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By: X. Marcus, M.B.A., M.D.

Co-Director, Indiana University School of Medicine However muscle relaxant xanax discount mestinon 60mg on line, the greater incidence of cancer in individuals exposed to known carcinogens indicates that the probability or risk of developing cancer is in- creased by exposure muscle spasms 8 weeks pregnant purchase mestinon overnight delivery. Compared to unexposed individuals spasms left shoulder blade cheap mestinon 60 mg free shipping, the elevated risks of exposed individuals are manifest by increased cancer rates in the latter group spasms posterior knee buy mestinon master card. Risks and rates are the basic measures used to compare disease occurrence in exposed and unexposed individuals. This section describes rates and risks and their relationship to one another as a prelude to the sections on modeling and model fitting. Incidence Rate A common measure of disease occurrence used in cancer epidemiology is the incidence rate. Incidence refers to new cases of disease occurring among previously unaffected individuals. The population incidence rate is the number of new cases of the disease occurring in the population in a specified time interval divided by the sum of observation times, in that interval, on all individuals who were disease free at the beginning of the time interval. In general an incidence rate is time dependent and depends on both the starting point and the length of the interval. With data from studies in which subjects are followed over time, incidence rates can be estimated by partitioning the following period into intervals of lengths Lj having midpoints tj for j = 1. Let nj denote the number of individuals who are disease free and still under observation at time tj, and dj the number of new diagnoses during the jth interval. An estimate of the incidence rate at time tj is obtained by dividing dj by the product of nj and Lj: dj ^ (t j ) =. As with the incidence rate, risk is time dependent and depends on both the starting point and the length of the interval. The risk of first disease occurrence in the interval (t, t + h), given no previous occurrence, is the conditional probability p(t, t + h) = F (t + h ) - F (t ). For the longitudinal follow-up study estimates defined above, the relationship is manifest by the equation ^ ^ p(t ) = (t ) L. However, the development of a general theory of risk and risk estimation requires definitions of rates and risks that are not tied to particular types of studies or methods of estimation. Probability models provide a mathematical framework for studying incidence rates and risks and also are used in defining statistical methods of estimation depending on the type of study and the data available. Models for studying the relationship between disease and exposure are usually formulated in terms of the instantaneous incidence rate, which is the theoretical counterpart of the incidence rate estimate defined below. The instantaneous incident rate is defined in terms of the probability distribution function F(t) of the time to disease occurrence. That is, F(t) represents the probability that an individual develops the disease of interest in the interval of time (0, t). Two functions derived from F(t) are used to define the instantaneous incidence rate. The second is the probability density function, which is the derivative of F(t) with respect to t, that is, f(t) = (d / dt)F(t), and measures the rate of increase in F(t). The instantaneous incidence rate, also known as the hazard function, is the ratio f (t ). This approximation is the theoretical counterpart of the relationship between risks and rates described in the discussion of risk. In the remainder of this chapter, incidence rate means instantaneous incidence rate unless explicitly noted otherwise. Incidence Rates and Excess Risks It is clear that the incidence rate plays an important role in the stochastic modeling of disease occurrence.

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