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20.02.2016
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Natural Resource Management: How do I estimate the odds ratio and confidence intervals from model-averaged estimates? I'm currently working on a model selection analysis in the field of natural resource management. How do you calculate the odds ratio and confidence intervals given that these estimates were derived from model-averaging and the typical code exp(cbind(OR = coef(results), confint(results))will not work because this code relies on a model whereas the estimates above were derived from 4 different models. Assuming you have an appropriate choice of model and outcome and regressors, let's return to the issue of model selection. What results do you get from a regression model controlling for all or most of the nesting site variables?
Not the answer you're looking for?Browse other questions tagged regression logistic odds-ratio odds analysis or ask your own question. Does having a significant result from chi-squared test for independence also means that the odds ratio is significantly different from 1? Why is the laser dish in the southern hemisphere of the Death Star rather than the northern one?
In a formal paper, should I censor "brainf**k", the name of a programming language? The risk difference quantifies the absolute difference in risk or prevalence, whereas the relative risk is, as the name indicates, a relative measure. The relative risk is a ratio and does not follow a normal distribution, regardless of the sample sizes in the comparison groups. These investigators randomly assigned 99 patients with stable congestive heart failure (CHF) to an exercise program (n=50) or no exercise (n=49) and followed patients twice a week for one year. The 95% confidence interval estimate for the relative risk is computed using the two step procedure outlined above.
Consider again the randomized trial that evaluated the effectiveness of a newly developed pain reliever for patients following joint replacement surgery. In case-control studies it is not possible to estimate a relative risk, because the denominators of the exposure groups are not known with a case-control sampling strategy.
Consider the following hypothetical study of the association between pesticide exposure and breast cancer in a population of 6, 647 people. If we had such data on all subjects, we would know the total number of exposed and non-exposed subjects, and within each exposure group we would know the number of diseased and non-disease people, so we could calculate the risk ratio. However, suppose the investigators planned to determine exposure status by having blood samples analyzed for DDT concentrations, but they only had enough funding for a small pilot study with about 80 subjects in total.
With this sampling approach we can no longer compute the probability of disease in each exposure group, because we just took a sample of the non-diseased subjects, so we no longer have the denominators in the last column. The probability that an event will occur is the fraction of times you expect to see that event in many trials.
The odds are defined as the probability that the event will occur divided by the probability that the event will not occur. If the probability of an event occurring is Y, then the probability of the event not occurring is 1-Y.
With the case-control design we cannot compute the probability of disease in each of the exposure groups; therefore, we cannot compute the relative risk. Notice that this odds ratio is very close to the RR that would have been obtained if the entire source population had been analyzed.
We emphasized that in case-control studies the only measure of association that can be calculated is the odds ratio.
As with a risk ratio, the convention is to place the odds in the unexposed group in the denominator. The odds of breast cancer in women with high DDT exposure are 6.65 times greater than the odds of breast cancer in women without high DDT exposure.
Note that, while this result is considered statistically significant, the confidence interval is very broad, because the sample size is small. Remember that in a true case-control study one can calculate an odds ratio, but not a risk ratio.
We now ask you to use these data to compute the odds of pain relief in each group, the odds ratio for patients receiving new pain reliever as compared to patients receiving standard pain reliever, and the 95% confidence interval for the odds ratio.
When the study design allows for the calculation of a relative risk, it is the preferred measure as it is far more interpretable than an odds ratio. The odds ratio (OR) is one of several statistics that have become increasingly important in clinical research and decision-making. There are a number of statistics that are helpful for making decisions about clinical interventions or drawing conclusions about effects of various substances or events in health-related situations, and one seen frequently is called the odds ratio. The odds ratio is used when one of two possible events or outcomes are measured, and there is a supposed causative factor. Where “PG1” represents the odds of the event of interest for Group 1, and “PG2” represents the odds of the event of interest for Group 2.
