluate differences between both aetiologies. Patients were followed for a mean period of 39 +/- 2 months. RESULTS: During follow-up, 42 patients (11.1%) developed HCC (16.5% vs 5.1%) in groups HCV and alcohol, respectively; p = 0.0008), and 131 patients (34.7%) died (42% vs 26.6% in groups HCV and alcohol, respectively; p = 0.002). Age and HCV-cirrhosis were independently related to HCC development, while baseline age and Child-Turcotte-Pugh score were independently correlated with survival. CONCLUSION: Survival in decompensated HCV-related or alcoholic cirrhosis is influenced by age and baseline Child-Turcotte-Pugh score, without differences in cirrhosis aetiology. The risk of developing HCC is greater in HCV-related cirrhosis than in alcoholic cirrhosis.

Age Distribution↗

Estimating the probability of a blood donation adverse event based on 1000 interviewed whole-blood donors.

BACKGROUND: Estimating the probability that a donor will have or not have an adverse event is useful for staff knowledge to give blood donors reassurance upon request. STUDY DESIGN AND METHODS: One-thousand donors from the general donor pool were interviewed for seven potential adverse events 3 weeks after a 525-mL whole-blood phlebotomy. The four most common adverse events were bruise (22.7%), sore arm (10.0%), fatigue (7.8%), and donor reaction (7.0%). A stepwise logistic regression analysis was performed based on five donor characteristics that were studied: age, weight, sex, race, and first-time donor status. The contribution of each significant or marginally significant factor to each adverse event was quantified. RESULTS: For donor reaction, weight (p < 0.0001) and age (p = 0.015) were significant contributors, and first-time donor status (p = 0.054) was a marginally significant contributor. An equation was derived, and the donor reaction rate can be estimated for a group based on the donor's weight, age, and first-time donor status. Similar analyses were performed for fatigue, sore arm, and bruise. CONCLUSION: Based on the derived formulas and with the use of a spreadsheet, data can be entered and the probability that a donor will have (or not have) a donor reaction, fatigue, sore arm, or bruise can be estimated.

Adult↗

Clinical trials with velnacrine: (PROPP) the physician reference of predicted probabilities--a statistical model for the estimation of hepatotoxicity risk with velnacrine maleate.

Safety observations during the clinical development of Mentane (velnacrine maleate) have included the occurrence of generally asymptomatic liver enzyme elevations confined to patients with Alzheimer's disease (AD). The clinical presentation of this reversible hepatocellular injury is analogous to that reported for tetrahydroaminoacridine (THA). Direct liver injury, possibly associated with the production of a toxic metabolite, would be consistent with reports of aberrant xenobiotic metabolism in Alzheimer's disease patients. Since a patient related aberration in drug metabolism was suspected, a biostatistical strategy was developed with the objective of predicting hepatotoxicity in individual patients prior to exposure to velnacrine maleate. The method used logistic regression techniques with variable selection restricted to those items which could be routinely and inexpensively accessed at screen evaluation for potential candidates for treatment. The model was to be predictive (a marker for eventual hepatotoxicity) rather than a causative model, and techniques employed "goodness of fit", percentage correct, and positive and negative predictive values. On the basis of demographic and baseline laboratory data from 942 patients, the PROPP statistic was developed (the Physician Reference Of Predicted Probabilities). Main effect variables included age, gender, and nine hematological and serum chemistry variables. The sensitivity of the current model is approximately 49%, specificity approximately 88%. Using prior probability estimates, however, in which the patient's likelihood of liver toxicity is presumed to be at least 30%, the positive predictive value ranged between 64-77%. Although the clinical utility of this statistic will require refinements and additional prospective confirmation, its potential existence speaks to the possibility of markers for idiosyncratic drug metabolism in patients with Alzheimer's disease.

Age Factors↗

Estimating background and threshold nitrate concentrations using probability graphs.

