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[R-meta] converting Odds Ratio to Risk Ratio in CHE model

7 messages · Liu Sicong, Wolfgang Viechtbauer, Dr. Gerta Rücker +1 more

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Dear All,

Hope all is well.

I have been applying the correlated and hierarchical model (CHE, Pustejovsky & Tipton, 2021) to fitting data consisting of ~98 clinical trials with binary outcomes. The effect sizes took the initial form of odds ratio (OR) and were converted to the standard mean difference (SMD) when fitting the CHE model. Because OR is challenging for interpretation and I wonder if there are ways to transform from OR to risk ratio (RR) when reporting the model parameter estimates? Or, as some literature (see Knol et al., 2012) suggests, converting to RR entails a change of model?

Thank you all very much!

Pustejovsky, J. E., & Tipton, E. (2022). Meta-analysis with robust variance estimation: Expanding the range of working models. Prevention Science, 23(3), 425-438.

Knol, M. J., Le Cessie, S., Algra, A., Vandenbroucke, J. P., & Groenwold, R. H. (2012). Overestimation of risk ratios by odds ratios in trials and cohort studies: alternatives to logistic regression. Cmaj, 184(8), 895-899.


Best regards,
Sicong

------------------------------------------
Sicong (Zone) Liu, Ph.D.
Professor
South China Normal University
------------------------------------------
1 day later
#
Dear Sicong,

I don't understand the question (seems to be pattern for me today ...). If you converted everything to SMDs, then the results from the model provides estimates in terms of this (SMD) measure. So where / why do you want to convert ORs to RRs?

Best,
Wolfgang
#
Thank you for your response Wolfgang!

I apologize for not being clear and the question is totally motivated by making the interpreation easier. The targeted audience of the work is in public health. Although OR is  used in this domain,  some people find it difficult to think in terms of ?odds", which is not as easy as ?chance?  interpreted from RR, hence the question. Thank you!


Cheers,

Sicong (Zone)

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From: Viechtbauer, Wolfgang (NP) <wolfgang.viechtbauer at maastrichtuniversity.nl>
Date: Thursday, April 18, 2024 at 6:16 PM
To: R Special Interest Group for Meta-Analysis <r-sig-meta-analysis at r-project.org>
Cc: Liu Sicong <64zone at gmail.com>
Subject: RE: converting Odds Ratio to Risk Ratio in CHE model

Dear Sicong,

I don't understand the question (seems to be pattern for me today ...). If you converted everything to SMDs, then the results from the model provides estimates in terms of this (SMD) measure. So where / why do you want to convert ORs to RRs?

Best,
Wolfgang

  
  
#
I totally understand that part, but I am not quite sure which OR values you want to convert. If you fitted a model to standardized mean differences, then one cannot really transform the estimates from such a model to risk ratios (well, maybe, with a lot of creativity, but let's not go there). If you are simply asking how to convert ORs to RRs, then this can be done, but requires assuming a baseline risk. The transf.lnortorr() function in metafor will do this (to be precise, it transforms log odds ratios to risk ratios). For example, say the OR is 2.5. Then the corresponding RR is:

transf.lnortorr(log(2.5), pc=0.10)

2.17, assuming that the baseline risk is 10%. But if the baseline risk is 20%, then

transf.lnortorr(log(2.5), pc=0.20)

shows that the corresponding RR is 1.92.

Best,
Wolfgang
#
Dear Sicong,

Why then were the effects transformed to SMDs in the first place? They could have been analysed as ORs (or RRs).

If you want to transform a pooled OR from a meta-analysis to an RR, you have to make an assumption of the "baseline risk" in a population which is the probability of the event of interest in the control group. If we denote the baseline risk with p_c and the risk under the active intervention with p_t, then we have

RR = p_t/p_c

OR = p_t * (1 - p_c)/ p_c / (1 - p_t)

Then, given OR and the assumed baseline risk p_c, we can solve OR for p_t:

OR * (1 - p_t) * p_c = p_t * (1 - p_c)  

Inserting this p_t into RR provides:

RR = p_t/p_c = OR /(1 +( OR - 1)* p_c)

Please note that this heavily depends on the assumption about the baseline risk, that is, on the population the intervention is thought for. This assumption should be based on evidence. See, for example, the Cochrane Handbook of Systematic Reviews for Interventions where you find similar considerations: https://training.cochrane.org/handbook/current/chapter-14#section-14-1

Best,
Gerta







UNIVERSIT?TSKLINIKUM FREIBURG
Institute for Medical Biometry and Statistics

Dr. Gerta R?cker
Guest Scientist

Stefan-Meier-Stra?e 26 ? 79104 Freiburg
gerta.ruecker at uniklinik-freiburg.de

https://www.uniklinik-freiburg.de/imbi-en/employees.html?imbiuser=ruecker

-----Urspr?ngliche Nachricht-----
Von: R-sig-meta-analysis <r-sig-meta-analysis-bounces at r-project.org> Im Auftrag von Sicong Liu via R-sig-meta-analysis
Gesendet: Donnerstag, 18. April 2024 13:04
An: Viechtbauer, Wolfgang (NP) <wolfgang.viechtbauer at maastrichtuniversity.nl>; R Special Interest Group for Meta-Analysis <r-sig-meta-analysis at r-project.org>
Cc: Sicong Liu <64zone at gmail.com>
Betreff: Re: [R-meta] converting Odds Ratio to Risk Ratio in CHE model

Thank you for your response Wolfgang!

I apologize for not being clear and the question is totally motivated by making the interpreation easier. The targeted audience of the work is in public health. Although OR is  used in this domain,  some people find it difficult to think in terms of ?odds", which is not as easy as ?chance?  interpreted from RR, hence the question. Thank you!


