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Neil Morrison
Can hazard ratios and odds ratio be used interchangeably in...
If there was an extremely low proportion of subjects with an event in all experiments (let's say <10%) and the hazard and odds ratios are vey close to 1, then hazard, odds and relative risk ratios will be relatively close to each other.
If there was an extremely low proportion of subjects with an event in all experiments (let's say <10%) and the hazard and odds ratios are vey close to 1, then hazard, odds and relative risk ratios will be relatively close to each other.
Another 2008 reference by Ian Scott addressed this issue, specifically in pages 14-15. Scott, I. Interpreting risks and ratios in therapy trails Australian Prescriber, 2008;31:12-16. http://www.australianprescriber.com/magazine/31/1/12/6
Another 2008 reference by Ian Scott addressed this issue, specifically in pages 14-15. Scott, I. Interpreting risks and ratios in therapy trails Australian Prescriber, 2008;31:12-16. http://www.australianprescriber.com/magazine/31/1/12/6
Dear Muhammad Ali, Risk (hazard) ratios and odds ratios cannot be used interchangeably in meta-analysis. Like euro and pound they have to be converted into the same value e.g. Swedish crowns. You find the formula here: http://hiv.cochrane.org/sites/hiv.cochrane.org/files/uploads/Ch09_Analysing.pdf Deeks JJ, Higgins JPT, Altman DG (editors). Chapter 9: Analysing data and undertaking meta-analyses. In: Higgins JPT, Green S (editors). Cochrane Handbook for Systematic Reviews of Interventions. Version 5.0.1 [updated September 2008]. The Cochrane Collaboration, 2008. Available from www.cochrane-handbook.org.
Dear Muhammad Ali, Risk (hazard) ratios and odds ratios cannot be used interchangeably in meta-analysis. Like euro and pound they have to be converted into the same value e.g. Swedish crowns. You find the formula here: http://hiv.cochrane.org/sites/hiv.cochrane.org/files/uploads/Ch09_Analysing.pdf Deeks JJ, Higgins JPT, Altman DG (editors). Chapter 9: Analysing data and undertaking meta-analyses. In: Higgins JPT, Green S (editors). Cochrane Handbook for Systematic Reviews of Interventions. Version 5.0.1 [updated September 2008]. The Cochrane Collaboration, 2008. Available from www.cochrane-handbook.org.
The widely cited 2007 paper by Jayne Tierney and colleagues "Practical methods for incorporating summary time-to event data into meta-analysis" addresses these issues, including methods for approximating hazard ratios using count data. The article is Open Access: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1920534/
The widely cited 2007 paper by Jayne Tierney and colleagues "Practical methods for incorporating summary time-to event data into meta-analysis" addresses these issues, including methods for approximating hazard ratios using count data. The article is Open Access: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1920534/
Dear Mohammed Ali The answer to your question is no - hazards and risks or odds are not interchangable! Regardsing the specific statistical differnces you would have to consult a statistician. But i can try to give you a lay-physician explanation. Risks refer to absolute numbers of an event (i.e. disease) in a popualation - we have no consideration of time in a risk. Hazards refers only to the "speed" of specific events in a population. A hazard is therefore a time to event estimate and will never reflect the absolute risk of an event in a population. Hazard risk and risk ratios are therefor two different measures of events in a population. They are based on two different infernential statistics and most likely also based on two different types of studies (propesctive cohort vs. interventional studies). The statistical question asked in a hazard rate is "does a specific exposure cause outcome quicker than to not being exposed" where the question in a risk ratio is "does exposure cause outcome more often compared to not being exposed". My advice to you is therefore not to include hazard ratios if you are making a meta analysis based on risks or odds ratios.
Dear Mohammed Ali The answer to your question is no - hazards and risks or odds are not interchangable! Regardsing the specific statistical differnces you would have to consult a statistician. But i can try to give you a lay-physician explanation. Risks refer to absolute numbers of an event (i.e. disease) in a popualation - we have no consideration of time in a risk. Hazards refers only to the "speed" of specific events in a population. A hazard is therefore a time to event estimate and will never reflect the absolute risk of an event in a population. Hazard risk and risk ratios are therefor two different measures of events in a population. They are based on two different infernential statistics and most likely also based on two different types of studies (propesctive cohort vs. interventional studies). The statistical question asked in a hazard rate is "does a specific exposure cause outcome quicker than to not being exposed" where the question in a risk ratio is "does exposure cause outcome more often compared to not being exposed". My advice to you is therefore not to include hazard ratios if you are making a meta analysis based on risks or odds ratios.
