32

predict.coxph() computes the hazard ratio relative to the sample average for all $p$ predictor variables. Factors are converted to dummy predictors as usual whose average can be calculated. Recall that the Cox PH model is a linear model for the log-hazard $\ln h(t)$: $$ \ln h(t) = \ln h_{0}(t) + \beta_{1} X_{1} + \dots + \beta_{p} X_{p} = \ln h_{0}(t) + \bf{...


9

I too speculate at the prevalence of logistic models in the literature when a relative risk model would be more appropriate. We as statisticians are all too familiar with adherence to convention or sticking to "drop-down-menu" analyses. These create far more problems than they solve. Logistic regression is taught as a "standard off the shelf tool" for ...


8

Interpretation of the graph in your case Note: The y-axis is not always the relative risk as in the example given in the vignette of the dlnm package. This is only the case in their example, because they used mortality data and Poisson regression models. In their framework, the exponentiated regression coefficient from the Poisson models $RR=\exp(\hat{\beta}...


7

Well, from what you've already said, I think you've got most of it covered but just need to put it in her language: One is a difference of risks, one is a ratio. So one hypothesis test asks if $p_2 - p_1 = 0$ while the other asks if $\frac{p_2}{p_1} = 1$. Sometimes these are "close" sometimes not. (Close in quotes because clearly they aren't close in the ...


6

Mind that in both tests, you test a completely different hypothesis with different assumptions. The results are not comparable, and that is a far too common mistake. In absolute risk you test whether the (average) difference in proportion differs significantly from zero. The underlying hypothesis in the standard test for this assumes that the differences in ...


6

You can use the Delta method to obtain an approximate distribution of your relative risk, as shown by that link. Then you can define a pivot and use this to obtain a CI. I understand that there might be some confusion regarding the use of the Delta method, so here are a few simple steps that show how to construct an approximate CI for the relative risk. ...


5

You can do this calculation for an adjusted OR (I presume from a logistic regression) to a RR, but the end result may not be useful for your goal of meta-analysis. The essential problem is that the adjusted OR $exp(\beta_1)$ from a logistic regression is not an "average" over the population. And so there's no way to calculate a population average relative ...


5

Zhang 1998 originally presented a method for calculating CIs for risk ratios suggesting you could use the lower and upper bounds of the CI for the odds ratio. This method does not work, it is biased and generally produces anticonservative (too tight) estimates of the risk ratio 95% CI. This is because of the correlation between the intercept term and the ...


5

Quoting from the documentation (help(escalc)): Cell entries with a zero count can be problematic, especially for the relative risk and the odds ratio. Adding a small constant to the cells of the 2x2 tables is a common solution to this problem. When to="only0" (the default), the value of add (the default is 1/2) is added to each cell of those 2x2 tables ...


4

It depends on what you mean by "better", but for most reasons I can think of, the "Risk Ratio" is the superior measure in terms of better reflecting what most people are looking for, having a slightly easier interpretation, etc. But there are some study types that prevent the calculation of a risk ratio (case-control studies) and logistic regression, which ...


4

The risk difference would be the simplest option to handle this scenario (with zero counts of events/non-events) and is calculable in situations where the relative risk or odds ratio cannot be estimated due to divisions involving zeros. The risk difference will of course have upper and lower bounds since the individual group risks are bounded by 0 and 1 [0% ...


4

The reasons for using odds instead of relative risk are probably easier to see if the formulas are first put on the table. Relative Risk = $\frac{\mbox{Incidence in exposed}}{\mbox{Incidence in unexposed}}$ Odd Ratio = $\frac{\mbox{Odds that an exposed person develops the outcome}}{\mbox{Odds that an unexposed person develops the outcome}}$ The main ...


4

Here is the derivation. I use the same notation as in this presentation (starting from page 29). Let's look at the familiar $2\times2$-Table below. The relative risk or risk ratio is defined as $$ \theta=\mathrm{RR}=\dfrac{\dfrac{p_{11}}{p_{11}+p_{12}}}{\dfrac{p_{21}}{p_{21}+p_{22}}}=\dfrac{p_{11}\cdot (p_{21}+p_{22})}{p_{21}\cdot (p_{11}+p_{12})} $$ We ...


4

You can't speak of magnitude of effect in isolation. This is a common source of confusion because we often encounter the term in a discipline-specific setting, but the hand-wavy discussions quickly lead one to speculate whether there is literature on a seemingly abstract biostatistical topic of "magnitude of effect". But no, the literature or scientific ...


