Sunday, August 21, 2011

Odds ratio and risk ratio in clinical trials #2

In my previous article, I discussed the odds ratio and risk ratio (or relative risk ratio). In clinical trials with binary outcome, both odds ratio and relative risk ratio are used. Since the clinical trials are similar to the cohort studies in epidemiology field, it seems to be more reasonable to use relative risk ratio in clinical trials. However, the odds ratio may be more commonly used in practice. This may be due to the fact that the odds ratio can be easily modeled using logistic regression. This could also be due to the fact that the odds ratio is typically larger than relative risk ratio that may be desired by the researcher.

For a non-inferiority or equivalence trials with binary outcome, one may desire to have a smaller standard error, therefore a narrower confidence interval – in this case, the relative risk ratio may be better than odds ratio.

Wikipedia gives an excellent comparison between relative risk ratio and odds ratio.

In an article “How can I estimate relative risk in SAS using proc genmod for common outcomes in cohort studies?”, the calculation of odds ratio, relative risk ratio, and their confidence intervals are illustrated.

Using SAS Proc Genmod, both odds ratio, relative risk ratio, and their confidence intervals can be easily calculated:

For odds ratio:

Proc genmod data = xxx descending;
class treatment;
model  outcomevariable = treatment
/ dist = binomial link = logit;
estimate 'Beta' treatment 1 -1/ exp;
run;

Here, the “link=logit” can be omitted since the logit link function is default when distribution is binomial.

For relative risk ratio,

proc genmod data = xxx descending;
class treatment;
model outcome = treatment
/ dist = binomial link = log;
estimate 'Beta' treatment 1 -1/ exp;
run;

Here, the “link=log” can NOT be omitted since the log link function is NOT default when distribution is binomial.

Relative risk ratio can also be estimated using poisson regression especially when the event ratio is small.

Proc genmod data = eyestudy;
class id;
model outcome = treatment
/ dist = poisson link = log;
repeated subject = id/ type = unstr;
estimate 'Beta' treatment 1 -1/ exp;
run;

Here, the “link=log” can be omitted since the log link function is default when distribution is poisson.

There are several advantages of using Proc Genmod to calculate the odds ratio and risk ratio. Adjusted odds ratio and adjusted relative risk ratio can be easily calculated when there are continuous or categorical covariates. The model can be easily modified to fit the longitudinal data.

Proc Logistic can be used for calculating the odds ratio (and the confidence interval) and can adjust for continuous or categorical covariates. However, Proc Logistic can not be used for calculating the relative risk ratio.

proc logistic;
model outcome = treatment;
run;

Proc FREQ can be used for calculating the odds ratio and relative risk ratio (and asymptotic confidence interval) using /cmh option. For adjusted odds ratio or risk ratio, only the categorical covariate can be used.

proc freq order=data;
tables covariate*treatment*response / CMH;
run;

In the output, the odds ratio will be explicitly indicated while relative risk ratio will be labeled as “col1 risk” or “col2 risk”.

There is no regulatory guidance forcing the use of odds ratio or relative risk ratio. However, in clinical trials, if we compare the ratio of two proportions (eg the proportion of success in treated group vs. the proportion of success in control group), relative risk ratio seems to be better. Relative risk ratio resemble the hazard ratio in may aspects.

In FDA’s guidance “Diabetes Mellitus — Evaluating Cardiovascular Risk in New Antidiabetic Therapies to
Treat Type 2 Diabetes” The calculation of risk ratio is suggested. The guidance indicated

"Sponsors should compare the incidence of important cardiovascular events occurring with the investigational agent to the incidence of the same types of events occurring with the control group to show that the upper bound of the two-sided 95 percent confidence interval for the estimated risk ratio is less than 1.8. This can be accomplished in several ways. The integrated analysis (meta-analysis) of the phase 2 and phase 3 clinical trials described above can be used. Or, if the data from all the studies that are part of the meta-analysis will not by itself be able to show that the upper bound of the two-sided 95 percent confidence interval for the estimated risk ratio is less than 1.8, then an additional single, large safety trial should be conducted that alone, or added to other trials, would be able to satisfy this upper bound before NDA/BLA submission. Regardless of the method used, sponsors should consider the entire range of possible increased risk consistent with the confidence interval and the point estimate of the risk increase. For example, it would not be reassuring to find a point estimate of 1.5 (a nominally significant increase) even if the 95 percent upper bound was less than 1.8.”

In a presentation by Dr Bob O’Neill “Non-Inferiority Clinical Trials Some key statistical issues and concepts” he suggested that Log (Hazard ratio) or Log(relative risk) is preferred when determining the non-inferiority margin

In statistical review for Maxipime (cefepime hydrochloride) NDA, the risk ratio and 95% confidence interval are used. In an article “Relative risks of reported serious injury and death associated with hemostasis devices by gender”, the risk ratio were reported.

However, there are also many cases of using odds ratio instead of risk ratio in clinical trials. Some examples are:

In summary, while both odds ratio and risk ratio can be used in clinical trials, risk ratio should be given the adequate emphasis in comparing the ratio of two proportions (between two treatment groups). In non-inferiority clinical trials, the risk ratio and its confidence interval are preferred.