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PubMed2005

Comprehensive algorithm for quantitative real-time polymerase chain reaction.

Quantitative real-time polymerase chain reactions (qRT-PCR) have become the method of choice for rapid, sensitive, quantitative comparison of RNA transcript abundance. Useful data from this method depend on fitting data to theoretical curves that allow computation of mRNA levels. Calculating accurate mRNA levels requires important parameters such as reaction efficiency and the fractional cycle number at threshold (CT) to be used; however, many algorithms currently in use estimate these important parameters. Here we describe an objective method for quantifying qRT-PCR results using calculations based on the kinetics of individual PCR reactions without the need of the standard curve, independent of any assumptions or subjective judgments which allow direct calculation of efficiency and CT. We use a four-parameter logistic model to fit the raw fluorescence data as a function of PCR cycles to identify the exponential phase of the reaction. Next, we use a three-parameter simple exponent model to fit the exponential phase using an iterative nonlinear regression algorithm. Within the exponential portion of the curve, our technique automatically identifies candidate regression values using the P-value of regression and then uses a weighted average to compute a final efficiency for quantification. For CT determination, we chose the first positive second derivative maximum from the logistic model. This algorithm provides an objective and noise-resistant method for quantification of qRT-PCR results that is independent of the specific equipment used to perform PCR reactions.

Algorithms↗
PubMed2006

Optimal crossover designs for logistic regression models in pharmacodynamics.

Pharmacodynamics (PD) is the study of the biochemical and physiological effects of drugs. The construction of optimal designs for dose-ranging trials with multiple periods is considered in this paper, where the outcome of the trial (the effect of the drug) is considered to be a binary response: the success or failure of a drug to bring about a particular change in the subject after a given amount of time. The carryover effect of each dose from one period to the next is assumed to be proportional to the direct effect. It is shown for a logistic regression model that the efficiency of optimal parallel (single-period) or crossover (two-period) design is substantially greater than a balanced design. The optimal designs are also shown to be robust to misspecification of the value of the parameters. Finally, the parallel and crossover designs are combined to provide the experimenter with greater flexibility.

Algorithms↗
PubMed1998

Application of logistic growth model to pharmacodynamic analysis of in vitro bactericidal kinetics.

A new pharmacodynamic model for the analysis of in vitro bactericidal kinetics was developed based on the logistic growth model, with the bacterial phases divided into two compartments. The model equations are expressed as nonlinear simultaneous differential equations, and the Runge-Kutta-Gill method was adopted to numerically solve the equations in both the simulation and the least squares curve-fitting procedures. The model can describe the initial killing and the regrowth phases and can explain the nonlinear dependence of the killing rate on the drug concentration. The model can also explain the plateau in the bacterial growth curve that is often observed in in vitro experiments. The model was applied to analysis of the in vitro time-killing data of beta-lactam antibiotics, S-4661, meropenem, imipenem, cefpirome, and ceftazidim against three types of bacteria, Escherichia coli, Pseudomonas aeruginosa, and Staphylococcus aureus. The results of curve-fitting using the least squares program MULTI (Runge) showed good fits for all types of drugs and bacteria. The relationship between the characteristics of the drug-bacteria interactions and the estimated pharmacodynamic parameters is discussed.

Anti-Bacterial Agents↗
PubMed2004

Apolipoprotein E genotype frequency patterns in aged Danes as revealed by logistic regression models.

Although the ApoE gene has been intensively studied in aging research, most of the studies conducted so far have been based on the traditional case-control design with subjects consisting of young controls and long-lived cases. The genotype frequency pattern in and between the two age-groups has been rarely investigated due to limitations in either research design or data analytical method. In this study, we genotyped 748 individuals (including both twin pairs and unrelated individuals) aged from 73 to 95 with aim at examining the genotype frequency trajectory of ApoE gene at high ages. Binomial and multinomial logistic regression models have been applied to model the gene frequency as a function of age and to investigate the modes of gene function (dominant, recessive, additive). The generalized estimation equations (GEEs) are introduced to account for the intra-pair genotype correlation in the twin pairs included in the data. Both the observed and the fitted frequencies show a constantly declining pattern of ApoE epsilon4 allele as age advances indicating a significant and steadily deleterious effect of the dominant allele that increases the hazard of death at high ages.

Aged↗
PubMedDate not supplied

[Analysis of mortality and relative prognostic factors in general surgery: use of the multiple logistic regression model].