Cheers,

Sicong (Zone)

-------------



From: Viechtbauer, Wolfgang (NP) <wolfgang.viechtbauer at maastrichtuniversity.nl>
Date: Thursday, April 18, 2024 at 6:16 PM
To: R Special Interest Group for Meta-Analysis <r-sig-meta-analysis at r-project.org>
Cc: Liu Sicong <64zone at gmail.com>
Subject: RE: converting Odds Ratio to Risk Ratio in CHE model

Dear Sicong,

I don't understand the question (seems to be pattern for me today ...). If you converted everything to SMDs, then the results from the model provides estimates in terms of this (SMD) measure. So where / why do you want to convert ORs to RRs?

Best,
Wolfgang

  
  
#
Just saw Wolfgang's post that metafor provides a function for the transformation.
The main message of both of us is that you need an evidence-based baseline risk.

Gerta


UNIVERSIT?TSKLINIKUM FREIBURG
Institute for Medical Biometry and Statistics

Dr. Gerta R?cker
Guest Scientist

Stefan-Meier-Stra?e 26 ? 79104 Freiburg
gerta.ruecker at uniklinik-freiburg.de

https://www.uniklinik-freiburg.de/imbi-en/employees.html?imbiuser=ruecker


-----Urspr?ngliche Nachricht-----
Von: R-sig-meta-analysis <r-sig-meta-analysis-bounces at r-project.org> Im Auftrag von Viechtbauer, Wolfgang (NP) via R-sig-meta-analysis
Gesendet: Donnerstag, 18. April 2024 13:24
An: Sicong Liu <64zone at gmail.com>; R Special Interest Group for Meta-Analysis <r-sig-meta-analysis at r-project.org>
Cc: Viechtbauer, Wolfgang (NP) <wolfgang.viechtbauer at maastrichtuniversity.nl>
Betreff: Re: [R-meta] converting Odds Ratio to Risk Ratio in CHE model

I totally understand that part, but I am not quite sure which OR values you want to convert. If you fitted a model to standardized mean differences, then one cannot really transform the estimates from such a model to risk ratios (well, maybe, with a lot of creativity, but let's not go there). If you are simply asking how to convert ORs to RRs, then this can be done, but requires assuming a baseline risk. The transf.lnortorr() function in metafor will do this (to be precise, it transforms log odds ratios to risk ratios). For example, say the OR is 2.5. Then the corresponding RR is:

transf.lnortorr(log(2.5), pc=0.10)

2.17, assuming that the baseline risk is 10%. But if the baseline risk is 20%, then

transf.lnortorr(log(2.5), pc=0.20)

shows that the corresponding RR is 1.92.

Best,
Wolfgang
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#
Dear Gerta and Wolfgang,

Your detailed responses are really helpful! They confirm my own feeling that ?baseline risk? needs to be assumed for pooled RR in my situation.

The transf.lnortorr() function is also good to know and very thoughtful! I am not sure I will eventually do that conversion ?  Thank you again!


Cheers,

Zone

-------------



From: Dr. Gerta R?cker <gerta.ruecker at uniklinik-freiburg.de>
Date: Thursday, April 18, 2024 at 7:41 PM
To: R Special Interest Group for Meta-Analysis <r-sig-meta-analysis at r-project.org>, Sicong Liu <64zone at gmail.com>
Cc: Viechtbauer, Wolfgang (NP) <wolfgang.viechtbauer at maastrichtuniversity.nl>
Subject: AW: converting Odds Ratio to Risk Ratio in CHE model

Just saw Wolfgang's post that metafor provides a function for the transformation.
The main message of both of us is that you need an evidence-based baseline risk.

Gerta


UNIVERSIT?TSKLINIKUM FREIBURG
Institute for Medical Biometry and Statistics

Dr. Gerta R?cker
Guest Scientist

Stefan-Meier-Stra?e 26 ? 79104 Freiburg
gerta.ruecker at uniklinik-freiburg.de

https://www.uniklinik-freiburg.de/imbi-en/employees.html?imbiuser=ruecker


-----Urspr?ngliche Nachricht-----
Von: R-sig-meta-analysis <r-sig-meta-analysis-bounces at r-project.org> Im Auftrag von Viechtbauer, Wolfgang (NP) via R-sig-meta-analysis
Gesendet: Donnerstag, 18. April 2024 13:24
An: Sicong Liu <64zone at gmail.com>; R Special Interest Group for Meta-Analysis <r-sig-meta-analysis at r-project.org>
Cc: Viechtbauer, Wolfgang (NP) <wolfgang.viechtbauer at maastrichtuniversity.nl>
Betreff: Re: [R-meta] converting Odds Ratio to Risk Ratio in CHE model

I totally understand that part, but I am not quite sure which OR values you want to convert. If you fitted a model to standardized mean differences, then one cannot really transform the estimates from such a model to risk ratios (well, maybe, with a lot of creativity, but let's not go there). If you are simply asking how to convert ORs to RRs, then this can be done, but requires assuming a baseline risk. The transf.lnortorr() function in metafor will do this (to be precise, it transforms log odds ratios to risk ratios). For example, say the OR is 2.5. Then the corresponding RR is:

transf.lnortorr(log(2.5), pc=0.10)

2.17, assuming that the baseline risk is 10%. But if the baseline risk is 20%, then

transf.lnortorr(log(2.5), pc=0.20)

shows that the corresponding RR is 1.92.

Best,
Wolfgang
_______________________________________________
R-sig-meta-analysis mailing list @ R-sig-meta-analysis at r-project.org
To manage your subscription to this mailing list, go to:
https://stat.ethz.ch/mailman/listinfo/r-sig-meta-analysis