19 resultados para estimating conditional probabilities
em DigitalCommons@The Texas Medical Center
Resumo:
The discrete-time Markov chain is commonly used in describing changes of health states for chronic diseases in a longitudinal study. Statistical inferences on comparing treatment effects or on finding determinants of disease progression usually require estimation of transition probabilities. In many situations when the outcome data have some missing observations or the variable of interest (called a latent variable) can not be measured directly, the estimation of transition probabilities becomes more complicated. In the latter case, a surrogate variable that is easier to access and can gauge the characteristics of the latent one is usually used for data analysis. ^ This dissertation research proposes methods to analyze longitudinal data (1) that have categorical outcome with missing observations or (2) that use complete or incomplete surrogate observations to analyze the categorical latent outcome. For (1), different missing mechanisms were considered for empirical studies using methods that include EM algorithm, Monte Carlo EM and a procedure that is not a data augmentation method. For (2), the hidden Markov model with the forward-backward procedure was applied for parameter estimation. This method was also extended to cover the computation of standard errors. The proposed methods were demonstrated by the Schizophrenia example. The relevance of public health, the strength and limitations, and possible future research were also discussed. ^
Resumo:
A Bayesian approach to estimating the intraclass correlation coefficient was used for this research project. The background of the intraclass correlation coefficient, a summary of its standard estimators, and a review of basic Bayesian terminology and methodology were presented. The conditional posterior density of the intraclass correlation coefficient was then derived and estimation procedures related to this derivation were shown in detail. Three examples of applications of the conditional posterior density to specific data sets were also included. Two sets of simulation experiments were performed to compare the mean and mode of the conditional posterior density of the intraclass correlation coefficient to more traditional estimators. Non-Bayesian methods of estimation used were: the methods of analysis of variance and maximum likelihood for balanced data; and the methods of MIVQUE (Minimum Variance Quadratic Unbiased Estimation) and maximum likelihood for unbalanced data. The overall conclusion of this research project was that Bayesian estimates of the intraclass correlation coefficient can be appropriate, useful and practical alternatives to traditional methods of estimation. ^
Resumo:
Breast cancer is the most common non-skin cancer and the second leading cause of cancer-related death in women in the United States. Studies on ipsilateral breast tumor relapse (IBTR) status and disease-specific survival will help guide clinic treatment and predict patient prognosis.^ After breast conservation therapy, patients with breast cancer may experience breast tumor relapse. This relapse is classified into two distinct types: true local recurrence (TR) and new ipsilateral primary tumor (NP). However, the methods used to classify the relapse types are imperfect and are prone to misclassification. In addition, some observed survival data (e.g., time to relapse and time from relapse to death)are strongly correlated with relapse types. The first part of this dissertation presents a Bayesian approach to (1) modeling the potentially misclassified relapse status and the correlated survival information, (2) estimating the sensitivity and specificity of the diagnostic methods, and (3) quantify the covariate effects on event probabilities. A shared frailty was used to account for the within-subject correlation between survival times. The inference was conducted using a Bayesian framework via Markov Chain Monte Carlo simulation implemented in softwareWinBUGS. Simulation was used to validate the Bayesian method and assess its frequentist properties. The new model has two important innovations: (1) it utilizes the additional survival times correlated with the relapse status to improve the parameter estimation, and (2) it provides tools to address the correlation between the two diagnostic methods conditional to the true relapse types.^ Prediction of patients at highest risk for IBTR after local excision of ductal carcinoma in situ (DCIS) remains a clinical concern. The goals of the second part of this dissertation were to evaluate a published nomogram from Memorial Sloan-Kettering Cancer Center, to determine the risk of IBTR in patients with DCIS treated with local excision, and to determine whether there is a subset of patients at low risk of IBTR. Patients who had undergone local excision from 1990 through 2007 at MD Anderson Cancer Center with a final diagnosis of DCIS (n=794) were included in this part. Clinicopathologic factors and the performance of the Memorial Sloan-Kettering Cancer Center nomogram for prediction of IBTR were assessed for 734 patients with complete data. Nomogram for prediction of 5- and 10-year IBTR probabilities were found to demonstrate imperfect calibration and discrimination, with an area under the receiver operating characteristic curve of .63 and a concordance index of .63. In conclusion, predictive models for IBTR in DCIS patients treated with local excision are imperfect. Our current ability to accurately predict recurrence based on clinical parameters is limited.