Does Breast Feeding Protect from Development of Breast Disease?
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We retrospectively analyzed the data base of the breast unit at King Fahd Hospital from January 2000 till May 2012. We calculated proportions with 95% confidence intervals (CI) and used Logistic regression analysis to explore the predictors. Odds ratios with 95% CI were reported and p value of 0.05 was considered for significance.Keywords:
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Objectives: The goal of this study was to describe hospitalizations of infants during the first year of life according to week of gestational age (GA). We hypothesized that odds of any hospitalization would generally decrease with increasing GA, with late preterm infants experiencing additional increased risk of specific hospitalizations, such as hyperbilirubinemia. Methods: Birth certificates for >6.6 million infants born in California hospitals between 1993 and 2005 and surviving to discharge were linked to hospital discharge records during the first year of life. Odds of any hospitalization and any hospitalization for specific diagnoses during the first year of life were determined for infants 23 to 44 weeks’ GA. Further analysis determined odds of any hospitalization within 14, 30, and 90 days of birth discharge, and observed odds were compared with expected odds obtained through quadratic modeling. Results: Odds of any hospitalization within the first year of life decreased with advancing GA, but observed odds of any hospitalization exceeded expected odds for 35-, 36-, and 37-week GA infants for all time periods after discharge. Odds of any hospitalization for hyperbilirubinemia were greatest for infants 33 to 38 weeks’ GA (peak odds ratio at 36 weeks’ GA: 2.86 [95% confidence interval: 2.73–3.00]), and a relative peak in odds of any hospitalization for specific infections was observed among infants 33 to 36 weeks’ GA. Conclusions: Odds of any hospitalization during the first year of life exceeded expected odds of hospitalization for 35-, 36-, and 37-week GA infants. GAs at risk overlapped with, but were not identical to, GAs identified as late preterm infants.
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In reporting results of case-control studies, odds ratios are useful methods of reporting findings. However, odds ratios are often misinterpreted in the literature and by general readers.We searched all original articles which were published in the Korean Journal of Family Medicine from 1980 to May 2011 and identified those that report "odds ratios." Misinterpretation of odds ratios as relative risks has been identified. Estimated risk ratios were calculated when possible and compared with odds ratios.One hundred and twenty-eight articles using odds ratios were identified. Among those, 122 articles were analyzed for the frequency of misinterpretation of odds ratios as relative risks. Twenty-two reports out of these 122 articles misinterpreted odds ratios as relative risks. The percentage of misinterpreting reports decreased over years. Seventy-seven reports were analyzed to compare the estimated risk ratios with odds ratios. In most of these articles, odds ratios were greater than estimated risk ratios, 60% of which had larger than 20% standardized differences.In reports published in the Korean Journal of Family Medicine, odds ratios are frequently used. They were misinterpreted in part of the reports, although decreasing trends over years were observed.
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The odds for the occurrence of an event (e.g. a particular disease) is the ratio of the probability that the event will occur and the probability that the event will not occur. The odds ratio for an event is the ratio of two odds for the occurrence of that event (e.g. for persons who have been exposed to a particular risk factor versus persons who have not been exposed). The odds ratio is a frequently applied measure of association in case control research. However, the odds ratio is not readily understandable. In case of a rare event (e.g. a rare disease) the odds ratio can be interpreted as a relative risk which is easier to understand (i.e. the factor with which the risk of disease increases in people exposed to a certain condition).
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In the world of public health and medicine, researchers are often trying to discover new ways of understanding and preventing diseases and other negative health outcomes. When public health researchers want to examine the relationship between some sort of exposure, like smoking, and a disease, such as lung cancer, they will often start by calculating what is called an odds ratio. An odds ratio is a comparison of odds between people who were exposed and people who were not exposed. However, odds ratios can be tricky to understand, even for experienced researchers. In this article, we will break down the odds ratio by reviewing the concepts and calculations of probability and odds. We will also discuss how to interpret an odds ratio, and how these ratios can be useful in real-world applications.