Dear Muhammad Ali, Risk (hazard) ratios and odds ratios cannot be used interchangeably in meta-analysis. Like euro and pound they have to be converted into the same value e.g. Swedish crowns. You find the formula here: http://hiv.cochrane.org/sites/hiv.cochrane.org/files/uploads/Ch09_Analysing.pdf Deeks JJ, Higgins JPT, Altman DG (editors). Chapter 9: Analysing data and undertaking meta-analyses. In: Higgins JPT, Green S (editors). Cochrane Handbook for Systematic Reviews of Interventions. Version 5.0.1 [updated September 2008]. The Cochrane Collaboration, 2008. Available from www.cochrane-handbook.org.
Dear Muhammad Ali, Risk (hazard) ratios and odds ratios cannot be used interchangeably in meta-analysis. Like euro and pound they have to be converted into the same value e.g. Swedish crowns. You find the formula here: http://hiv.cochrane.org/sites/hiv.cochrane.org/files/uploads/Ch09_Analysing.pdf Deeks JJ, Higgins JPT, Altman DG (editors). Chapter 9: Analysing data and undertaking meta-analyses. In: Higgins JPT, Green S (editors). Cochrane Handbook for Systematic Reviews of Interventions. Version 5.0.1 [updated September 2008]. The Cochrane Collaboration, 2008. Available from www.cochrane-handbook.org.
Dear Mohammed Ali The answer to your question is no - hazards and risks or odds are not interchangable! Regardsing the specific statistical differnces you would have to consult a statistician. But i can try to give you a lay-physician explanation. Risks refer to absolute numbers of an event (i.e. disease) in a popualation - we have no consideration of time in a risk. Hazards refers only to the "speed" of specific events in a population. A hazard is therefore a time to event estimate and will never reflect the absolute risk of an event in a population. Hazard risk and risk ratios are therefor two different measures of events in a population. They are based on two different infernential statistics and most likely also based on two different types of studies (propesctive cohort vs. interventional studies). The statistical question asked in a hazard rate is "does a specific exposure cause outcome quicker than to not being exposed" where the question in a risk ratio is "does exposure cause outcome more often compared to not being exposed". My advice to you is therefore not to include hazard ratios if you are making a meta analysis based on risks or odds ratios.
Dear Mohammed Ali The answer to your question is no - hazards and risks or odds are not interchangable! Regardsing the specific statistical differnces you would have to consult a statistician. But i can try to give you a lay-physician explanation. Risks refer to absolute numbers of an event (i.e. disease) in a popualation - we have no consideration of time in a risk. Hazards refers only to the "speed" of specific events in a population. A hazard is therefore a time to event estimate and will never reflect the absolute risk of an event in a population. Hazard risk and risk ratios are therefor two different measures of events in a population. They are based on two different infernential statistics and most likely also based on two different types of studies (propesctive cohort vs. interventional studies). The statistical question asked in a hazard rate is "does a specific exposure cause outcome quicker than to not being exposed" where the question in a risk ratio is "does exposure cause outcome more often compared to not being exposed". My advice to you is therefore not to include hazard ratios if you are making a meta analysis based on risks or odds ratios.
Not really, and without assumption on baseline hazard ( hazards for each group in absolute terms, not just the ratio, and how it changes over time) the answer can be very different. For example, assuming an exponential distribution for survival function (one of the simplest), S(t) = exp(- lambda * t), hazard ratio of 2 would mean that the second group has lambda 2x that of the first. Then, if all population is of the same "age", odds ratio at time t would be [1-S2(t)]/S2(t) / [1-S1(t)/S1(t) ] = (1-exp(-2*L1*t) / (1-exp(-L1*t). So as Mohamad mentioned below, if lambdas are small, this is close to 2L / L, or 2. While playing with this a bit, I found that depending on distribution of age in the population and how prevalent a condition is, hazard of 2 can correspond to odds ratios of anything from 2 till 10 (realistically) and even higher, at the same time risk ratios for very prevalent conditions would be biased towards one if population is rather "old" and close to 2 is young. In short, one can not infer OR from HR without further assumptions, but the smaller OR is the closer these should be
Not really, and without assumption on baseline hazard ( hazards for each group in absolute terms, not just the ratio, and how it changes over time) the answer can be very different. For example, assuming an exponential distribution for survival function (one of the simplest), S(t) = exp(- lambda * t), hazard ratio of 2 would mean that the second group has lambda 2x that of the first. Then, if all population is of the same "age", odds ratio at time t would be [1-S2(t)]/S2(t) / [1-S1(t)/S1(t) ] = (1-exp(-2*L1*t) / (1-exp(-L1*t). So as Mohamad mentioned below, if lambdas are small, this is close to 2L / L, or 2. While playing with this a bit, I found that depending on distribution of age in the population and how prevalent a condition is, hazard of 2 can correspond to odds ratios of anything from 2 till 10 (realistically) and even higher, at the same time risk ratios for very prevalent conditions would be biased towards one if population is rather "old" and close to 2 is young. In short, one can not infer OR from HR without further assumptions, but the smaller OR is the closer these should be
If there was an extremely low proportion of subjects with an event in all experiments (let's say <10%) and the hazard and odds ratios are vey close to 1, then hazard, odds and relative risk ratios will be relatively close to each other.