Given the algebraic rule of cross products, the second formula will produce the same result as the other two formulae for odds ratio and is the more commonly reported formula. The first thing to understand when considering a significance test for the OR is that the true neutral value (indicating equal odds for both conditions) is one (1), not 0 (zero). Often, the OR dataset takes the form of a 2 x 2 table, and for that situation, a Fisher’s Exact Ratio test should be used. Where “p” is the Fisher’s Exact Probability, “a, b, c, d” represent the counts in the cells, and “n” represents the total sum of the values in all four cells. When there are more than 4 cells (or at the researcher’s convenience), the Chi-Square test should be used. The Likelihood Ratio Chi-Square, like all likelihood ratio statistics is a logarithmic formula. Where “G” represents the Likelihood Ratio statistic, ¦ represents observed values, ¦i represents expected values, and “ln” indicates the log to be taken. The odds ratio is skewed, so it is not possible to directly calculate the standard error of the statistic. Then all one needsto do to construct confidence intervals about the natural logarithm is to calculate the standard error using the above formula and add that value (or a multiple of that value) to the log of the odds ratio value for the upper CI (confidence interval) and subtract that value (or a multiple of that value) to the log of the odds ratio value for the lower CI. It should be remembered that the concept of “no difference” in most statistics refers to a difference of zero, and is generally measured with the variable means. One common use of the OR is in determination of the effect size of a difference in two drug interventions. The odds ratio is simply the ratio between the following two ratios: The ratio between standard treatment and the new drug for those who died, and the ratio between standard treatment and the new drug for those who survived.
In epidemiology studies, the researchers often use the odds ratio to determine post hoc if different groups had different outcomes on a particular measure. The great value of the odds ratio is that it is simple to calculate, very easy to interpret, and provides results upon which clinical decisions can be made. Odds ratios are one of a category of statistics clinicians often use to make treatment decisions. Although recurrent laryngeal carcinoma is a common clinical problem, the data regarding its natural history and prognostic factors are limited. A retrospective analysis of 224 consecutive cases of recurrent laryngeal carcinoma, treated between 1996 and 2009, was performed.
Our results suggest that lower initial T stage, no initial cervical lymph node metastasis, only local recurrence and patients suitable for salvage surgery are favourable prognostic factors for overall survival of patients with recurrent laryngeal cancer.
In the United States, it is estimated that about 49,260 new cases of oral cavity, pharyngeal and laryngeal cancers occurred in 2010.
This retrospective study reviews a series of 224 consecutive recurrent laryngeal carcinomas observed at our institutions and managed with the aforementioned therapeutic choices. Between 1996 and 2009, 1621 consecutive patients with neoplasms of the larynx were observed at the Sun Yat-sen University Cancer Center, China. When selecting treatment approaches, a comprehensive consideration of each individual patient, their economic situation and their treatment preferences was made by the multidisciplinary team at our cancer centre. In the surgical treatment of the neck, 72 patients were managed by neck dissection, including 27 cases with modified radical neck dissection (MRND) and 45 cases with selective neck dissection (SND). Survival was defined as the interval between the date of diagnosis of recurrent disease and date of death or the last date on which the patient was known to be alive. As many as 151 patients (67.4%) had local recurrence, either alone (140 patients) or with regional (11 patients) recurrence. As shown in Table 3, survival after recurrence was significantly influenced by variables related to both primary and recurrent tumour. Multivariate survival analysis was performed using the Cox regression model to calculate the odds ratio and 95% confidence intervals. Dealing with recurrent laryngeal cancer is arguably the greatest challenge faced by the physicians who treat these patients. On multivariate analysis, our results showed the 5-year overall survival (OS) was significantly related to the initial T stage, nodal status, extent of recurrence and operability of the recurrent tumour. The major criticism of retrospective studies is that the data collected were not originally designed for a research application.
Above all, our data suggest that initial lower T stage, no initial cervical lymph node metastasis, only local recurrence and patients suitable for salvage surgery are favourable prognostic factors for OS of patients with recurrent laryngeal cancer.
All authors contributed to the conception, design, and preparation of the manuscript, as well as read and approved the final manuscript. My research question is: what variables are important to an avian species nest site selection. Visit the wiki on specific dataset analysis requests for suggestions on how to improve this question.


