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PubMed1984

Methodological issues in case-control studies IV: Validity and efficiency of various analysis strategies for continuous variables using the unconditional logistic regression model.

Computer simulation has been used to evaluate the performance of the unconditional logistic regression model when used to analyse continuous data from case-control studies. The size of the bias in the odds ratio estimate introduced by small sample sizes and by the use of the incorrect analysis model has been estimated for various underlying population conditions, together with the power as a measure of efficiency. It is concluded that the model is robust over a wide range of exposures to the risk factor, in the sense that both small sample sizes and use of the incorrect model introduced relatively small biases. The power of the test is again little altered by use of the incorrect analysis model.

Aged↗
PubMed1980

Bias and efficiency in logistic analyses of stratified case-control studies.

Two approaches to the estimation of the parameters in the logistic model applied to the analysis of stratum matched case-control studies are compared. It is shown that the "unconditional likelihood method' gives estimates of odds ratios which may be severely exaggerated if the stratum sizes are not large; however, if stratum sizes are not small the "conditional likelihood method' is computationally prohibitive. The use of small stratum sizes (e.g., 1-to-1 matching) leads to some loss of efficiency if the matching is irrelevant but it is shown that the loss is small for odds ratios up to at least 3. There would seem to be strong arguments for the routine use of matched designs as the reduction in confounding bias produced by such matching may be considerable whereas there is only a small loss in efficiency compared with unmatched designs.

Humans↗
PubMed1991

Logistic models describing effects of temperature and humidity on residual effectiveness of chlorpyrifos and cyfluthrin formulations against German cockroaches (Dictyoptera: Blattellidae).

Multifactored logistic models were developed for chlorpyrifos and cyfluthrin formulations based on mortality data from laboratory studies with the German cockroach, Blattella germanica (L.). Insecticides were applied to stainless steel surfaces and aged at three different temperatures (23, 30, and 37 degrees C) and two levels of relative humidity (40 and 70%). After the insecticides dried, the treated panels were placed opposite plywood panels to simulate a crack and crevice application. At appropriate aging times, treated panels were removed from environmental chambers for bioassay. The combined effects of high temperature, high humidity, and aging of residues caused the greatest decline in cockroach mortality for chlorpyrifos. Increasing temperature and aging of residues resulted in decreased cockroach mortality for cyfluthrin formulations; however, mortality was greater than 87% for all formulations through 84 d. Information from this study can be incorporated into integrated pest management programs for German cockroaches.

Animals↗
PubMed1987

Use of simultaneous curve fitting and a four-parameter logistic model to evaluate the nutritional quality of protein sources at growth rates of rats from maintenance to maximum gain.

A four-parameter logistic model was used to describe the dose-response relationship of rats fed diets containing 12 levels of casein, peanut meal or wheat gluten. The model was capable of accurately describing the entire response curve of rats fed diets containing each of the three protein sources. Incorporation of a technique known as parameter sharing into the curve-fitting process facilitated convergence of the parameter estimates for b (the response of rats fed a protein-free diet) and Rmax (maximum response) for all curves when compared with the values observed experimentally. Parameter sharing also provided a method by which the curves could be differentiated on a statistical basis. These data indicate that the relative value of a protein source is dependent on the concentration of the protein in the diet. The application of nonlinear models combined with parameter sharing provides a technique by which protein values can be evaluated at levels of animal response from maintenance to maximum growth.

Animals↗
PubMed1987

Use of a four-parameter logistic model to evaluate the protein quality of mixtures of Mormon cricket meal and corn gluten meal in rats.

Weanling Sprague-Dawley rats were fed diets containing corn gluten meal (CGM), Mormon cricket meal (MCM), MCM supplemented with methionine (MCM + Met) or CGM-MCM mixtures as the sole source of dietary protein in purified diets. Animal response (weight or nitrogen gain) was analyzed as a function of nitrogen intake and described by a series of curves using a four-parameter logistic model. Parameter sharing was used to differentiate statistically between the response curves. When used for maximum nitrogen retention the quality of the protein sources could be ranked as follows: MCM + Met greater than 40 CGM-60 MCM greater than 50 CGM-50 MCM greater than 60 CGM-40 MCM greater than MCM greater than CGM. When used for maximum weight gain the ranking was as follows: MCM + Met greater than 40 CGM-60 MCM greater than 50 CGM-50 MCM greater than 60 CGM-40 MCM greater than MCM greater than CGM. The rankings of the protein sources when used for weight maintenance or nitrogen equilibrium were similar to those seen for maximum weight or nitrogen gain except for the ranking of MCM, which changed from fifth to first. These results show MCM to be a good quality protein source and that methionine is the first limiting amino acid when used for growth but not for maintenance. The shape of the response curves was dependent upon the response criteria as well as the source of dietary protein. The factors that may affect the shape of the dose-response curves and the application of nonlinear models toward animal feeding programs are discussed.