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OBJECTIVE: To determine whether high patient inflow volumes to an intensive care unit are associated with unplanned readmissions to the unit.DESIGN: Retrospective comparative analysis.SETTING: The setting is a large urban tertiary care academic medical center.PATIENTS: Patients (n = 3233) discharged from an adult neurosciences critical care unit to a lower level of care from January 1, 2006 through November 30, 2007.INTERVENTIONS: None.MEASUREMENTS AND MAIN RESULTS: The main outcome variable is unplanned patient readmission to the neurosciences critical care unit within 72 hrs of discharge to a lower level of care. The odds of one or more discharges becoming an unplanned readmission within 72 hrs were nearly two and a half times higher on days when > or =9 patients were admitted to the neurosciences critical care unit (odds ratio, 2.43; 95% confidence interval, 1.39-4.26) compared with days with < or =8 admissions. The odds of readmission were nearly five times higher on days when > or =10 patients were admitted (odds ratio, 4.99; 95% confidence interval, 2.45-10.17) compared with days with < or =9 admissions. Adjusting for patient complexity, the odds of an unplanned readmission were 2.34 times higher for patients discharged to a lower level of care on days with > or =10 admissions to the neurosciences critical care unit (odds ratio, 2.34; 95% confidence interval, 1.27-4.34) compared with similar patients discharged on days of < or =9 admissions.CONCLUSIONS: Days of high patient inflow volumes to the unit were associated significantly with subsequent unplanned readmissions to the unit. Furthermore, the data indicate a possible dose-response relationship between intensive care unit inflow and patient outcomes. Further research is needed to understand how to defend against this risk for readmission. PMID: 19866504
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Odds ratios are commonly presented in the medical literature, including dermatology journals. Even when used appropriately, odds ratios are often difficult to interpret. This article illustrates this problem using an example from the recent dermatology literature. It then reviews the definitions of odds and odds ratio, as well as how odds and odds ratio relate to probability and relative risk. The divergence of odds ratios from relative risks when events are common (occurring in > or =10% of a sample) is explained. Methods to convert odds ratios to relative risks (and the reasons why conversion should be considered) are discussed.
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In Brief Odds and odds ratios are hard for many clinicians to understand. Odds are the probability of an event occurring divided by the probability of the event not occurring. An odds ratio is the odds of the event in one group, for example, those exposed to a drug, divided by the odds in another group not exposed. Odds ratios always exaggerate the true relative risk to some degree. When the probability of the disease is low (for example, less than 10%), the odds ratio approximates the true relative risk. As the event becomes more common, the exaggeration grows, and the odds ratio no longer is a useful proxy for the relative risk. Although the odds ratio is always a valid measure of association, it is not always a good substitute for the relative risk. Because of the difficulty in understanding odds ratios, their use should probably be limited to case-control studies and logistic regression, for which odds ratios are the proper measures of association. Odds ratios are difficult to understand and are often inappropriately used as proxies for relative risks when describing research results.
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The odds ratio and the risk ratio are related measures of relative risk. The risk ratio is easier to understand and interpret, but, for mathematical reasons, the odds ratio appears more frequently in the medical literature. When the outcome is rare, odds ratios and risk ratios have similar values and can be used interchangeably. However, when the outcome is common, odds ratios should not be interpreted as risk ratios because doing so can greatly exaggerate the size of an effect. This column explains what odds ratios are, how to correctly interpret them, and how to avoid being misled by them. A risk is just the probability of an event happening (in a defined time period). An odds is the risk of an event happening divided by the risk of it not happening. Odds are frequently used in gambling, for example, if a sports team is believed to have a 1 in 5 probability of winning (.20), then the odds are 1 to 4 (.25), or 1 win for every 4 losses. More examples are given in Table 1. When viewed as a fraction, an odds is always bigger than its corresponding risk (eg, 1/999 > 1/1000). Small risks and odds are close in value (eg, 1/1000 versus 1/999), but large risks and odds can be quite different (eg, 9/10 versus 9/1). When a study has a binary outcome (eg, disease or no disease), then investigators can calculate risk ratios and odds ratios. Risk and odds ratios are calculated by using either cumulative risk (from longitudinal studies) or prevalence (from cross-sectional studies). The risk ratio gives the relative increase or decrease in the risk (or prevalence) of the outcome given a particular exposure or treatment; the odds ratio is similar but gives the relative increase or decrease in the odds. The risk ratio divides the risk (or prevalence) in an exposed group by the risk in a reference group. For example, in a longitudinal study, if 50% of heavy drinkers develop hypertension, then the cumulative risk of hypertension in this group is estimated as 50%. (Or, in a cross-sectional study, if 50% of heavy drinkers