The link is clear about the need for scientific context, and rationale for the analysis and results. However, the natural log (Ln) of the sample RR, is approximately normally distributed and is used to produce the confidence interval for the relative risk.
Using the data in the table below, compute the point estimate for the relative risk for achieving pain relief, comparing those receiving the new drug to those receiving the standard pain reliever.
The problem, of course, is that the outcome is rare, and if they took a random sample of 80 subjects, there might not be any diseased people in the sample. However, we can compute the odds of disease in each of the exposure groups, and we can compare these by computing the odds ratio. The explanation for this is that if the outcome being studied is fairly uncommon, then the odds of disease in an exposure group will be similar to the probability of disease in the exposure group.
However, in cohort-type studies, which are defined by following exposure groups to compare the incidence of an outcome, one can calculate both a risk ratio and an odds ratio. In addition, like a risk ratio, odds ratios do not follow a normal distribution, so we use the log transformation to promote normality. If a 95% CI for the odds ratio does not include one, then the odds are said to be statistically significantly different.
However, one can calculate a risk difference (RD), a risk ratio (RR), or an odds ratio (OR) in cohort studies and randomized clinical trials.
The odds ratio is extremely important, however, as it is the only measure of effect that can be computed in a case-control study design.
It is particularly useful because as an effect-size statistic, it gives clear and direct information to clinicians about which treatment approach has the best odds of benefiting the patient.
The OR evaluates whether the odds of a certain event or outcome is the same for two groups. Chi-Square (c2) assumes that the numbers in the cells represent counts and not proportions or averages, and it assumes that the value of the expecteds is 5 or greater in 80% or more of the cells.
If the data are entered into a statistical analysis program, this is the most appropriate test of significance for the Odds Ratio. However, the standard error for the natural logarithm of the odds ratio is quite simple to calculate.
More advanced information on direct computation of the confidence intervals for odds ratios can be obtained from the paper published by Sorana Bolboaca and Andrei Achimas Cadariu (7) and from the paper published by Simundic (8).
As an example, consider the treatment of patients with endocarditis caused by Staphylococcus aureus (SA).
Based on these results the researcher would recommend that all males aged 30 to 60 diagnosed with bacterial endocarditis caused by SA be prescribed the new drug.
An OR higher than 1 means that the first group (in this case, standard care group) was more likely to experience the event (death) than the second group. Furthermore, it is sometimes helpful in clinical situations to be able to provide the patient with information on the odds of one outcome versus another.
Other statistics commonly used to make treatment decisions include risk assessment statistics such as absolute risk reduction and relative risk reduction statistics. Prevalence and factors associated with aflatoxin contamination of peanuts from Western Kenya. Welding occupations and mortality from Parkinson’s disease and other neurodegenerative diseases among United States men, 1985-1999.
Risk factors and characteristics of H5N1 Highly Pathogenic Avian Influenza (HPAI) post-vaccination outbreaks.
Effect of treatment and adherence on ethnic differences in blood pressure control among adults with hypertension. Breast biopsy patterns and outcomes in surveillance, epidemiology, and end results - Medicare data.
The aims of this study were to evaluate the treatment outcomes of patients with recurrent laryngeal carcinoma and to identify the value of several prognostic factors.
On univariate analysis, the age, smoking index, grade, primary site, initial T stage, initial Union for International Cancer Control (UICC) stage and nodal status of the primary tumour, as well as disease-free interval, extent of recurrence and suitability for surgery were all powerful prognostic factors for survival. The aim of this study was to report our results and try to identify, in a retrospective analysis, potential prognostic factors and possible guidelines in tailoring the most appropriate treatment for patients with recurrent laryngeal carcinoma. Patients who died of no other documented cause were considered to have died from recurrent laryngeal cancer. The age, smoking index, grade, primary site, initial T stage, initial UICC stage and nodal status of the primary tumour, as well as the disease-free interval, extent of the recurrence and suitable for surgery were powerful prognostic factors for survival (Figure 1).
This group of patients presents a unique set of dilemmas because the chance for a cure is low, and prior treatment generally has a negative impact on all current therapeutic options. Therefore, some factors responsible for the ultimate treatment outcome might be omitted in the analysis, thereby contributing to bias.
