incidence density formula

concluded that some modeling approaches are better suited to investigating the etiology of a disease, whereas others provide a better synthesis in terms of an individual's outcome. However, at least the proportional hazards assumption appears to hold rather well because both curves in panel C of Figure 4 are approximately linear, indicating that the event-specific ID analysis here is reasonable. Results are in line with the semiparametric analyses of Beyersmann et al. There are 3 subtypes of prevalence: This function constructs confidence intervals for incidence rate differences and ratios where there are two exposures (i.e. Generally, prevalence is expressed as a fraction, percentage or the number of cases per 10.000 or 100.000 people in a population. (11) recently pointed out the relevance of competing risks in epidemiologic studies. Incidence density can be useful when dealing with a dynamic population, allowing you to include additional participants during the study. That is, in a more involved regression setup, one would need to compute the individual ID predictions, which could then be averaged and subsequently used in the multistate-type graphic. Among recorded covariates were history of injection drug use at enrollment, age, CD4 nadir, and race. To judge the performance of the estimates, nonparametric Aalen-Johansen estimates for bloodstream infection (thick step curves) and corresponding log-log transformed 95% confidence intervals (thin step curves) are also depicted. For full access to this pdf, sign in to an existing account, or purchase an annual subscription. of people in the population on this date In this case, when performing an ID analysis, the competing risks should be accounted for separately, meaning that event-specific IDs should be calculated, which is rarely found in the literature (refer, for example, to Glynn and Rosner (2) and Dignam and Kocherginsky (10)). The following figure shows when participants enter or leave the study, and for each participant the person-time is calculated on the right side. Copyright © 2000-2020 StatsDirect Limited, all rights reserved. (15), and Fine and Gray (26) discuss assessing a potential covariate effect on the subdistribution hazard λ(t), which is implicitly defined by a 1-to-1 relation with the CIF, ⁠. C) Goodness-of-fit plot for HAART and AIDS/death. The aim of the study was to assess the impact of HIV infection on US women. Search for other works by this author on: In assuming the event-specific hazards to be, However, although parametric survival analysis provides a powerful tool (refer, for example, to Cox et al.

you use a population-based disease registry to identify all new cases of disease during a defined time period. Menu location: Analysis_Rates_Compare Two Crude Rates. A total of 913 (56.5%) of 1,616 patients received allogeneic transplants, of whom 193 (21.1%) acquired bloodstream infection; of the patients with an autologous transplant, 126 (17.9%) acquired bloodstream infection. Racial Disparities in Health among College Educated African-Americans: Can HBCU Attendance Reduce the Risk of Metabolic Syndrome in Midlife? (11, refer to Figure 3 or Table 4) report a time-averaged effect on HAART-CIF based on either a proportional subdistribution hazards model or their parametric mixture model for nonproportional hazards (with subsequent averaging). Under a constant hazards assumption, IDs are the standard maximum likelihood estimators. Whenever all event-specific IDs and an estimate of the censoring survival probability (33) are available, the least false parameter can be estimated numerically by plugging in the respective estimates and using, for example, the function uniroot of the software environment for statistical computing R (17); the respective R code is provided in the Web material. of disease onsets sum of person-time no. Incidence-density sampled controls may be matched with cases on various demographic characteristics such as age, sex, year of diagnosis of disease, or initiation of a … Lifetime prevalence: The proportion of a population that at some point during their life have experienced the disease/condition.

of disease onsets ≅ N⋅∆t Prevalence = no. Researchers next calculate the IR (also known as incidence density), which reflects variation in the lengths of time that at-risk individuals are observed. Compared with the bloodstream-infection ID, the competing end-of-neutropenia ID is much more pronounced, especially for the autologous groups. ONKO-KISS considers patients with hematologic malignancies who have undergone peripheral blood stem cell transplantation. Details are given elsewhere (11, 16).

The Nelson-Aalen estimates of the cumulative event-specific hazards (Figure 4, panel B), especially for HAART, show a slight time-dependent course.

For example, event times are often left-truncated if the time scale of interest is age. Incidence rates and prevalence proportions are commonly used to express the populations health status. However, it is also questionable because of potentially nonconstant hazards; piecewise IDs (32) or even semiparametric approaches, for example, proportional hazards models (23), might be preferred. Still, the subdistribution analysis offers a summary analysis in that it estimates the least false parameter, a time-averaged effect on the cumulative event probabilities (27–30). This paper is organized as follows: The next section introduces competing risks and expands on the parametric approach using event-specific IDs that allow one to perform further inference easily. (2).

Lau et al. The aged hematopoietic system promotes hippocampal-dependent cognitive decline.

