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. ^

Penetrating injuries of the thorax and abdomen: Type of medical-care institution and case fatality

The purpose of this study was to determine, for penetrating injuries (gunshot, stab) of the chest/abdomen, the impact on fatality of treatment in trauma centers and shock trauma units compared with general hospitals. Medical records of all cases of penetrating injury limited to chest/abdomen and admitted to and discharged from 7 study facilities in Baltimore city 1979-1980 (n = 581) were studied: 4 general hospitals (n = 241), 2 area-wide trauma centers (n = 298), and a shock trauma unit (n = 42). Emergency center and transferred cases were not studied. Anatomical injury severity, measured by modified Injury Severity Score (mISS), was a significant prognostic factor for death, as were cardiovascular shock (SBP $\le$ 70), injury type (gunshot vs stab), and ambulance/helicopter (vs other) transport. All deaths occurred in cases with two or more prognostic factors. Unadjusted relative risks of death compared with general hospitals were 4.3 (95% confidence interval = 2.2, 8.4) for shock trauma and 0.8 (0.4, 1.7) for trauma centers. Controlling for prognostic factors by logistic regression resulted in these relative risks: shock trauma 4.0 (0.7, 22.2), and trauma centers 0.8 (0.2, 3.2). Factors significantly associated with increased risk had the following relative risks by multiple logistic regression: SBP $\le$ 70 (RR = 40.7 (11.0, 148.7)), highest mISS (42 (7.7, 227)), gunshot (8.4 (2.1, 32.6)), and ambulance/helicopter transport (17.2 (1.3, 228.1)). Controlling for age, race, and gender did not alter results significantly. Actual deaths compared with deaths predicted from a multivariable model of general-hospital cases showed 3.7 more than predicted deaths in shock trauma (SMR = 1.6 (0.8, 2.9)) and 0.7 more than predicted deaths in area-wide trauma centers (SMR = 1.05 (0.6, 1.7)). Selection bias due to exclusion of transfers and emergency center cases, and residual confounding due to insufficient injury information, may account for persistence of adjusted high case fatality in shock trauma. Studying all cases prospectively, including emergency center and transferred cases, is needed. ^

REGRESSION ANALYSIS FOR STANDARDIZED MORTALITY RATIOS WITH APPLICATION TO OCCUPATIONAL FOLLOW-UP STUDIES

Traditional comparison of standardized mortality ratios (SMRs) can be misleading if the age-specific mortality ratios are not homogeneous. For this reason, a regression model has been developed which incorporates the mortality ratio as a function of age. This model is then applied to mortality data from an occupational cohort study. The nature of the occupational data necessitates the investigation of mortality ratios which increase with age. These occupational data are used primarily to illustrate and develop the statistical methodology.^ The age-specific mortality ratio (MR) for the covariates of interest can be written as MR(,ij...m) = ((mu)(,ij...m)/(theta)(,ij...m)) = r(.)exp (Z('')(,ij...m)(beta)) where (mu)(,ij...m) and (theta)(,ij...m) denote the force of mortality in the study and chosen standard populations in the ij...m('th) stratum, respectively, r is the intercept, Z(,ij...m) is the vector of covariables associated with the i('th) age interval, and (beta) is a vector of regression coefficients associated with these covariables. A Newton-Raphson iterative procedure has been used for determining the maximum likelihood estimates of the regression coefficients.^ This model provides a statistical method for a logical and easily interpretable explanation of an occupational cohort mortality experience. Since it gives a reasonable fit to the mortality data, it can also be concluded that the model is fairly realistic. The traditional statistical method for the analysis of occupational cohort mortality data is to present a summary index such as the SMR under the assumption of constant (homogeneous) age-specific mortality ratios. Since the mortality ratios for occupational groups usually increase with age, the homogeneity assumption of the age-specific mortality ratios is often untenable. The traditional method of comparing SMRs under the homogeneity assumption is a special case of this model, without age as a covariate.^ This model also provides a statistical technique to evaluate the relative risk between two SMRs or a dose-response relationship among several SMRs. The model presented has application in the medical, demographic and epidemiologic areas. The methods developed in this thesis are suitable for future analyses of mortality or morbidity data when the age-specific mortality/morbidity experience is a function of age or when there is an interaction effect between confounding variables needs to be evaluated. ^