In this paper, we examine comparative analysis of rates with a view to each of the usual comparative parameters-rate difference (RD), rate ratio (RR) and odds ratio (OR)-and with particular reference to first principles. For RD and RR we show the prevailing statistical practices to be rather poor. We stress the need for restricted estimation of variance in the chi-square function underlying interval estimation (and also point estimation and hypothesis testing). For RR analysis we propose a chi-square formulation analogous to that for RD and, thus, one which obviates the present practice of log transformation and its associated use of Taylor series approximation of the variance. As for OR analysis, we emphasize that the chi-square function, introduced by Cornfield for unstratified data, and extended by Gart to the case of stratified analysis, is based on the efficient score and thus embodies its optimality properties. We provide simulation results to evince the better performance of the proposed (parameter-constrained) procedures over the traditional ones.
Proportion of disease caused or prevented by a given exposure, trait or intervention. Am J Epidemiol 99: 325-332, 1974.-The structures of two epidemiologic parameters are explored. One, the "etiologic fraction." relates to markers of increased risk, and it is the proportion of disease attributable to the marker and/or to factors associated with it. The other, the "prevented fraction," is the equivalent of this for a marker of reduced risk. It is shown that both parameters depend-in different ways-on the frequency of the marker among cases of the disease, and on the "standardized morbidity ratio" for those with the marker. Point estimation of these parameters is often straightforward , particularly in case-control studies. biometry; epidemiologic methods
The concepts that case-referent studies provide for the estimation of "relative risk" only if the illness is "rare", and that the rates and risks themselves are inestimable, are overly superficial and restrictve. The ratio of incidence densities (forces of morbidity)-and thereby the instantaneous risk-ratio-is estimable without any rarity-assumption. Long-term risk-ratio can be computed through the coupling of case-referent data on exposure rates for various age-categories with estimates, possibly from the study itself, or the corresponding age-specific incidence-densities for the exposed and nonexposed combined-but again, no rarity-assumption is involved. Such data also provide for the assessment of exposure-specific absolute incidence-rates and risks. Point estimation of the various parameters can be based on simple relationships among them, and in interval estimation it is sufficient simply to couple the point estimate with the value of the chi square statistic used in significance testing.
In 55 Sprague-Dawley rats (mean wt, 277 +/- 6.2 g) exposed to hypobaric hypoxia (air at 380 mmHg), and 23 weight-matched controls kept in room air, pulmonary and systemic artery pressures were measured daily for 2 wk via indwelling catheters. After each day of exposure, 1 or 2 hypoxic rats, to a total of 20, and 5 control rats were killed during the experiment. In these rats, the pulmonary arterial tree was injected post mortem with barium-gelatin and inflated with formaldehyde solution, and three structural features were quantified microscopically: 1) abnormal extension of muscle into peripheral arteries where it is not normally present (EMPA); 2) increased wall thickness of the normally muscular arteries, expressed as a percentage of external diameter (%WT); and 3) reduction in artery number expressed as an increase in the ratio of alveoli to arteries (A/a). Mean pulmonary artery pressure (Ppa) rose significantly after day 3 of hypoxic exposure (P less than 0.05) and had doubled by day 14; the mean systemic artery pressure (Psa) of hypoxic rats and Ppa and Psa of control rats were unchanged. The level of Ppa correlated with the degree of structural changes; for EMPA, r = 0.84; for %WT, r = 0.64; and for A/a, r = 0.73 (P less than 0.001 in all.
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