Animal Nutritional Physiological Phenomena↗
PubMed1989

Use of a four-parameter logistic model to evaluate the quality of the protein from three insect species when fed to rats.

The quality of three insect protein sources [Mormon cricket meal (MCM), house cricket meal (HCM) and Eastern tent caterpillar meal (TCM)] was evaluated relative to that of lactalbumin (LA) and soy protein (SP) by using both amino acid analysis and a rat bioassay. The amino acid pattern of the three insect meals indicated that methionine should be the first limiting amino acid for growing rats. In the rat bioassay, weanling Sprague-Dawley rats were fed graded levels of the five proteins in purified diets and the response (weight or nitrogen gain) evaluated as a function of nitrogen intake. The individual nitrogen intake-animal response results could be described by a series of curves using a four-parameter logistic model. The use of parameter sharing permitted the full range of responses to be described so that statistical differences between the dose-response curves could be identified. When used for either weight maintenance, nitrogen equilibrium, maximum weight gain or maximum nitrogen retention, the five protein sources could be ranked in the following order: LA greater than HCM greater than MCM = SP greater than TCM. Relative to lactalbumin, the value of all four protein sources decreased with increasing nitrogen intake. The low values obtained for TCM may have been related to factors other than protein quality. The results of this study indicate that some insect proteins are equivalent or superior to soy protein as a source of amino acids for growing rats.

Amino Acids↗
PubMed1978

The use of logistic regression for modelling risk factors: with application to non-melanoma skin cancer.

Logistic regression was used to estimate the "relative" risk of basal and squamous skin cancer for such factors as cumulative lifetime solar exposure, age, complexion, and tannability. In previous reports, a subject's exposure was estimated indirectly, by latitude, or by the number of sun days in a subject's habitat. In contrast, these results are based on interview data gathered for each subject. A relatively new technique was used to estimate "relative" risk by controlling for confounding and testing for effect modification. A linear effect for the "relative" risk of cancer versus exposure was found. Tannability was shown to be a more important risk factor than complexion. This result is consistent with the work of Silverstone and Searle.

Age Factors↗
PubMed1979

Work activity and fatal heart attack studied by multiple logistic risk analysis.

A group of 3975 San Francisco longshoremen in cohorts classified annually by work activity (WA) was followed for fatal heart attack (FHA) over a 22-year period. In 57,632 person-years of follow-up, 410 men died from heart attack. A multi-factor logistic analysis was used to study work energy output adjusted for age, race, systolic blood pressure, smoking, body mass index, glucose intolerance and EKG status as predictors of FHA. After adjustment for these factors, men with a high WA of 7 kcal/min above basal metabolism at the beginning of a yearly follow-up period had a FHA rate about one-half the rate for men in the lowest WA category of 1 kcal/min above basal metabolism (p = 0.0003). In addition, the predictability of average WA during the four years preceding a yearly follow-up period was isolated to see if the lower risk associated with high WA derives from selective factors. After adjustment for factors described above and also for rate of change in WA used to represent selective factors, subjects with WA of 7 kcal/min still had about one-half the FHA rate observed for men at the lowest WA level (p = 0.0006). The findings from these and other phases of the analysis are consistent with the hypothesis that a substantial protective effect against FHA results from vigorous physical exertion.

Adult↗
PubMed1980

Logistic model estimation of death attributable to risk factors for cardiovascular disease in Evans County, Georgia.