Not that complicated prediction approaches don't have their place, but it's a little hard to trust the importance of a factor that doesn't show up in a "simpler" model.
If a 95% CI for the relative risk includes the null value of 1, then there is insufficient evidence to conclude that the groups are statistically significantly different.
Those assigned to the treatment group exercised 3 times a week for 8 weeks, then twice a week for 1 year. Therefore, exercisers had 0.44 times the risk of dying during the course of the study compared to non-exercisers. Since the 95% confidence interval does not include the null value (RR=1), the finding is statistically significant. Then compute the 95% confidence interval for the relative risk, and interpret your findings in words.
However, the small control sample of non-diseased subjects gives us a way to estimate the exposure distribution in the source population.
Consequently, the odds ratio provides a relative measure of effect for case-control studies, and it provides an estimate of the risk ratio in the source population, provided that the outcome of interest is uncommon.
As a result, the procedure for computing a confidence interval for an odds ratio is a two step procedure in which we first generate a confidence interval for Ln(OR) and then take the antilog of the upper and lower limits of the confidence interval for Ln(OR) to determine the upper and lower limits of the confidence interval for the OR.
We again reconsider the previous examples and produce estimates of odds ratios and compare these to our estimates of risk differences and relative risks. The null value is 1, and because this confidence interval does not include 1, the result indicates a statistically significant difference in the odds of breast cancer women with versus low DDT exposure.
Consider again the data in the table below from the randomized trial assessing the effectiveness of a newly developed pain reliever as compared to the standard of care.
When the outcome of interest is relatively rare (<10%), then the odds ratio and relative risk will be very close in magnitude. Significance statistics used for the OR include the Fisher’s Exact Probability statistic, the Maximum-Likelihood Ratio Chi-Square and Pearson’s Chi-Square. Specifically, the OR measures the ratio of the odds that an event or result will occur to the odds of the event not happening.
For example, it can calculate the odds of an event happening given a particular treatment intervention (1). The most common are the Fisher’s Exact Probability test, the Pearson Chi-Square and the Likelihood Ratio Chi-Square. The value of the probability must be evaluated through a table of Fisher’s Exact Probability values for one degree of freedom to obtain the significance value for the test.
The “no difference” value for this statistic is 1 and therefore, when a confidence interval includes the value of 1, the researcher or clinician will know that the odds of the measured outcome are the same for both (or all) treatment groups, even without a significance test. Although the mortality rate for this disease ranges from 25% to 47% (6), let us assume that in the population of interest, White males aged 30 to 60 the mortality rate is 38% with the standard antibiotic treatment of penicillin, methycillin, vancomycin and other antibiotics.
This recommendation assumes, of course, that the experience of side effects with the two categories of drugs is similar.
Patients may decide to accept or forego painful or expensive treatments if they understand what their odds are for obtaining a desired result from the treatment. The odds ratio supports clinical decisions by providing information on the odds of a particular outcome relative to the odds of another outcome. Log-rank test was employed to identify significant prognostic factors for overall survival. On multivariate analysis, four variables retained statistical significance: the initial T stage, nodal status, extent of recurrence and suitability for surgery.
Surgical treatment can either be endoscopic laser treatment or laryngectomy (partial or total), depending on the size and site of the tumour. Patients were seen every 2 months during the first year, every 3 months for the subsequent 2 years and then every 6 months thereafter until death. Further, 62 and 33 patients were treated with partial and total laryngectomy, respectively.
Model A included variables related to both primary and recurrent tumour, while model B was composed of only the former and model C was composed of only the latter. In this study, we retrospectively evaluated the significance of various prognostic factors related to both primary and recurrent tumour in 224 patients with recurrent laryngeal cancer treated at the Sun Yat-sen University Cancer Center, China to gain a better understanding of the natural course of this entity and the factors predicting outcome. The estimated 5-year survival rate of the patients that had local recurrence was only 55.8%. Such censure correctly refers to the present study, in which the data were heterogeneous and of lesser quality according to present standards. My sample size is 72 nests (used) and 72 random locations where I extracted the same habitat variables. What are the summaries of these variables in terms of significance levels for their wald tests? By convention we typically regard the unexposed (or least exposed) group as the comparison group, and the proportion of successes or the risk for the unexposed comparison group is the denominator for the ratio. First, a confidence interval is generated for Ln(RR), and then the antilog of the upper and lower limits of the confidence interval for Ln(RR) are computed to give the upper and lower limits of the confidence interval for the RR.