^ The American Joint Committee on Cancer (AJCC) staging of breast cancer is widely used to determine prognosis, yet survival within each AJCC stage shows wide variation and remains unpredictable. For the third part of this dissertation, biologic markers were hypothesized to be responsible for some of this variation, and the addition of biologic markers to current AJCC staging were examined for possibly provide improved prognostication. The initial cohort included patients treated with surgery as first intervention at MDACC from 1997 to 2006. Cox proportional hazards models were used to create prognostic scoring systems. AJCC pathologic staging parameters and biologic tumor markers were investigated to devise the scoring systems. Surveillance Epidemiology and End Results (SEER) data was used as the external cohort to validate the scoring systems. Binary indicators for pathologic stage (PS), estrogen receptor status (E), and tumor grade (G) were summed to create PS+EG scoring systems devised to predict 5-year patient outcomes. These scoring systems facilitated separation of the study population into more refined subgroups than the current AJCC staging system. The ability of the PS+EG score to stratify outcomes was confirmed in both internal and external validation cohorts. The current study proposes and validates a new staging system by incorporating tumor grade and ER status into current AJCC staging. We recommend that biologic markers be incorporating into revised versions of the AJCC staging system for patients receiving surgery as the first intervention.^ Chapter 1 focuses on developing a Bayesian method to solve misclassified relapse status and application to breast cancer data. Chapter 2 focuses on evaluation of a breast cancer nomogram for predicting risk of IBTR in patients with DCIS after local excision gives the statement of the problem in the clinical research. Chapter 3 focuses on validation of a novel staging system for disease-specific survival in patients with breast cancer treated with surgery as the first intervention. ^
Resumo:
Cells infected with MuSVts110 express a viral RNA which contains an inherent conditional defect in RNA splicing. It has been shown previously that splicing of the MuSVts110 primary transcript is essential to morphological transformation of 6m2 cells in vitro. A growth temperature of 33$\sp\circ$C is permissive for viral RNA splicing,and, consequently, 6m2 cells appear morphologically transformed at this temperature. However, 6m2 cells appear phenotypically normal when incubated at 39$\sp\circ$C, the non-permissive temperature for viral RNA splicing.^ After a shift from 39$\sp\circ$C to 33$\sp\circ$C, the coordinate splicing of previously synthesized and newly transcribed MuSVts110 RNA was achieved. By S1 nuclease analysis of total RNA isolated at various times, 5$\sp\prime$ splice site cleavage of the MuSVts110 transcript appeared to occur 60 minutes after the shift to 33$\sp\circ$C, and 30 minutes prior to detectable exon ligation. In addition, consistent with the permissive temperatures and the kinetic timeframe of viral RNA splicing after a shift to 33$\sp\circ$C, four temperature sensitive blockades to primer extension were identified 26-75 bases upstream of the 3$\sp\prime$ splice site. These blockades likely reflect four branchpoint sequences utilized in the formation of MuSVts110 lariat splicing-intermediates.^ The 54-5A4 cell line is a spontaneous revertant of 6m2 cells and appears transformed at all growth temperatures. Primer extension sequence analysis has shown that a five base deletion occurred at the 3$\sp\prime$ splice site in MuSVts110 RNA allowing the expression of a viral transforming protein in 54-5A4 in the absence of RNA splicing, whereas in the parental 6m2 cell line, a splicing event is necessary to generate a similar transforming protein. As a consequence of this deletion, splicing cannot occur and the formation of the four MuSVts110 branched-intermediates were not observed at any temperature in 54-5A4 cells. However, 5$\sp\prime$ splice site cleavage was still detected at 33$\sp\circ$C.^ Finally, we have investigated the role of the 1488 bp deletion which occurred in the generation of MuSVts110 in the activation of temperature sensitive viral RNA splicing. This deletion appears solely responsible for splice site activation. Whether intron size is the crucial factor in MuSVts110 RNA splicing or whether inhibitory sequences were removed by the deletion is currently unknown. (Abstract shortened with permission of author.) ^
Resumo:
Environmental data sets of pollutant concentrations in air, water, and soil frequently include unquantified sample values reported only as being below the analytical method detection limit. These values, referred to as censored values, should be considered in the estimation of distribution parameters as each represents some value of pollutant concentration between zero and the detection limit. Most of the currently accepted methods for estimating the population parameters of environmental data sets containing censored values rely upon the assumption of an underlying normal (or transformed normal) distribution. This assumption can result in unacceptable levels of error in parameter estimation due to the unbounded left tail of the normal distribution. With the beta distribution, which is bounded by the same range of a distribution of concentrations, $\rm\lbrack0\le x\le1\rbrack,$ parameter estimation errors resulting from improper distribution bounds are avoided. This work developed a method that uses the beta distribution to estimate population parameters from censored environmental data sets and evaluated its performance in comparison to currently accepted methods that rely upon an underlying normal (or transformed normal) distribution. Data sets were generated assuming typical values encountered in environmental pollutant evaluation for mean, standard deviation, and number of variates. For each set of model values, data sets were generated assuming that the data was distributed either normally, lognormally, or according to a beta distribution. For varying levels of censoring, two established methods of parameter estimation, regression on normal ordered statistics, and regression on lognormal ordered statistics, were used to estimate the known mean and standard deviation of each data set. The method developed for this study, employing a beta distribution assumption, was also used to estimate parameters and the relative accuracy of all three methods were compared. For data sets of all three distribution types, and for censoring levels up to 50%, the performance of the new method equaled, if not exceeded, the performance of the two established methods. Because of its robustness in parameter estimation regardless of distribution type or censoring level, the method employing the beta distribution should be considered for full development in estimating parameters for censored environmental data sets. ^
Resumo:
Although bone morphogenetic proteins (BMPs) were initially identified for their potent bone-inducing activity, their precise roles in processes of endochondral and intramembranous bone formation are far from being clear. Tissue-specific loss-of-function experiments using the BMP receptor type IA (BMPR-IA) are particularly attractive since this receptor is thought to be essential for signaling by the closely related BMPs -2, 4, and 7. To ablate signaling through this receptor during chondrogenesis, we have generated transgenic mice expressing Cre recombinase under the control of the collagen type II (Col2a1) gene regulatory sequences. Mice lacking BMPR-IA function in chondrocytes display a number of skeletal abnormalities, including defects in bones of the chondrocranium, abnormal dorsal vertebral processes, scapulae with severe hypoplasia of dorsal elements, and shortening of the long bones. Alterations in the growth plate of long bones in mutants suggest that BMPR-IA is not required for early steps of the chondrocyte specification, but is rather important in regulation of terminal differentiation. Molecular analysis revealed noticeable downregulation of the Ihh/Ptch signalling pathway, decreased chondrocyte proliferation rate and deregulation of hypertrophy. ^ In order to elucidate the role of BMP signalling in development of the limb and intramembranous ossification, we have used mice expressing Cre recombinase under control of the Prx1 (MHox) regulatory elements (M. Logan, pers comm.). Cre activity was found in those mice in the developing limb bud mesenchyme, as well as in a subset of cranial neural crest cells. Prx1-Cre-induced conditional mutants display prominent defects in distal limb outgrowth, as well as ossification defects in a number of neural crest-derived calvarial bones. Intriguingly, mutant limbs displayed alterations in patterning along all three axes. Molecular analysis revealed ectopic anterior Shh/Ptch signalling pathway activation and expression of some Hox genes. Observed loss of Msx1 and Msx2 expression in the progress zone correlates with downregulation of Cyclin D1 and decreased distal outgrowth. Abnormal ventral localization of Lmx1b-expressing cells along with observed later morphological abnormalities suggest a novel role for BMP signalling in establishment or maintaining of the dorso-ventral polarity in the limb mesoderm. ^
Resumo:
Sry and Wnt4 cDNAs were individually introduced into the ubiquitously-expressed Rosa26 ( R26) locus by gene targeting in embryonic stem (ES) cells to create a conditional gene expression system in mice. In the targeted alleles, expression of these cDNAs should be blocked by a neomycin resistance selection cassette that is flanked by loxP sites. Transgene expression should be activated after the blocking cassette is deleted by Cre recombinase. ^ To test this conditional expression system, I have bred R26-stop- Sry and R26-stop-Wnt4 heterozygotes with a MisRII-Cre mouse line that expresses Cre in the gonads of both sexes. Analysis of these two types of bigenic heterozygotes indicated that their gonads developed normally like those of wild types. However, one XX R26-Sry/R26-Sry; MisR2-Cre/+ showed epididymis-like structures resembling those of males. In contrast, only normal phenotypes were observed in XY R26-Wnt4/R26-Wnt4; MisR2-Cre /+ mice. To interpret these results, I have tested for Cre