Linear logistic analysis of the relationship of cardiovascular disease risk factors to an overall measure of health effect, ten-year mortality, revealed significant associations of death with systolic blood pressure, age, sex, diabetes mellitus, smoking, cholesterol, obesity (Quetelet index), race and social index. Attributable risk and population attributable risk estimates were derived from the model by changing actual variable values to target values. The results confirmed systolic hypertension and smoking as major public health problems and diabetes mellitus as a powerful risk factor for death. The small detrimental effect of cholesterol on probability of death limits the potential for an overall beneficial effect of preventive intervention. In fact, drug intervention in two reported trials of cholesterol reduction had negative overall effects. Demonstration of the association of a characteristic with a specific disease state does not alone justify attempts to eliminate the high risk state from a population. An overall detrimental health effect must be documented by suitable studies before trials of preventive intervention are undertaken or recommendations made to the public.

Adult↗
PubMed1982

A review of goodness of fit statistics for use in the development of logistic regression models.

Several statistics have recently been proposed for the purpose of assessing the goodness of fit of an estimated logistic regression model. These statistics are reviewed and compared to other, less formal, procedures in the context of applications in epidemiologic research. One statistic is recommended for use and its computation is illustrated using data from a recent study of mortality of intensive care unit patients.

Humans↗
PubMed1983

Multivariate logistic analysis of risk factors for stroke in Tilburg, The Netherlands.

By means of a case-control study conducted between October 1, 1978, and July 31, 1981, in Tilburg, The Netherlands, various characteristics and events, including personal data, health-related behavior, and medical history, were evaluated as risk factors for stroke. The study subjects included 132 stroke patients and 239 age- and sex-matched control patients interviewed at the two city hospitals. To assess joint effects and possible interactions, and to control for multiple confounding factors, a series of multivariate logistic models for matched data were studied. From this analysis, it appeared that hypertension, acute myocardial infarction, cardiac arrhythmias, transient cerebral ischemic attacks, obesity, physical activity during leisure time, education of head of household, and Rhesus factor were all significant stroke risk factors. These risk determinants demonstrated a multiplicative effect in general; however, the influence of some variables on stroke risk was not constant with age (hypertension, acute myocardial infarction, cardiac arrhythmias, obesity, and Rhesus factor) and sex (hypertension and education of head of household). The relationship of diabetes mellitus to stroke slightly decreased and became nonsignificant after adjustment for factors besides age and sex. Stroke risk was not associated with cigarette and alcohol use, family history of stroke and related disorders, marital status, and ABO blood typing.

Adult↗
PubMed1985

Applications of microcomputer spreadsheet packages as adjuncts to multiple logistic regression analysis.

This paper illustrates how a microcomputer spreadsheet package can be used by epidemiologists to facilitate the computation of multiple logistic regression (MLR) probabilities, as well as odds ratios and associated confidence intervals, given the coefficients of the MLR model. By formatting a spreadsheet, data entry is greatly simplified, and computations are accomplished without any arithmetic manipulations on the part of the user. This approach makes it feasible for clerical support staff to assist in the computation of seemingly complex expressions. The increasing availability of microcomputers in clinical and research settings suggests that numerous analytic applications are amenable to this approach, thereby decreasing reliance on mainframe computers and desk-top calculators.

Computers↗
PubMed1987

Use of the logistic regression model for the analysis of proportionate mortality data.

A new statistical analysis strategy for proportionate mortality data is proposed. It is assumed that the occupational exposure, if it has an effect on mortality, increases the rate of death for some subset of causes by a multiplicative factor while not affecting the rates for the remaining causes of death. The unconditional logistic regression model is shown to provide a structure for the data analysis, with one of the predictors being the logit of the probability in the reference population that death was due to the affected causes. Using this model, one can estimate the effect of exposure while simultaneously controlling for a number of potential confounding and selection variables. Also, this model avoids the problems of comparing standardized proportionate mortality ratios, which are indirectly standardized measures. The model is demonstrated on a set of proportionate mortality data for factory workers from the northeastern United States.

Epidemiologic Methods↗
PubMed1987

Analysis of proportionate mortality data using logistic regression models.

When only proportionate mortality data are available to an investigator studying the effect of an exposure on a particular cause of death, controls must be selected from among persons dying of other causes believed to be uninfluenced by the exposure under study. When qualitative or quantitative estimates of exposure history can be obtained for the deceased individuals, it is shown that one can use logistic regression models for the mortality odds to efficiently estimate the effect of exposure while controlling for relevant confounding factors by incorporating a priori information on baseline mortality rates available from US life tables. The proposed method is used to reanalyze data from a cohort of arsenic-exposed workers in a Montana copper smelter.