Because of the ubiquitous nature of anthropogenic nitrate (NO3(-)) in many parts of the world, determining background concentrations of NO3(-) in shallow ground water from natural sources is probably impossible in most environments. Present-day background must now include diffuse sources of NO3(-) such as disruption of soils and oxidation of organic matter, and atmospheric inputs from products of combustion and evaporation of ammonia from fertilizer and livestock waste. Anomalies can be defined as NO3(-) derived from nitrogen (N) inputs to the environment from anthropogenic activities, including synthetic fertilizers, livestock waste, and septic effluent. Cumulative probability graphs were used to identify threshold concentrations separating background and anomalous NO(3)-N concentrations and to assist in the determination of sources of N contamination for 232 spring water samples and 200 well water samples from karst aquifers. Thresholds were 0.4, 2.5, and 6.7 mg/L for spring water samples, and 0.1, 2.1, and 17 mg/L for well water samples. The 0.4 and 0.1 mg/L values are assumed to represent thresholds for present-day precipitation. Thresholds at 2.5 and 2.1 mg/L are interpreted to represent present-day background concentrations of NO(3)-N. The population of spring water samples with concentrations between 2.5 and 6.7 mg/L represents an amalgam of all sources of NO3(-) in the ground water basins that feed each spring; concentrations > 6.7 mg/L were typically samples collected soon after springtime application of synthetic fertilizer. The 17 mg/L threshold (adjusted to 15 mg/L) for well water samples is interpreted as the level above which livestock wastes dominate the N sources.

Analysis of Variance↗

CAN'T MISS--conquer any number task by making important statistics simple. Part 2. Probability, populations, samples, and normal distributions.

Healthcare quality improvement professionals need to understand and use inferential statistics to interpret sample data from their organizations. In quality improvement and healthcare research studies all the data from a population often are not available, so investigators take samples and make inferences about the population by using inferential statistics. This three-part series will give readers an understanding of the concepts of inferential statistics as well as the specific tools for calculating confidence intervals for samples of data. This article, Part 2, describes probability, populations, and samples. The uses of descriptive and inferential statistics are outlined. The article also discusses the properties and probability of normal distributions, including the standard normal distribution.

Data Interpretation, Statistical↗

An analysis of the relationship between radiosensitivity and volume effects in tumor control probability modeling.

The dependence of local tumor control probability (tcp) on tumor volume is analyzed and discussed with the help of radiobiological modeling; in particular the impact of possible correlations between mean tumor radiosensitivity and tumor dimensions on the tcp volume dependence is explored. The linear-quadratic Poissonian tumor control probability (tcp) model was modified to account for the possible dependence of clonogenic cell density and radiosensitivity parameters on tumor volume; then the original and modified versions of the model were fitted to published clinical and laboratory tumor control data. These different versions of the tcp model often fitted tumor control data equally well, because of the high degree of correlation between the parameters. Nevertheless the results were very different from a physical point of view and we suggest that sometimes it is possible to choose between equally good fits on the basis of physical considerations. Possible links between the volume dependence of the mean radiosensitivity and the degree of tumor hypoxia were also analyzed through a comparison of the results of the tcp fit to published measurements of oxygen tension in tumors.

Animals↗

Probability distributions for locations of calling animals, receivers, sound speeds, winds, and data from travel time differences.

A new nonlinear sequential Monte Carlo technique is used to estimate posterior probability distributions for the location of a calling animal, the locations of acoustic receivers, sound speeds, winds, and the differences in sonic travel time between pairs of receivers from measurements of those differences, while adopting realistic prior distributions of the variables. Other algorithms in the literature appear to be too inefficient to yield distributions for this large number of variables (up to 41) without recourse to a linear approximation. The new technique overcomes the computational inefficiency of other algorithms because it does not sequentially propagate the joint probability distribution of the variables between adjacent data. Instead, the lower and upper bounds of the distributions are propagated. The technique is applied to commonly encountered problems that were previously intractable such as estimating how accurately sound speed and poorly known initial locations of receivers can be estimated from the differences in sonic travel time from calling animals, while explicitly modeling distributions of all the variables in the problem. In both cases, the new technique yields one or two orders of magnitude improvements compared with initial uncertainties. The technique is suitable for accurately estimating receiver locations from animal calls.