recombinase activity by Southern blot and transcription of the Sry and Wnt4 transgenes by RT-PCR. Results showed that bigenic mutants had insufficient activation of the transgenes in their gonads at E12.5 and E13.5. Therefore, the failure to observe mutant phenotypes may have resulted from low activity of MisR2-Cre recombination at the appropriate time. ^ Col2a1-Cre transgenic mice express Cre in differentiating chondrocytes. R26-Wnt4; Col2a1-Cre bigenic heterozygous mice were found to exhibit a dramatic alteration in growth presumably caused by Wnt4 overexpression during chondrogenesis. R26-Wnt4; Col2a1-Cre mice exhibited dwarfism beginning approximately 10 days after birth. In addition, they also had craniofacial abnormalities, and had delayed ossification of the lumbar vertebrate and pelvic bones. Histological analysis of the growth plates of R26-Wnt4; Col2a1-Cre mice revealed less structural organization and a delay in onset of the primary and secondary ossification centers. Molecular studies confirmed that overexpression of Wnt4 causes decreased proliferation and early maturation of chondrocytes. In addition, R26-Wnt4; Col2a1-Cre mice had decreased expression of vascular endothelial growth factor (VEGF), suggesting that defects in vascularization may contribute to the dwarf phenotype. Finally, 9-month-old R26-Wnt4; Col2a1-Cre mice had significantly more fat cells in the marrow cavities of their metaphysis long bones, implying that long-term overexpression of Wnt4may cause bone marrow pathologies. In conclusion, Wnt4 was activated by Col2a1-Cre recombinase and was overexpressed in the growth plate, resulting in aberrant proliferation and differentiation of chondrocytes, and ultimately leads to dwarfism in mice. ^
Resumo:
Although mechanisms regulating the formation of embryonic skeletal muscle are well characterized, less is known about muscle formation in postnatal life. This disparity is unfortunate because the largest increases in skeletal muscle mass occur after birth. Adult muscle stem cells (satellite cells) appear to recapitulate the events that occur in embryonic myoblasts. In particular, the myogenic basic helix-loop-helix factors, which have crucial functions in embryonic muscle development, are assumed to have similar roles in postnatal muscle formation. Here, I test this assumption by determining the role of the myogenic regulator myogenin in postnatal life. Myogenin-null mice die at birth, necessitating the generation of floxed alleles of myogenin and the use of cre-recombinase lines to delete myogenin. Removing myogenin before embryonic muscle development resulted in myofiber deficiencies identical to those observed in myogenin-null mice. However, mice in which myogenin was deleted following embryonic muscle development had normal skeletal muscle, except for modest alterations in MRF4 and MyoD expression. Notably, myogenin-deleted mice were 30% smaller than controls, suggesting that myogenin's absence disrupted general body growth. These results suggest that skeletal muscle growth in postnatal life is controlled by mechanisms distinct from those occurring in embryonic muscle development. ^
Resumo:
Over 50% of sporadic tumors in humans have a p53 mutation highlighting its importance as a tumor suppressor. Considering additional mutations in other genes involved in p53 pathways, every tumor probably has mutant p53 or impaired p53-mediated functions. In response to a variety of cellular and genotoxic stresses, p53, mainly through its transcriptional activity, induces pathways involved in apoptosis and growth arrest. In these circumstances and under normal situations, p53 must be tightly regulated. Mdm2 is an important regulator of p53. Mdm2 inhibits p53 function by binding and blocking its transactivation domain. In addition, Mdm2 helps target p53 for degradation through its E3 ligase activity. Mdm2 null mice are embryonic lethal due to apoptosis in the blastocysts. However, a p53 null background rescues this lethality demonstrating the importance of the p53-Mdm2 interaction, particularly during development. The lethality of the Mdm2 null mouse prior to implantation limits the ability to investigate the role of Mdm2 in regulating p53 in a temporal and tissue specific manner. Does p53 need to be regulated in all tissues throughout the life of a mouse? Does Mdm2 always have to regulate it? To address these questions, we created a conditional Mdm2 allele. The conditional allele, Mdm2FM, in the presence of Cre recombinase results in the deletion of exons 5 and 6 of Mdm2 (most of the p53 binding domain) and represents a null allele. ^ The Mdm2FM allele was crossed with a heart muscle specific Cre expressing mouse (α-myosin heavy chain promoter driven Cre) to ask whether Mdm2 acts as a negative regulator of p53 in the heart. The heart is the most prominent organ early in embryogenesis and is shaped by cell death and proliferation. p53 does not appear to be active in the heart in response to some types of stress, so it remained to be determined if it has to be regulated in normal heart development. Loss of Mdm2 in the heart results in heart defects as early as E9.5. Loss of Mdm2 results in stabilized p53 and apoptosis. This apoptosis leads to a thinning of the myocardial wall particularly in the ventricles and abnormal ventricular structure. Eventually the abnormal heart fails resulting in lethality by E13.5. The embryonic lethality is rescued in a p53 null background. Thus, Mdm2 is important in regulating p53 in the development of the heart. ^