have hypertension already, then the prevalence of hypertension in this group is estimated as 50%.) If the risk of hypertension in nondrinkers from the same study is 25%, then the risk ratio is RR = ; interpretation: drinkers have twice the risk of hypertension as nondrinkers (a 100% increase in risk). Alternatively, we could calculate the risk ratio by comparing nondrinkers to drinkers: RR = ; that is, nondrinkers have half the risk of hypertension as drinkers (a 50% decrease in risk). The odds ratio divides the odds in the exposed group by the odds in the reference group. For our hypothetical example, the odds of hypertension for drinkers is 50%/50% or 1 to 1; and the odds for nondrinkers is 25%/75% or 1 to 3; thus, the odds ratio is OR = , or, equivalently, OR = . This means that drinkers have 3 times the odds of nondrinkers (a 200% increase in odds). Alternatively, the odds ratio that compares nondrinkers with drinkers is: OR = ; that is, nondrinkers have one-third the odds of drinkers (a 66.7% decrease in odds). Note that, if these odds ratios were misinterpreted as risk ratios, then they would overestimate the size of the effect, as we have already seen, risk is doubled, not tripled in drinkers (or cut by half, not by two-thirds for nondrinkers). In this hypothetical example, the distortion is clear because the risk ratio is available; but often, only the odds ratio is available (for reasons explained below). Why are odds ratios used at all when risk ratios are easier to understand? The main reason is that logistic regression, the multivariate regression technique for modeling binary outcomes, yields odds ratios, not risk ratios. (Odds have better mathematical properties for regression modeling; for example, odds can range from zero to infinity, whereas risks can only range from 0 to 1.) By using logistic regression, investigators can adjust for confounding, examine the effects of multiple predictors simultaneously, and quantify the effects of continuous predictors. Because most investigators want to take advantage of this powerful technique, they wind up reporting odds ratios rather than risk ratios. Odds ratios are also valid in certain situations when risk ratios are not, such as in case-control studies. models the ln(odds), the natural log of the odds, of the outcome as a function of predictors; estimates adjusted odds ratios for these predictors. investigators recruit participants who already have a disease and controls without the disease. Because participants are selected based on their disease status, it is not possible to calculate the risk of disease. Odds ratios are always a distortion of their corresponding risk ratios. The extent of the distortion depends on the frequency of the outcome under study and the size of the effect (see In-Depth box for mathematical details). When the outcome is rare, the distortion is small; in this case, the odds ratio provides a good approximation of the risk ratio and can be interpreted as such. But, when the outcome is common, the distortion can be large and the odds ratio should not be interpreted as a risk ratio. Larger effect sizes (bigger differences between the groups) also magnify the distortion. These relationships are graphically illustrated in Figure 1. As a general rule of thumb, it is acceptable to interpret the odds ratio as a risk ratio when the risk (or prevalence) of the outcome in the reference group is less than 10% [1, 2]. In most cases, the odds ratio and risk ratio are similar when the outcome is this rare (Figure 1). Illustration of the distortion between the odds ratio and the risk ratio (RR). The solid black arrows give one example of how to read the graphic. When the prevalence is 25% and the risk ratio is 2.0 (as in the hypothetical hypertension example), then the odds ratio will be 3.0. The area to the left of the dashed line represents the region in which outcomes are considered rare (less than 10%), the odds ratio and risk ratio are similar in this region for most effect sizes. Reproduced with permission from Reference 1. When outcomes are common, the odds ratio should not be interpreted as a risk ratio or this can result in misleading and erroneous statements, as illustrated by the examples that follow (summarized in Table 2). Vgontzas et al [3] performed a cross-sectional study that looked at the relationship between sleep characteristics and hypertension. After adjusting for potential confounders by using logistic regression, they found strong associations between sleep problems and hypertension. The odds ratios for hypertension in the 2 highest-risk sleep groups (insomniacs who slept ≤5 hours or 5-6 hours per night) compared with the reference group (good sleepers) were 5.12 and 3.53, respectively. The investigators concluded that these groups have a "risk of hypertension 500% or 350% higher" than the reference group; and this interpretation was widely repeated in media coverage of the study. However, it is easy to see that this exaggerates the effect. The reference group had a hypertension prevalence of about 25%; thus; a 5-fold higher risk would put the prevalence of hypertension in the highest-risk group at 125%, a clear impossibility. For cross-sectional and cohort studies, one can convert an odds ratio from logistic regression into an estimate of the risk ratio by using a simple formula [1]. Here, the odds ratios, 5.12 and 3.53, translate into risk ratios of 2.5 and 2.2, respectively. Thus, risk is doubled, not quintupled or tripled [4]. As another example, take a cross-sectional study that looked at the relationship between smoking and wrinkles [5]. After adjusting for potential confounders by using logistic regression, the investigators found a strong relationship between a history of heavy smoking and the presence of prominent facial