Surgical risk is defined as the occurrence of complications arising in the individual as a result of surgical stress. The ability to forecast these consequences is an important factor in determining decision taken by surgeon. Several attempts have been made to quantify postsurgical prospects but up till now no overall solution has been found. This paper attempts to define a multifactorial risk index for adults subjected to surgery, with respect to immediate and early per- and post-surgical complications. 1182 adult patients, 14 yrs or more, surgically treated not for urgency during 1985 in six Italian centres, were prospectively studied in order to derive a multivariate prognostic index of after surgery mortality. Stepwise logistic regression model was applied to a set of preoperative and operative factors, five of which were found significantly correlate with death: nutritional status, renal failure, reintervention, bacterial contamination during surgery, age greater than 70 years. Thus, from regression coefficients, scores were derived for modalities of significant variables, allowing to build four classes of risk patients: low (less than 1%), medium (between 1% and 10%), high (between 10% and 50%), extremely high risk (greater than 50%).

Adolescent↗
PubMed1991

[Evaluation of a logistic regression model in predicting the prognosis of Graves' disease treated by antithyroid drugs].

One hundred and twelve new cases of Graves' disease were treated by tapazole for 6 months and followed up for another 12 months. The initial dose was 30 mg/d. Clinical and biochemical euthyroidism was achieved within 1 to 3 months, then a maintenance was given until cessation of drugs at 6 months. One hundred and eleven cases completed the study. Remission and relapse were defined at the end of follow-up for 1 year according to the presence or absence of clinical manifestation of hyperthyroidism and the levels of T3 and T4. The results of the 12-month follow-up showed that 46 of 111 cases were in remission, and the remaining 65 cases suffered relapse. A logistic regression model with 4 variables was established, which included thyroid suppression rate and goitre size by palpation at the end of drug treatment, the level of T3 before therapy, and the patients' age. The model had 81.5% sensitivity, 84.8% specificity and 82.9% (92/111) accuracy in predicting the outcome of Graves' disease after withdrawal of drug for 1 year. The results were much better than any other univariate analysis in this study.

Adolescent↗
PubMed1988

Evaluating the discriminatory power of a multiple logistic regression model.

Various measures for estimating the goodness-of-fit of the multiple logistic regression (MLR) model have been suggested, although there is no clear consensus as to which measure is most suitable. In this paper, a simple measure of the discriminatory power of the fitted MLR model, based on maximization of Youden's J index (J*), is proposed and compared with several goodness-of-fit statistics described previously. The relative effectiveness of the measure is illustrated using data from the Lipid Research Clinics Prevalence Study. It is suggested that J* may be a useful alternative index of goodness-of-fit of an MLR model, with the added advantage of having a simple practical interpretation.

Adult↗
PubMed2006

Characterization of Holstein heifer fertility in the United States.

The overall object of this research was to characterize US Holstein (virgin) heifer fertility. This included investigation of factors influencing heifer fertility and estimation of heritability, as well as correlations with cow fertility and first-lactation milk yield. A secondary objective was to compare linear and logistic model estimates of fixed effects and linear and threshold model estimates of heritability. Data consisted of Holstein heifers, which were artificially inseminated, with their first breeding between March 2003 and August 2005. Herds were required to have at least 60 breedings across the 3 yr of data and an overall mean conception rate (CR) between 20 and 80%. After edits there were 537,938 breedings of 362,512 heifers in 2,668 herds from 41 states used for analysis. After edits, the overall mean CR for US Holstein heifers was 57%. Linear and logistic model estimates for all factors were nearly identical. Year of breeding accounted for the most variation in heifer CR, with heifer age and month of breeding being the next most important factors. Conception rate in heifers is maximal at an intermediate age of 15 to 16 mo. Heifers at 26 mo of age and older have roughly a 10% lower CR than heifers bred at younger ages. Although month of breeding affected heifer CR, effects are less than for cows. In contrast to cow fertility, heifer CR is nearly as good in the hotter summer months as in cooler months. Approximately 88% of US herds had a 40 to 70% heifer CR. Heritability estimates of heifer CR on first service were 0.5% from the linear model and 1.0% from the threshold model. Genetic correlation estimates of heifer CR on first service with cow CR on first service and with first-lactation milk yield were 0.39 and -0.19, respectively. Results indicated that selection on either the currently available US daughter pregnancy rate evaluations for cow fertility or on cow CR will also improve heifer fertility. Furthermore, heritability of heifer CR is lower than for cow CR and reporting of heifer breedings is currently less complete than for cow breedings. Thus, there are currently no immediate plans to implement a US genetic evaluation for heifer CR.