Resumo:
External beam radiation therapy is used to treat nearly half of the more than 200,000 new cases of prostate cancer diagnosed in the United States each year. During a radiation therapy treatment, healthy tissues in the path of the therapeutic beam are exposed to high doses. In addition, the whole body is exposed to a low-dose bath of unwanted scatter radiation from the pelvis and leakage radiation from the treatment unit. As a result, survivors of radiation therapy for prostate cancer face an elevated risk of developing a radiogenic second cancer. Recently, proton therapy has been shown to reduce the dose delivered by the therapeutic beam to normal tissues during treatment compared to intensity modulated x-ray therapy (IMXT, the current standard of care). However, the magnitude of stray radiation doses from proton therapy, and their impact on this incidence of radiogenic second cancers, was not known. ^ The risk of a radiogenic second cancer following proton therapy for prostate cancer relative to IMXT was determined for 3 patients of large, median, and small anatomical stature. Doses delivered to healthy tissues from the therapeutic beam were obtained from treatment planning system calculations. Stray doses from IMXT were taken from the literature, while stray doses from proton therapy were simulated using a Monte Carlo model of a passive scattering treatment unit and an anthropomorphic phantom. Baseline risk models were taken from the Biological Effects of Ionizing Radiation VII report. A sensitivity analysis was conducted to characterize the uncertainty of risk calculations to uncertainties in the risk model, the relative biological effectiveness (RBE) of neutrons for carcinogenesis, and inter-patient anatomical variations. ^ The risk projections revealed that proton therapy carries a lower risk for radiogenic second cancer incidence following prostate irradiation compared to IMXT. The sensitivity analysis revealed that the results of the risk analysis depended only weakly on uncertainties in the risk model and inter-patient variations. Second cancer risks were sensitive to changes in the RBE of neutrons. However, the findings of the study were qualitatively consistent for all patient sizes and risk models considered, and for all neutron RBE values less than 100. ^
Resumo:
Objective. To measure the demand for primary care and its associated factors by building and estimating a demand model of primary care in urban settings.^ Data source. Secondary data from 2005 California Health Interview Survey (CHIS 2005), a population-based random-digit dial telephone survey, conducted by the UCLA Center for Health Policy Research in collaboration with the California Department of Health Services, and the Public Health Institute between July 2005 and April 2006.^ Study design. A literature review was done to specify the demand model by identifying relevant predictors and indicators. CHIS 2005 data was utilized for demand estimation.^ Analytical methods. The probit regression was used to estimate the use/non-use equation and the negative binomial regression was applied to the utilization equation with the non-negative integer dependent variable.^ Results. The model included two equations in which the use/non-use equation explained the probability of making a doctor visit in the past twelve months, and the utilization equation estimated the demand for primary conditional on at least one visit. Among independent variables, wage rate and income did not affect the primary care demand whereas age had a negative effect on demand. People with college and graduate educational level were associated with 1.03 (p < 0.05) and 1.58 (p < 0.01) more visits, respectively, compared to those with no formal education. Insurance was significantly and positively related to the demand for primary care (p < 0.01). Need for care variables exhibited positive effects on demand (p < 0.01). Existence of chronic disease was associated with 0.63 more visits, disability status was associated with 1.05 more visits, and people with poor health status had 4.24 more visits than those with excellent health status. ^ Conclusions. The average probability of visiting doctors in the past twelve months was 85% and the average number of visits was 3.45. The study emphasized the importance of need variables in explaining healthcare utilization, as well as the impact of insurance, employment and education on demand. The two-equation model of decision-making, and the probit and negative binomial regression methods, was a useful approach to demand estimation for primary care in urban settings.^
Resumo:
The economic impact of research misconduct in medical research has been unexplored. While research misconduct in publicly funded medical research has increasingly been the object of discussion, public policy debate, government and institutional action, and scientific research, the costs of research misconduct have been unexamined. The author develops a model to estimate the per case cost of research misconduct, specifically the costs of fabrication, falsification, and plagiarism, in publicly funded medical research. Using the database of Research Misconduct Findings maintained by the Office of Research Integrity, Department of Health and Human Services, the model is used to estimate costs of research misconduct in public funded medical research among faculty during the period 2000-2005.^