wrinkling. The odds ratio that compared heavy smokers to nonsmokers was 3.92. The investigators concluded that a heavy smoker "has 3.92 times the risk of developing prominent wrinkles as does a nonsmoker." However, because 45% of the nonsmoker group had prominent wrinkles, this would put the prevalence in the heavy smoker group at a nonsensical 180%. I estimate that the risk ratio is actually about 1.7. So, risk is increased 70%, still a large and important amount but not as dramatic as a 290% increase. A few simple tricks can help readers spot misleading odds ratios. These work only for study designs in which it is possible to directly calculate risk (or prevalence), such as cohort or cross-sectional studies. The risk ratio always has a maximum possible value. For example, if the risk in the reference group is 50%, then risk cannot be more than doubled; otherwise, the exposed group will have a risk greater than 100% (see Table 3 for more examples). In the wrinkles study, because the prevalence of wrinkles is about 45% in nonsmokers, the maximum possible risk ratio is 100%/45% = 2.2. Because the odds ratio (3.92) exceeds this value, it likely greatly overestimates the risk ratio. Investigators often fail to provide readers with the risk in the reference group, but it is usually possible to (roughly) estimate this value from other data in the article. Investigators should report the absolute risk of the outcome in the different groups under study. Although not adjusted for confounders, these values will give readers a sense of the magnitude of the effect, both in relative and absolute terms. For example, if the prevalence of hypertension is 20% in reference group and 35% in the exposed group, then the unadjusted risk ratio is 1.75, and the increase in risk is likely to be in this vicinity, even after adjusting for confounding. Furthermore, the absolute risk difference is 15% (35% versus 20%), arguably a more informative number than the relative risk. Unfortunately, investigators often omit this information (it was not given in the articles described above), and it may be difficult to estimate directly. When a study has a binary outcome, investigators typically use logistic regression to analyze the data. Logistic regression yields odds ratios. If the outcome is rare (occurring in less than 10% of the reference group), then the odds ratio closely approximates the risk ratio and can be interpreted as a relative increase or decrease in risk. However, if the outcome is common, as is the case for many studies in physiatry, then interpreting odds ratios as risk ratios can lead to exaggerated statements about the size of the effect. To avoid being misled, readers may use a simple formula to convert odds ratios into approximate adjusted risk ratios. They should also look for information on absolute risks, which are often more informative than relative risks.
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Background: Studies about the influence of patient characteristics on mechanical failure of cups in total hip replacement have applied different methodologies and revealed inconclusive results. The fixation mode has rarely been investigated. Therefore, we conducted a detailed analysis of the influence of patient characteristics and fixation mode on cup failure risks. Methods: We conducted a case-control study of total hip arthroplasties in 4420 patients to test our hypothesis that patient characteristics of sex, age, weight, body mass index, and diagnosis have different influences on risks for early mechanical failure in cemented and uncemented cups. Results: Women had significantly reduced odds for failure of cups with cemented fixation (odds ratio = 0.59; 95% confidence interval, 0.43 to 0.83; p = 0.002) and uncemented fixation (odds ratio = 0.63; 95% confidence interval, 0.5 to 0.81; p = 0.0003) compared with that for men (odds ratio = 1). Each additional year of patient age at the time of surgery reduced the failure odds by a factor of 0.98 for both cemented cups (odds ratio = 0.98; 95% confidence interval, 0.96 to 0.99; p = 0.016) and uncemented cups (odds ratio = 0.98; 95% confidence interval, 0.97 to 0.99; p = 0.0002). In patients with cemented cups, the weight group of 73 to 82 kg had significantly lower failure odds (odds ratio = 0.63; 95% confidence interval, 0.4 to 0.98) than the lightest (<64 kg) weight group or the heaviest (>82 kg) weight group (odds ratios = 1.00 and 1.07, respectively). No significant effects of weight were noted in the uncemented group. In contrast, obese patients (a body mass index of >30 kg/m2) with uncemented cups had significantly elevated odds relative to patients with a body mass of <25 kg/m2 (odds ratio = 1.41; 95% confidence interval, 1.03 to 1.91) for early failure of the cups compared with an insignificant effect in the cemented arm of the study. Compared with osteoarthritis as the reference diagnosis (odds ratio = 1), developmental dysplasia (odds ratio = 0.52; 95% confidence interval, 0.28 to 0.97) and hip fracture (odds ratio = 0.38; 95% confidence interval, 0.16 to 0.92) were significantly protective in cemented cups. Conclusions: Female sex and older age have similarly protective effects on the odds for early failure of cemented and uncemented cups. Although a certain body-weight range has a significant protective effect in cemented cups, the more important finding was the significantly increased risk for failure of uncemented cups in obese patients. Patients with developmental dysplasia and hip fracture were the only diagnostic groups with a significantly decreased risk for cup failure, but only with cemented fixation. Level of Evidence: Therapeutic Level III. See Instructions to Authors for a complete description of levels of evidence.
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