Exercise training was associated with lower mortality (9 versus 20) for those with training versus those without. The investigators then take a sample of non-diseased people in order to estimate the exposure distribution in the total population. So, we can't compute the probability of disease in each exposure group, but we can compute the odds of disease in the exposed subjects and the odds of disease in the unexposed subjects. Remember that we used a log transformation to compute the confidence interval, because the odds ratio is not normally distributed. Typically the data consist of counts for each of a set of conditions and outcomes and are set in table format.
Clinically, that often means that the researcher measures the ratio of the odds of a disease occurring or a death from a specific injury or illness happening to the odds of the disease or death not occurring. It can calculate the odds of a health outcome given exposure versus non-exposure to a substance or event (2). Most statistical computer programs such as Stata and SPSS will calculate the Fisher’s Exact and Chi-Square values and provide the significance value of the result. However, a new drug has been developed that attacks the bacteria’s ability to protect itself from the human immune system rather than interfering with cell wall development.
Severe side effects or development of allergic reactions to the new drug could change that recommendation. Through use of the odds ratio, they discovered that use of the needle biopsy was associated with a reduced probability of multiple surgeries. Many patients want to be involved in decisions about their treatment, but to be able to participate effectively, they must have information about their likely results in terms they can understand. In the endocarditis example, the risk (or odds) of dying if treated with the new drug is relative to the risk (odds) of dying if treated with the standard treatment antibiotic protocol. The Cox proportional hazards model was applied to identify covariates significantly associated with the aforementioned endpoint.
All loco-regional tumours were diagnosed by clinical examination, magnetic resonance imaging (MRI) or intensive computed tomography (CT), fiberoptic endoscopy and biopsy. The survival rate and univariate analysis were performed by the Kaplan–Meier method[12] and log-rank test. Unilateral neck node dissection was performed in 25 patients, whereas bilateral neck node dissection was performed in 5 patients. Because the initial UICC stage depends on the initial T stage and nodal status, this variable was omitted from the analysis. When regional disease was involved, the survival rate decreased to 40.2%, with a further decline to 0% when distant metastases were present. Considering these factors, one should realize that conclusions from this study should be validated by future projects. Therefore, the confidence interval is asymmetric, because we used the log transformation to compute Ln(OR) and then took the antilog to compute the lower and upper limits of the confidence interval for the odds ratio. Because the 95% confidence interval for the risk difference did not contain zero (the null value), we concluded that there was a statistically significant difference between pain relievers. The clinical literature exhibits many instances of the odds ratio being used in research to estimate reduction in disease or disease complications if patients receive a particular drug or vaccine (3,4,5). The question is this: What are the odds of dying with the new drug as opposed to the standard antibiotic therapy protocol?
The degree to which the first group is less likely to experience the event is not the OR result. At least in the industrialized world, most patients have received enough schooling to understand basic percentages and the meaning of probabilities. Relative risk assessment statistics are particularly suited to diagnostic and treatment decision-making and will be addressed in a future paper. The rate of recurrence in patients with T1 tumours of the larynx ranges from 5% to 13%, and in patients with T2 tumours, from 25% to 30%[2]. Larger tumours and those with subglottic extension are generally treated by total laryngectomy. The study was approved by the Research Ethics Committee of the Sun Yat-sen University Cancer Center.
Distant metastases were diagnosed by clinical symptoms, physical examinations and imaging methods, including chest X-ray, bone scan, abdominal sonography, MRI, intensive CT or positron emission CT.
Multivariate analyses with the Cox proportional hazards model[13] were used to test the independent significance by forward elimination of insignificant explanatory variables of different parameters. According to model A, the initial T stage, nodal status and suitability for surgery strongly predicted patient outcome. Multivariate analysis only revealed that the initial site and site of recurrence retained statistical significance.
