Evaluation of the Hosmer -Lemeshow global goodness -of-fit statistic for mixed variable logistic regression models

The performance of the Hosmer-Lemeshow global goodness-of-fit statistic for logistic regression models was explored in a wide variety of conditions not previously fully investigated. Computer simulations, each consisting of 500 regression models, were run to assess the statistic in 23 different situations. The items which varied among the situations included the number of observations used in each regression, the number of covariates, the degree of dependence among the covariates, the combinations of continuous and discrete variables, and the generation of the values of the dependent variable for model fit or lack of fit.^ The study found that the $\rm\ C$g* statistic was adequate in tests of significance for most situations. However, when testing data which deviate from a logistic model, the statistic has low power to detect such deviation. Although grouping of the estimated probabilities into quantiles from 8 to 30 was studied, the deciles of risk approach was generally sufficient. Subdividing the estimated probabilities into more than 10 quantiles when there are many covariates in the model is not necessary, despite theoretical reasons which suggest otherwise. Because it does not follow a X$\sp2$ distribution, the statistic is not recommended for use in models containing only categorical variables with a limited number of covariate patterns.^ The statistic performed adequately when there were at least 10 observations per quantile. Large numbers of observations per quantile did not lead to incorrect conclusions that the model did not fit the data when it actually did. However, the statistic failed to detect lack of fit when it existed and should be supplemented with further tests for the influence of individual observations. Careful examination of the parameter estimates is also essential since the statistic did not perform as desired when there was moderate to severe collinearity among covariates.^ Two methods studied for handling tied values of the estimated probabilities made only a slight difference in conclusions about model fit. Neither method split observations with identical probabilities into different quantiles. Approaches which create equal size groups by separating ties should be avoided. ^

Detection of nonrandom association of alleles from the distribution of the number of heterozygous loci in a sample.

The distribution of the number of heterozygous loci in two randomly chosen gametes or in a random diploid zygote provides information regarding the nonrandom association of alleles among different genetic loci. Two alternative statistics may be employed for detection of nonrandom association of genes of different loci when observations are made on these distributions: observed variance of the number of heterozygous loci (s2k) and a goodness-of-fit criterion (X2) to contrast the observed distribution with that expected under the hypothesis of random association of genes. It is shown, by simulation, that s2k is statistically more efficient than X2 to detect a given extent of nonrandom association. Asymptotic normality of s2k is justified, and X2 is shown to follow a chi-square (chi 2) distribution with partial loss of degrees of freedom arising because of estimation of parameters from the marginal gene frequency data. Whenever direct evaluations of linkage disequilibrium values are possible, tests based on maximum likelihood estimators of linkage disequilibria require a smaller sample size (number of zygotes or gametes) to detect a given level of nonrandom association in comparison with that required if such tests are conducted on the basis of s2k. Summarization of multilocus genotype (or haplotype) data, into the different number of heterozygous loci classes, thus, amounts to appreciable loss of information.

IN-VIVO CT DOSIMETRY DURING VIRTUAL COLONOSCOPY

Virtual colonoscopy (VC) is a minimally invasive means for identifying colorectal polyps and colorectal lesions by insufflating a patient’s bowel, applying contrast agent via rectal catheter, and performing multi-detector computed tomography (MDCT) scans. The technique is recommended for colonic health screening by the American Cancer Society but not funded by the Centers for Medicare and Medicaid Services (CMS) partially because of potential risks from radiation exposure. To date, no in‐vivo organ dose measurements have been performed for MDCT scans; thus, the accuracy of any current dose estimates is currently unknown. In this study, two TLDs were affixed to the inner lumen of standard rectal catheters used in VC, and in-vivo rectal dose measurements were obtained within 6 VC patients. In order to calculate rectal dose, TLD-100 powder response was characterized at diagnostic doses such that appropriate correction factors could be determined for VC. A third-order polynomial regression with a goodness of fit factor of R2=0.992 was constructed from this data. Rectal dose measurements were acquired with TLDs during simulated VC within a modified anthropomorphic phantom configured to represent three sizes of patients undergoing VC. The measured rectal doses decreased in an exponential manner with increasing phantom effective diameter, with R2=0.993 for the exponential regression model and a maximum percent coefficient of variation (%CoV) of 4.33%. In-vivo measurements yielded rectal doses ranged from that decreased exponentially with increasing patient effective diameter, in a manner that was also favorably predicted by the size specific dose estimate (SSDE) model for all VC patients that were of similar age, body composition, and TLD placement. The measured rectal dose within a younger patient was favorably predicted by the anthropomorphic phantom dose regression model due to similarities in the percentages of highly attenuating material at the respective measurement locations and in the placement of the TLDs. The in-vivo TLD response did not increase in %CoV with decreasing dose, and the largest %CoV was 10.0%.