(11), we considered the study sample of 1,164 women who were alive, infected with HIV, and free of clinical AIDS on December 6, 1995 (baseline), the day on which the first protease inhibitor was approved by the US Federal Drug Administration. It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide, This PDF is available to Subscribers Only.

Competing events and even more complex event patterns may be adequately addressed with the suggested methodology.

AIDS, acquired immunodeficiency syndrome; HAART, highly active antiretroviral therapy; HIV, human immunodeficiency virus; IDU, injection drug use. Is there an association between nosocomial infection rates and bacterial cross transmissions? In addition, Poisson regression models may be used in a person-time setting, which will typically provide maximum likelihood estimates that closely agree with those of the Cox model if the baseline event-specific hazards are assumed to be piecewise constant (9, 24, 25). They suggest a simple multistate-type graphic based on IDs, which immediately displays the competing event situation. American Journal of Epidemiology © The Author 2010.

Person-time data from prospective studies of two groups with different exposures may be expressed as a difference between incidence rates or as a ratio of incidence rates.. IR is especially useful in hospital surveillance, where patients may enter and leave the surveillance at varying times (e.g., patients may be lost to follow up or die from a cause other than that being studied). By assuming event-specific IDs to hold, the Cox model for the subdistribution hazard is generally misspecified. Poisson distribution and test-based methods are used to construct the confidence intervals (Sahai and Kurshid, 1996): - where IRD hat and IRR hat are point estimates of incidence rate difference and ratio respectively, m is the total number of events observed, PT is the total person-time observed, Z is a quantile of the standard normal distribution and F is a quantile of the F distribution (denominator degrees of freedom are quoted last). Examples include studies of cardiovascular diseases (1, 2), human immunodeficiency virus (HIV) infection (3), and hospital-acquired infection (4–6). and Barkan et al. When dealing with competing risks, it is important to analyze event-specific IDs for every event instead of considering just the ID of interest. (11)), in which an ID analysis even offers good quantitative insight in terms of a time-averaged effect on the CIF. Because patients may also leave the critical phase without a prior bloodstream infection, either alive or dead, this constitutes a competing risks setting.

Events per person-time (incidence rate): a misleading statistic? Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health. During this 6 year period, additional participants enter our population and are included in our study. Oxford University Press is a department of the University of Oxford. Thus, the follow up period does not have to be uniform for all participants. exposed or not exposed, defined according to certain risk factors) (Sahai and Kurshid, 1996). To illustrate this analysis, we perform a second competing risks analysis, considering data from the Women's Interagency HIV Study on HIV-infected US women (refer, for example, to Lau et al. Examples include studies of cardiovascular diseases (1, 2), human immunodeficiency virus (HIV) infection , and hospital-acquired infection . C:\DATA\HS161\formulas.wpd January 17, 2003 Page 2 Risk = Cumulative Incidence = no. Combined, these individuals contributed to 410 days of person days at risk (person-time). (This graphic is part of the worked example outlined in the supplementary material posted on the Journal's Web site (http://aje.oupjournals.org/).). As with the case-cohort design, . We look at how long someone has been ‘at risk’ during the timespan of a study. However, there are situations in which the presence of competing events obscures the analysis more than nonconstant hazards do. However, for some diseases it is possible that the same person contracts the disease multiple times during the timespan of the study (e.g. IDs are attractive because they are computationally simple and allow for right-censoring as well as left-truncation (7). The cumulative incidence is then 34 cases per 1000 persons per two years, i.e. The subdistribution hazard is build such that it directly relates to the CIF for the event of interest. There are 3 subtypes of prevalence: Using this formula, incidence is expressed as the number of new cases per 100 people in the population in time period P. Cumulative incidence is also frequently expressed as the number of new cases per 1.000, 10.000 or even 100.000 people in the population in time period P. DG Sante, Chafea and the third EU Health Programme, The internal market and free movement of goods.

Because of this latter fact, the ID-based CIF estimates are close to the Aalen-Johansen estimates. Furthermore, all members of a population have to be ‘at risk’ at T = 0 (time), so we exclude all prevalent cases at T = 0 (people that already have the disease at T = 0 are excluded in incidence counts). Following Lau et al. B) Estimated cumulative event-specific hazards for BSI (lower 2 curves) and end of neutropenia (EndNP; upper 2 curves) for each transplant type. The following statistical analysis concentrates on the effect of injection drug use on time until initiation of HAART without prior occurrence of clinical AIDS.

For instance, quite differential effects on the CIF for the event of interest can be observed in the ONKO-KISS study (13, 14), our first application example. Wiley series in probability and mathematical statistics.

and that subjects entering the population during the evaluation period are not included in the evaluation. Finally, we close with a discussion. (15), who found similar effects of female gender and allogeneic transplants on the ID for bloodstream infection but observed quite differential effects on the CIF for the event of interest because of different effects on the competing IDs.

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