Adult↗
PubMed1987

Polychotomous logistic regression methods for matched case-control studies with multiple case or control groups.

Two statistical methods, a polychotomous and pairwise approach, are presented to derive estimates of the relative odds in a matched case-control design when multiple case or control groups are used. Test statistics are derived to determine if the relative odds between groups are different. The polychotomous method is limited to case-control sets, i.e., where data are available on all members of a matched set. In contrast, the pairwise method makes use of data from both complete and incomplete sets. Nonetheless, efficiency calculations show that the polychotomous logistic regression model is more efficient even when 40 per cent of the case-control sets are incomplete. An example using a single dichotomous variable is provided.

Adolescent↗
PubMed1992

Logistical problems in prehospital thrombolysis.

In this study we compared efficacy and safety of prehospital with in-hospital thrombolytic treatment with anistreplase in patients with acute myocardial infarction (AMI). Three-hundred and fifty patients with chest pain were screened for eligibility by the municipal ambulance staff and/or the general practitioner. Patients were included in the absence of contraindications and if the telephone-transmitted ECG showed AMI. In a 6 month period 16 patients (5%) were eligible, but only seven (2%) were randomized. Age over 70 years, duration of chest pain for longer than 4 h and logistic problems were the major factors responsible for the low inclusion rate. The mean time spent at home with and without the ECG procedure was 38 +/- 14 and 14 +/- 8 min, respectively (P less than 0.001). These results demonstrate that in a medium sized town prehospital delivery of intravenous thrombolytic therapy by paramedics and/or the general practitioner is not feasible, leads to unnecessary time delay and may therefore yield no clinical benefits.

Adult↗
PubMedDate not supplied

Logistic growth curve of chickens: heritability of parameters.

Parameters of the logistic function of growth, fit to individual body weight curves of two randombred control populations of each sex of chickens from hatching to 45 weeks of age, were evaluated. Growth-rate constant and age at the infection point in the curve were estimated by the method of sample quantiles from individual weekly body weights of 225 males and 281 females of the Rhode Island Red (RIR) line, and 164 males and 239 females of the White Leghorn (WL) line. Heritability estimates, based on correlation among full-sibs, of growth rate constant were 0.18 +/- 0.32 in males and 0.29 +/- 0.29 in females of the RIR line, and 0.41 +/- 0.40 in males and 0.46 +/- 0.32 in females of the WL line. Estimates of heritability of age at the inflection point were 0.36 +/- 0.44 in males and 0.42 +/- 0.32 in females of the RIR line, and 0.46 +/- 0.41 in males and 0.50 +/- 0.28 in females of the WL line. Observed variation for each trait probably does not provide evidence for heritable differences. No genetic correlations were evident among growth-rate constant, age at the point of inflection, and initial or maximum weight. According to these results, it does not appear that selection for growth-rate constant or age at the point of inflection will change the shape of the growth curve of these populations genetically. Moreover, correlated genetic change in initial or maximum weight would not be expected.

Aging↗
PubMed2000

Reliability of pharmacodynamic analysis by logistic regression: a computer simulation study.

BACKGROUND: Many pharmacologic studies record data as binary yes-or-no variables, and analysis is performed using logistic regression. This study investigates the accuracy of estimation of the drug concentration associated with a 50% probability of drug effect (C50) and the term describing the steepness of the concentration-effect relation (gamma). METHODS: The authors developed a technique for simulating pharmacodynamic studies with binary yes-or-no responses. Simulations were conducted assuming either that each data point was derived from the same patient or that data were pooled from multiple patients in a population with log-normal distributions of C50 and gamma. Coefficients of variation were calculated. The authors also determined the percentage of simulations in which the 95% confidence intervals contained the true parameter value. RESULTS: The coefficient of variation of parameter estimates decreased with increasing n and gamma. The 95% confidence intervals for C50 estimation contained the true parameter value in more than 90% of the simulations. However, the 95% confidence intervals of gamma did not contain the true value in a substantial number of simulations of data from multiple patients. CONCLUSION: The coefficient of variation of parameter estimates may be as large as 40-50% for small studies (n < or = 20). The 95% confidence intervals of C50 almost always contain the true value, underscoring the need for always reporting confidence intervals. However, when data from multiple patients is naively pooled, the estimates of gamma may be biased, and the 95% confidence intervals may not contain the true value.

Algorithms↗