Forecasting cost based on a stochastic utilization plan and a fixed cost function

The application of Markov processes is very useful to health-care problems. The objective of this study is to provide a structured methodology of forecasting cost based upon combining a stochastic model of utilization (Markov Chain) and deterministic cost function. The perspective of the cost in this study is the reimbursement for the services rendered. The data to be used is the OneCare database of claim records of their enrollees over a two-year period of January 1, 1996–December 31, 1997. The model combines a Markov Chain that describes the utilization pattern and its variability where the use of resources by risk groups (age, gender, and diagnosis) will be considered in the process and a cost function determined from a fixed schedule based on real costs or charges for those in the OneCare claims database. The cost function is a secondary application to the model. Goodness-of-fit will be used checked for the model against the traditional method of cost forecasting. ^

Logistic regression models for ordinal response: A study of self-efficacy in colorectal cancer screening

The ordinal logistic regression models are used to analyze the dependant variable with multiple outcomes that can be ranked, but have been underutilized. In this study, we describe four logistic regression models for analyzing the ordinal response variable. ^ In this methodological study, the four regression models are proposed. The first model uses the multinomial logistic model. The second is adjacent-category logit model. The third is the proportional odds model and the fourth model is the continuation-ratio model. We illustrate and compare the fit of these models using data from the survey designed by the University of Texas, School of Public Health research project PCCaSO (Promoting Colon Cancer Screening in people 50 and Over), to study the patient’s confidence in the completion colorectal cancer screening (CRCS). ^ The purpose of this study is two fold: first, to provide a synthesized review of models for analyzing data with ordinal response, and second, to evaluate their usefulness in epidemiological research, with particular emphasis on model formulation, interpretation of model coefficients, and their implications. Four ordinal logistic models that are used in this study include (1) Multinomial logistic model, (2) Adjacent-category logistic model [9], (3) Continuation-ratio logistic model [10], (4) Proportional logistic model [11]. We recommend that the analyst performs (1) goodness-of-fit tests, (2) sensitivity analysis by fitting and comparing different models.^

A comparative analysis of CHIP Perinatal policy in twelve states

The purpose of this comparative analysis of CHIP Perinatal policy (42 CFR § 457) was to provide a basis for understanding the variation in policy outputs across the twelve states that, as of June 2007, implemented the Unborn Child rule. This Department of Health and Human Services regulation expanded in 2002 the definition of “child” to include the period from conception to birth, allowing states to consider an unborn child a “targeted low-income child” and therefore eligible for SCHIP coverage. ^ Specific study aims were to (1) describe typologically the structural and contextual features of the twelve states that adopted a CHIP Perinatal policy; (2) describe and differentiate among the various designs of CHIP Perinatal policy implemented in the states; and (3) develop a conceptual model that links the structural and contextual features of the adopting states to differences in the forms the policy assumed, once it was implemented. ^ Secondary data were collected from publicly available information sources to describe characteristics of states’ political system, health system, economic system, sociodemographic context and implemented policy attributes. I posited that socio-demographic differences, political system differences and health system differences would directly account for the observed differences in policy output among the states. ^ Exploratory data analysis techniques, which included median polishing and multidimensional scaling, were employed to identify compelling patterns in the data. Scaled results across model components showed that economic system was most closely related to policy output, followed by health system. Political system and socio-demographic characteristics were shown to be weakly associated with policy output. Goodness-of-fit measures for MDS solutions implemented across states and model components, in one- and two-dimensions, were very good. ^ This comparative policy analysis of twelve states that adopted and implemented HHS Regulation 42 C.F.R. § 457 contributes to existing knowledge in three areas: CHIP Perinatal policy, public health policy and policy sciences. First, the framework allows for the identification of CHIP Perinatal program design possibilities and provides a basis for future studies that evaluate policy impact or performance. Second, studies of policy determinants are not well represented in the health policy literature. Thus, this study contributes to the development of the literature in public health policy. Finally, the conceptual framework for policy determinants developed in this study suggests new ways for policy makers and practitioners to frame policy arguments, encouraging policy change or reform. ^

Utilization behavior of the elderly in an HMO: A causal analysis

Planning and providing health care services for the elderly represents a major challenge to the health care system. One part of that challenge is the identification of those factors which determine the utilization of services by this population. The purpose of this study is to explain the use of health care services by elderly subscribers in a prepaid group health plan, using the theoretical framework developed by Andersen and Aday. The impact of the predisposing, enabling and need factors on utilization was modelled through a structural equation approach using LISREL. The data were derived from Kaiser-Permanente's Medicare Prospective Payment Project, August 1980-December 1982. Need factors, in general, were the most significant determinants of utilization, with the predisposing and enabling factors found to be secondary but necessary links in the causal chain. The model was fitted to the data from the youngest age group (65-74 years) and then evaluated for goodness of fit in the two older groups (75-84 and 85+ years). Implications of the study's findings and suggestions for further modelling the utilization behavior of the elderly are discussed. ^