I then used the information-theoretic approach (Burnham and Anderson 2002) and Akaike's Information Criteria adjusted for small sample size (AICc) to compare models. The odds ratio is a measure of effect size (as is the Pearson Correlation Coefficient) and therefore provides information on the strength of relationship between two variables. The odds ratio is a way of comparing whether the odds of a certain outcome is the same for two different groups (9).
It is important to put the group expected to have higher odds of the event in the first column.
The odds ratio provides information that both clinicians and their patients can use for decision-making. For patients with advanced laryngeal cancer, the rate of recurrence is approximately 30%–50% as reported by some studies[3,4,5]. There were 105 cases of good differentiation, 94 cases of moderate differentiation and 25 cases of poor differentiation. When the analysis was limited to factors related with primary tumour (model B), initial T stage and nodal status were the only factors that predicted survival. When factors related to the primary disease were excluded from the analysis, the site of recurrence and its operability were the only predictors of survival. Because this confidence interval did not include 1, we concluded once again that this difference was statistically significant. In addition to assisting health care providers to make treatment decisions, the information provided by the odds ratio is simple enough that patients can also understand the results and can participate in treatment decisions based on their odds of treatment success.
It is an indirect measure however, as will be seen in the section on interpretation of the statistic.
It is not valid to try to determine how much less the first group’s odds of the event was than the second group’s.
The most frequent site of recurrence is the larynx itself, including the peristomal area followed by the regional lymph nodes and, less often, distant sites[6,7]. If the recurrence is unresectable and the patient did not have prior radiotherapy, then radiotherapy with concurrent systemic therapy is recommended, depending on the performance status.
When the analysis was limited to recurrence-related factors (model C), extent of recurrence and suitability for surgery were independent prognostic factors in recurrent laryngeal SCC patients. In addition, Lacy et al.[15] found that the site of recurrence was a significant prognostic factor for survival, in addition to the method of treatment of the primary tumour and original TNM stage. Salvage surgery is generally considered to be the first option if the recurrent disease is resectable and the patient is able to undergo the required surgery. The Akaike weight (wi) for each model was calculated as an estimate of the probability of the model being the most parsimonious of the developed models. We will now use these data to generate a point estimate and 95% confidence interval estimate for the odds ratio. When the odds of the first group experiencing the event is less than the odds of the second group, one must reverse the two columns so that the second group becomes the first and the first group becomes the second.
For patients with recurrent disease not amenable to curative-intent radiation or surgery, the treatment approach is the same as that for patients with metastatic disease. The operability of the recurrent tumour was also found to predict survival, but only on univariate analysis.
Fortunately, due to natural barriers to tumour spread, the ability to remove the entire larynx without threatening vital function and the relatively early onset of symptoms associated with recurrent disease, surgical salvage is highly successful[17]. I then used model-averaging using package MUMin in R to calculate parameter estimates, conditional standard errors, and variable weights of the top-performing models within 4 AICc units based on their adjusted Akaike weights (wi) (Burnham and Anderson 2002). Then it will be possible to interpret the difference because that reversal will calculate how many more times the second group experienced the event than the first. They found that good prognosis was strongly dependent on the TNM stage of recurrent disease at the time of surgical salvage, weakly dependent on the site of disease and not dependent on the time to recurrence after initial therapy.
In fact, this arrangement produces a result that can only be interpreted as “the odds of the first group experiencing the event is less than the odds of the second group experiencing the event”. The survival rate after local recurrence and salvage surgery varies greatly from 22% to 66%[8,9,10,11].
The degree to which the first group’s odds are lower than that of the second group is not known. Some authors even report an overall 5-year survival rate of as low as 2% in this patient population[4]. Induction chemotherapy plus radiation compared with surgery plus radiation in patients with advanced laryngeal cancer.. Larynx preservation in pyriform sinus cancer: preliminary results of a European Organization for Research and Treatment of Cancer phase III trial.
Development of a new staging system for patients with recurrent laryngeal squamous cell carcinoma..



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