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The odds is not the same as the probability. The odds is the number of "successes" (deaths) per "failure" (continue to live), while the probability is the proportion of "successes". I find it instructive to compare how one would estimate these two: An estimate of the odds would be the ratio of the number of successes over the number of failures, while an ...

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It sounds like you have a lot of data, but no model yet. What do you learn from the $1$ run scored from a ball? There are a lot of possibilities. You might learn just what happened on that ball. You might learn something about the batter. You might learn something about the bowler. You might learn something about the overall skill levels of the teams. ...

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If the regression coefficient of your logistic regression is 1.76 on the logit-scale, then the odds ratio for 1 unit increase in temperature is $\mathrm{OR_{+1}}=\exp(\beta) = \exp(1.76)\approx 5.81$, as you already stated. The odds ratio for an increase in temperature for $a$ degrees is $\mathrm{OR_{+a}}=\exp(\beta\times a)$. In your case, $a$ is 2 and 3, ...

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To answer your question consider a binary outcome Y (0 or 1) and a binary exposure variable X (0 or 1). In prospective studies we are interested in $P[Y = 1 | X = 0]$ v. $P[Y = 1 | X = 1]$ whereas in retrospective studies we are interested in $P[X = 1 | Y = 0]$ v. $P[X = 1 | Y = 1]$. First let's consider a prospective study with the setting below: $P_0 = ... 3 This probability tree represents the game and guides the calculations: The blue node at the left represents the start. At this point there is a 5% chance of success (leading to the up and left). If success is achieved now, only one attempt is made, as indicated in the orange circle. Lacking success, we progress down and to the right to the next blue ... 2 Here is a common example: we want to investigate the relationship between smoking and lung cancer, so smoking (yes/no) is the "exposure" variable and lung cancer (yes/no) is the "outcome" variable. We could do a prospective cohort study by finding a large group of smokers and a large group of non-smokers and following them for a period of time and ... 2 No, unfortunately you can't simply add the odds ratios. If you look up any text or reputable source on logistic regression you'll find formulas with which to estimate either the logit or the odds or the probability (depending on what's most useful to you) of admission to a given hospital, given certain values on the predictors. I agree with @Simon and ... 1 It might be a good idea to look up the details of the Duckworth Lewis scheme used to decide the winner of a match affected by rain. IIRC this is a non-parametric method that attempts to work out a fair target for a curtailed innings. Comparison with the Duckworth Lewis target would give a good indication of progress, but it is possible that their methods ... 1 If you really want to test the null hypothesis that the true odds for success are exactly zero for each individual level$j$of your factor$X$, then the statistical test is very simple. The null-hypothesis odds$p_{0j}/(1-p_{0j})$for success in group$j$are zero iff$p_{0j}=0$. Under this null hypothesis, the probability of observing at least$1\$ success ...

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You fit a binomial probability model with - by default - a logit link function (see ?binomial). The problem is that the logistic function (the inverse of the logit) never reaches zero. Therefore, all model fits will yield nonzero odds for success. In particular, all classical confidence intervals for success odds will not include zero. Therefore, in ...

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In a sense, odds ratios are more universal than risk ratios so we spend too much time on risk ratios. Risk ratios are incapable of being constant over a wide range of risks, whereas an odds ratio is capable of being constant. For example, if a risk ratio is 3, the starting risk level cannot exceed 1/3. Because of this, models stated in terms of odds ...

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Answering, even though this question is quite old. The biggest caveat is that you cannot use a measurement of RR in a case-control study, because it cannot be calculated. If you have the data to compare between them, then there's no reason not to - differences between the two measures can often yield some insight. Note however that in circumstances of ...

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