Air↗

High-probability uniquantal transmission at excitatory synapses in barrel cortex.

The number of vesicles released at excitatory synapses and the number of release sites per synaptic connection are key determinants of information processing in the cortex, yet they remain uncertain. Here we show that the number of functional release sites and the number of anatomically identified synaptic contacts are equal at connections between spiny stellate and pyramidal cells in rat barrel cortex. Moreover, our results indicate that the amount of transmitter released per synaptic contact is independent of release probability and the intrinsic release probability is high. These properties suggest that connections between layer 4 and layer 2/3 are tuned for reliable transmission of spatially distributed, timing-based signals.

Action Potentials↗

On the probability of matching DNA fingerprints.

Forensic scientists commonly assume that DNA fingerprint patterns are infrequent in the general population and that genotypes are independent across loci. To test these assumptions, the number of matching DNA patterns in two large databases from the Federal Bureau of Investigation (FBI) and from Lifecodes was determined. No deviation from independence across loci in either database was apparent. For the Lifecodes database, the probability of a three-locus match ranges from 1 in 6,233 in Caucasians to 1 in 119,889 in Blacks. When considering all trios of five loci in the FBI database, there was only a single match observed out of more than 7.6 million comparisons. If independence is assumed, the probability of a five-locus match ranged from 1.32 x 10(-12) in Southeast Hispanics to 5.59 x 10(-14) in Blacks, implying that the minimum number of possible patterns for each ethnic group is several orders of magnitude greater than their corresponding population sizes in the United States. The most common five-locus pattern can have a frequency no greater than about 10(-6). Hence, individual five-locus DNA profiles are extremely uncommon, if not unique.

Black People↗

Computation of most probable numbers.

A rapid computational method for maximum likelihood estimation of most-probable-number values, incorporating a modified Newton-Raphson method, is presented. The method offers a much greater reliability for the most-probable-number estimate of total viable bacteria, i.e., those capable of growth in laboratory media.

Bacteria↗

Analysis of sample preparation procedures for enumerating fecal coliforms in coarse southwestern U.S. bottom sediments by the most-probable-number method.

The determination of bacterial densities in aquatic sediments generally requires that a dilution-mixing treatment be used before enumeration of organisms by the most-probable-number fermentation tube method can be done. Differential sediment and organism settling rates may, however, influence the distribution of the microbial population after the dilution-mixing process, resulting in biased bacterial density estimates. For standardization of sample preparation procedures, the influence of settling by suspended sediments on the fecal coliform distribution in a mixing vessel was examined. This was accomplished with both inoculated (Escherichia coli) and raw, uninoculated freshwater sediments from Saguaro Lake, Ariz. Both test sediments were coarse (greater than 90% gravel and sand). Coarse sediments are typical of southwestern U.S. lakes. The distribution of fecal coliforms, as determined by the most-probable-number method, was not significantly influenced by sediment settling and remained homogenous over a 16-min postmix period. The technique developed for coarse sediments may be useful for standardizing sample preparation techniques for other sediment types.

Bacteriological Techniques↗

Probability of recovering pathogenic Escherichia coli from foods.

The probability of recovering pathogenic Escherichia coli from food by the Bacteriological Analytical Manual method was determined by the effects of several factors: the number of strains per food, the ability of pathogenic strains to survive enrichment, and the frequency of plasmid loss during enrichment. Biochemical patterns indicated the presence of about six E. coli strains per food sample. About half of the strains isolated from humans did not survive enrichment. Among those which grew, plasmid loss, as determined by gel electrophoresis and DNA colony hybridization, ranged from 20 to 95%. The combined effects of failure to survive enrichment and plasmid loss decreased the relative numbers of these strains and reduced the chance of detecting pathogens. To counteract this tendency and obtain a 90 to 95% probability off recovering a given pathogenic strain, 40 to 50 colonies per food sample should be picked during the routine testing of foods.

Anti-Bacterial Agents↗