Resumo:
Interim clinical trial monitoring procedures were motivated by ethical and economic considerations. Classical Brownian motion (Bm) techniques for statistical monitoring of clinical trials were widely used. Conditional power argument and α-spending function based boundary crossing probabilities are popular statistical hypothesis testing procedures under the assumption of Brownian motion. However, it is not rare that the assumptions of Brownian motion are only partially met for trial data. Therefore, I used a more generalized form of stochastic process, called fractional Brownian motion (fBm), to model the test statistics. Fractional Brownian motion does not hold Markov property and future observations depend not only on the present observations but also on the past ones. In this dissertation, we simulated a wide range of fBm data, e.g., H = 0.5 (that is, classical Bm) vs. 0.5< H <1, with treatment effects vs. without treatment effects. Then the performance of conditional power and boundary-crossing based interim analyses were compared by assuming that the data follow Bm or fBm. Our simulation study suggested that the conditional power or boundaries under fBm assumptions are generally higher than those under Bm assumptions when H > 0.5 and also matches better with the empirical results. ^
Resumo:
A Bayesian approach to estimation of the regression coefficients of a multinominal logit model with ordinal scale response categories is presented. A Monte Carlo method is used to construct the posterior distribution of the link function. The link function is treated as an arbitrary scalar function. Then the Gauss-Markov theorem is used to determine a function of the link which produces a random vector of coefficients. The posterior distribution of the random vector of coefficients is used to estimate the regression coefficients. The method described is referred to as a Bayesian generalized least square (BGLS) analysis. Two cases involving multinominal logit models are described. Case I involves a cumulative logit model and Case II involves a proportional-odds model. All inferences about the coefficients for both cases are described in terms of the posterior distribution of the regression coefficients. The results from the BGLS method are compared to maximum likelihood estimates of the regression coefficients. The BGLS method avoids the nonlinear problems encountered when estimating the regression coefficients of a generalized linear model. The method is not complex or computationally intensive. The BGLS method offers several advantages over Bayesian approaches. ^
Resumo:
Investigation into the medical care utilization of elderly Medicare enrollees in an HMO (Kaiser - Portland, Oregon): The specific research topics are: (1) The utilization of medical care by selected determinants such as: place of service, type of service, type of appointment, physician status, physician specialty and number of associated morbidities. (2) The attended prevalence of 3 chronic diseases: hypertension, diabetes and arthritis in addition to pneumonias as an example of acute diseases. The selection of these examples was based on their importance in morbidity/or mortality results among the elderly. The share of these diseases in outpatient and inpatient contacts was examined as an example of the relation between morbidity and medical care utilization. (3) The tendency of individual utilization patterns to persist in subsequent time periods. The concept of contagion or proneness was studied in a period of 2 years. Fitting the negative binomial and the Poisson distributions was applied to the utilization in the 2nd year conditional on that in the 1st year as regards outpatient and inpatient contacts.^ The present research is based on a longitudinal study of 20% random sample of elderly Medicare enrollees. The sample size is 1683 individuals during the period from August 1980-December 1982.^ The results of the research were: (1) The distribution of contacts by selected determinants did not reveal a consistent pattern between sexes and age groups. (2) The attended prevalence of hypertension and arthritis showed excess prevalence among females. For diabetes and pneumonias no female excess was noticed. Consistent increased prevalence with increasing age was not detected.^ There were important findings pertaining to the relatively big share of the combined 3 chronic diseases in utilization. They accounted for 20% of male outpatient contacts vs. 25% of female outpatients. For inpatient contacts, they consumed 20% in case of males vs. 24% in case of females. (3) Finding that the negative binomial distribution fit the utilization experience supported the research hypothesis concerning the concept of contagion in utilization. This important finding can be helpful in estimating liability functions needed for forecasting future utilization according to previous experience. Such information has its relevance to organization, administration and planning for medical care in general. (Abstract shortened with permission of author.) ^