3

Consider that we have noisy estimates; where the exposure is very low, the rate is very unreliable, so it's impossible to reliably construct an ordering that includes them. You may be able to do some pooling (pulling toward the overall rate) that improves the mean square error, but at the expense of some bias. This is a common tool in actuarial work, where ...


3

If you do a two-sided level 0.05 test of hypothesis that the relative risk is different from 1 and get a p-value less than 0.05 then this is equivalent to a two-sided 95% confidence interval that does not contain 1. So given the p-value of 0.049 you would expect that 1 would fall outside the interval. What are the possible explanations? 1. The confidence ...


3

Although the convention exists that does not make it useful of course. Since it compares the shift in location with variability it means that two studies which achieve the same effect in absolute terms (say a reduction of 10 mm Hg in mean systolic blood pressure) would differ in their value of Cohen's d if the variability differed with the one which used a ...


3

You are of course right and it is a common mistake to describe an odds ratio like a relative risk ratio. I would suggest that it would be helpful to propose a more appropriate phrasing to them such as "suggesting that the odds of [participants] [doing X in] [A condition] is 1.90 times higher than in [B condition]." Once the authors realise that is all they ...


3

An intuitive way to understand this is to consider the basic definitions of odds and risk. Odds are simply the ratio of the number of events ($E$) to the number of non-events ($NE$) whereas risk is the the ratio of events to total events ($E+NE$). As an event becomes more rare, the number of non-events approaches the number of total events. Take a simple ...


3

It is not true in all situations. The odds ratio only gives an estimate of the relative risk if the outcome is a low probability outcome. (Same insight as Poisson approximation to the binomial distribution). Imagine a case-control study for lung cancer, then we check the number of smokers in both groups. Technically, the only thing we can test is given that ...


3

The quote surely just means to say that the odds ratio is a relative risk measure - rather than an estimate of the relative risk, which as already point out is only approximately the case in cohort studies/randomized trials for very low proportions. By relative risk measure I mean something that is given relative to some comparison group in a way that the ...


3

In biostatistics, time-dependent responses are often inspected in terms of the area under the curve. This is not to be confused to be the AUC of the ROC which is a classification metric. For instance, in an oral glucose challenge, blood is drawn hourly to see the glucose concentration over a period of time. Because diabetes and its complications are caused ...


3

The language is a stretch. If they cite no source, it is because they actually mean risk difference is clinically important and an absolute scale. Rather than clinically important, risk difference is conservative and less likely to be exaggerated by a clinical audience, compared with risk ratio or the nefarious odds ratio. This is especially true for rare ...


3

Your question is a bit disjointed, so I'll offer a few thoughts in a similarly scattershot fashion. First, to the distinction you're making between "predict the outcome class" and "know the risk factors," the only way to get to the latter is through the former. A risk factor is just a feature that helps us assess the risk of something, and in binary ...


2

My hint for question a) to get you started is that 32+41=73% of those receiving the new compound have got more than a 50% reduction in the size of the wound (which is what is defined as "success") and hence 73% would be the point estimate of the percent success of patients receiving the new compound. To turn this point estimate into a confidence interval ...


2

Fisher test can be inverted to get a confidence interval about the odds ratio, not about the relative risk. Therefore Michael's reason number 3 is necessarily the good one.


2

Email the authors. Without some serious guesswork, there's no way I can think of to pull the unweighted data back out of a weighted data set like this without knowing the weights. For reference, here's what happened in that study: Each patient has an exposure X, and outcome Y, and a set of confounding covariates Z A model is built to estimate the ...


2

It seems surprising that the paper would not report the number of events, but if it reports the crude survival curves, either in a table or figure, then you can easily get the risk and thus the number of events, at any time t: risk(t) = 1-survival(t). Or if you have the overall survival probability: risk = 1-survival. Then the number of events is N*risk. If ...


2

I think relative risk is the best index of effect size when using binomial data. Odds ratios are somewhat difficult to interpret (you can read the article entitled "Down with odds ratios!" by Sackett and colleagues). In contrast, relative risk provides an intuitive and easily interpretable value (e.g., one group has 40% greater risk of belonging to group X). ...


2

Here is more or less the replication of the SAS example mentioned in the comments to the question. library("sas7bdat") eyestudy =read.sas7bdat("eyestudy.sas7bdat") sapply(1:ncol(eyestudy),function(z)summary(eyestudy[,z])) for(i in c(2:3))eyestudy[,i]<-as.factor(eyestudy[,i]) tabfq=with(eyestudy, table(carrot, lenses)) (tabfqm=addmargins(tabfq)) prop....


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