A multiplicative model for standardizing vital rates without using external standards

Standardization is a common method for adjusting confounding factors when comparing two or more exposure category to assess excess risk. Arbitrary choice of standard population in standardization introduces selection bias due to healthy worker effect. Small sample in specific groups also poses problems in estimating relative risk and the statistical significance is problematic. As an alternative, statistical models were proposed to overcome such limitations and find adjusted rates. In this dissertation, a multiplicative model is considered to address the issues related to standardized index namely: Standardized Mortality Ratio (SMR) and Comparative Mortality Factor (CMF). The model provides an alternative to conventional standardized technique. Maximum likelihood estimates of parameters of the model are used to construct an index similar to the SMR for estimating relative risk of exposure groups under comparison. Parametric Bootstrap resampling method is used to evaluate the goodness of fit of the model, behavior of estimated parameters and variability in relative risk on generated sample. The model provides an alternative to both direct and indirect standardization method. ^

Design of long-term animal bioassay for low-dose extrapolation using a multistage model

Conventional designs of animal bioassays allocate the same number of animals into control and dose groups to explore the spontaneous and induced tumor incidence rates, respectively. The purpose of such bioassays are (a) to determine whether or not the substance exhibits carcinogenic properties, and (b) if so, to estimate the human response at relatively low doses. In this study, it has been found that the optimal allocation to the experimental groups which, in some sense, minimize the error of the estimated response for low dose extrapolation is associated with the dose level and tumor risk. The number of dose levels has been investigated at the affordable experimental cost. The pattern of the administered dose, 1 MTD, 1/2 MTD, 1/4 MTD,....., etc. plus control, gives the most reasonable arrangement for the low dose extrapolation purpose. The arrangement of five dose groups may make the highest dose trivial. A four-dose design can circumvent this problem and has also one degree of freedom for testing the goodness-of-fit of the response model.^ An example using the data on liver tumors induced in mice in a lifetime study of feeding dieldrin (Walker et al., 1973) is implemented with the methodology. The results are compared with conclusions drawn from other studies. ^

Circadian rhythm profiles in porcine ICU subjects

Purpose: To explore the natural trajectory of circadian rhythms of sedation requirement, core body temperature (CBT), pulmonary mechanics (PM), and gas exchange (GE) in mechanically ventilated swine, as these variables affect the duration of mechanical ventilation. ^ Design: A secondary analysis to describe and compare circadian rhythms of study variables in swine mechanically ventilated for ≤ 7 days. ^ Setting: Porcine Intensive Care Unit (ICU).^ Sample: Six male swine. ^ Methods: Sedation requirements were recorded hourly and the CBT, PM and GE variables were sampled every 1 s – 1 min for ≤ 7 days. The data sets for each pig with > 5 days ICU length of stay were divided into one section representing the first 3 days and one section representing subsequent days. The Lomb periodogram was used to estimate the circadian time period for each variable, and cosinor analysis with the estimated time period to obtain amplitude and mesor. Circadian to ultradian bandpower ratio to assess rhythm quality and stability over time and goodness-of-fit index to describe biological significance of a rhythm were used. Together, these two parameters were used to define rhythm robustness over time. The masking effect of sedation as a potential confounder of the circadian rhythms of CBT, PM, and GE was explored, and circadian rhythm profiles of CBT of pigs in the ICU setting were compared with those of the same pigs in the ambulatory setting. ^ Results: All pigs had significant rhythms in CBT, respiratory rate, and peripheral oxygen saturation across ICU data sets. Healthier pigs had more robust rhythms of study variables over time. Sedation did not appear to mask the circadian rhythms of CBT, PM, and GE. The circadian rhythm of CBT was less robust in the ICU setting than in the ambulatory setting. ^ Conclusions: Individual subject observations provided preliminary evidence that robustness of rhythms varies with subject acuity. Comparison of profiles of circadian rhythms among ICU subjects with similar acuity and disease processes is warranted to determine if the profiles in the present study are reproducible. Identification of consistent patterns may provide insight into subject morbidity and timing of such therapeutic interventions as weaning from mechanical ventilation. ^

Longitudinal categorical data analysis: A continuous -time Markov chain approach

In this dissertation, we propose a continuous-time Markov chain model to examine the longitudinal data that have three categories in the outcome variable. The advantage of this model is that it permits a different number of measurements for each subject and the duration between two consecutive time points of measurements can be irregular. Using the maximum likelihood principle, we can estimate the transition probability between two time points. By using the information provided by the independent variables, this model can also estimate the transition probability for each subject. The Monte Carlo simulation method will be used to investigate the goodness of model fitting compared with that obtained from other models. A public health example will be used to demonstrate the application of this method. ^