Animals↗
PubMedDate not supplied

Predictive value of different prognostic factors in breast cancer recurrences: multivariate analysis using a logistic regression model.

BACKGROUND: The aim of this study was to compare the sensitivity of different pre-operative parameters in patients with breast cancer (BC) recurrence using univariate and multivariate analysis. MATERIALS AND METHODS: We retrospectively analyzed a series of 387 women (median age 60 years, range 35-83 years) who underwent curative surgery for pT1-2 BC. The patients were divided into two groups: Group 1: 325 (84.0%) patients with no evidence of disease during a median follow-up of 53 months (range 25-149 months) and Group 2: 62 (16.0%) patients who developed local or distant recurrences. RESULTS: Univariate analysis showed significant (p<0.01) differences between the two Groups in age, size and grading of the tumor and hormone receptor rate. MIB1 proliferation rate, serum markers CEA and CA 15-3, and lymph node status were not useful in predicting relapse. Multivariate analysis using a logistic regression model showed that only age, size of the tumor and hormone receptor rate independently correlate with the onset of recurrences. CONCLUSION: There is no clear correlation between BC recurrence and the majority of the prognostic factors available. Multivariate analysis of several pre-operative parameters may help to correctly select the high risk population.

Adult↗
PubMed1998

Analysis of survival data with multiple causes of failure: a comparison of hazard- and logistic-regression models with application in demography.

"The purpose of the paper is to compare results of estimation and inference concerning covariate effects as obtained from two approaches to the analysis of survival data with multiple causes of failure. The first approach involves a dynamic model for the cause-specific hazard rate. The second is based on a static logistic regression model for the conditional probability of having had an event of interest. The influence of sociodemographic characteristics on the rate of family initiation and, more importantly, on the choice between marriage and cohabitation as a first union, is examined. We found that results, generally, are similar across the methods considered. Some issues in relation to censoring mechanisms and independence among causes of failure are discussed."

Family Characteristics↗
PubMed2002

Repeated measures with zeros.

Consider repeated measures data with many zeros. For the case with one grouping factor and one repeated measure, we examine several models, assuming that the nonzero data are roughly lognormal. One of the simplest approaches is to model the zeros as left-censored observations from the lognormal distribution. A random effect is assumed for subjects. The censored model makes a strong assumption about the relationship between the zeros and the nonzero values. To check on this, you can instead assume that some of the zeros are 'true' zeros and model them as Bernoulli. Then the other values are modeled with a censored lognormal. A logistic model is used for the Bernoulli p, the probability of a true nonzero. The fit of the pure left-censored lognormal can be assessed by testing the hypothesis that p is 1, as described by Moulton and Halsey. The model can also be simplified by omitting the censoring, leaving a logistic model for the zeros and a lognormal model for the nonzero values. This is approximately equivalent to modeling the zero and nonzero values separately, a two-part model. In contrast to the censored model, this model assumes only a slight relationship (a covariance component) between the occurrence of zeros and the size of the nonzero values. The models are compared in terms of an example with data from children's private speech.

Biometry↗
PubMed1992

The use of cusums and other techniques in modelling continuous covariates in logistic regression.

The assessment of continuous covariates singly as possible predictors in a multivariable logistic regression model is an important first step in the analysis. An approach to plotting which uses a cusum (cumulative sum) of the binary response variable is described. Extreme-deviation statistics associated with the cusum may be used to detect monotonic and non-monotonic trends. Probability plots of the covariate in the two groups defined by the response variable may help to determine the appropriate scale (transformation) of the covariate and to anticipate possible problems with the logistic fit. The ratio of the variances in the response/non-response groups is informative about the need for a quadratic term in the logistic model. Smoothed scatterplots of the response are valuable in displaying the observed and fitted values. The techniques are illustrated with two data sets.

Binomial Distribution↗
PubMedDate not supplied

Analysis of logistic growth models.

A variety of growth curves have been developed to model both unpredated, intraspecific population dynamics and more general biological growth. Most predictive models are shown to be based on variations of the classical Verhulst logistic growth equation. We review and compare several such models and analyse properties of interest for these. We also identify and detail several associated limitations and restrictions.A generalized form of the logistic growth curve is introduced which incorporates these models as special cases. Several properties of the generalized growth are also presented. We furthermore prove that the new growth form incorporates additional growth models which are markedly different from the logistic growth and its variants, at least in their mathematical representation. Finally, we give a brief outline of how the new curve could be used for curve-fitting.

Animals↗