If there was an extremely low proportion of subjects with an event in all experiments (let's say <10%) and the hazard and odds ratios are vey close to 1, then hazard, odds and relative risk ratios will be relatively close to each other.
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Can RR be used interchangebly with HR while doing the meta-analysis?
Can RR be used interchangebly with HR while doing the meta-analysis?
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I have no idea.
I have no idea.
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Another 2008 reference by Ian Scott addressed this issue, specifically in pages 14-15. Scott, I. Interpreting risks and ratios in therapy trails Australian Prescriber, 2008;31:12-16. http://www.australianprescriber.com/magazine/31/1/12/6
Another 2008 reference by Ian Scott addressed this issue, specifically in pages 14-15. Scott, I. Interpreting risks and ratios in therapy trails Australian Prescriber, 2008;31:12-16. http://www.australianprescriber.com/magazine/31/1/12/6
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Yes they can be used.
Yes they can be used.
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Dear Muhammad Ali,
Risk (hazard) ratios and odds ratios cannot be used interchangeably in meta-analysis. Like euro and pound they have to be converted into the same value e.g. Swedish crowns. You find the formula here:
http://hiv.cochrane.org/sites/hiv.cochrane.org/files/uploads/Ch09_Analysing.pdf
Deeks JJ, Higgins JPT, Altman DG (editors). Chapter 9: Analysing data and undertaking meta-analyses. In: Higgins JPT, Green S (editors).
Cochrane Handbook for Systematic Reviews of Interventions. Version 5.0.1 [updated September 2008]. The Cochrane Collaboration, 2008. Available from www.cochrane-handbook.org.
Dear Muhammad Ali,
Risk (hazard) ratios and odds ratios cannot be used interchangeably in meta-analysis. Like euro and pound they have to be converted into the same value e.g. Swedish crowns. You find the formula here:
http://hiv.cochrane.org/sites/hiv.cochrane.org/files/uploads/Ch09_Analysing.pdf
Deeks JJ, Higgins JPT, Altman DG (editors). Chapter 9: Analysing data and undertaking meta-analyses. In: Higgins JPT, Green S (editors).
Cochrane Handbook for Systematic Reviews of Interventions. Version 5.0.1 [updated September 2008]. The Cochrane Collaboration, 2008. Available from www.cochrane-handbook.org.
More
VOTE
The widely cited 2007 paper by Jayne Tierney and colleagues "Practical methods for incorporating summary time-to event data into meta-analysis" addresses these issues, including methods for approximating hazard ratios using count data. The article is Open Access: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1920534/
The widely cited 2007 paper by Jayne Tierney and colleagues "Practical methods for incorporating summary time-to event data into meta-analysis" addresses these issues, including methods for approximating hazard ratios using count data. The article is Open Access: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1920534/
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Dear Mohammed Ali
The answer to your question is no - hazards and risks or odds are not interchangable! Regardsing the specific statistical differnces you would have to consult a statistician. But i can try to give you a lay-physician explanation.
Risks refer to absolute numbers of an event (i.e. disease) in a popualation - we have no consideration of time in a risk.
Hazards refers only to the "speed" of specific events in a population. A hazard is therefore a time to event estimate and will never reflect the absolute risk of an event in a population.
Hazard risk and risk ratios are therefor two different measures of events in a population. They are based on two different infernential statistics and most likely also based on two different types of studies (propesctive cohort vs. interventional studies). The statistical question asked in a hazard rate is "does a specific exposure cause outcome quicker than to not being exposed" where the question in a risk ratio is "does exposure cause outcome more often compared to not being exposed".
My advice to you is therefore not to include hazard ratios if you are making a meta analysis based on risks or odds ratios.
Dear Mohammed Ali
The answer to your question is no - hazards and risks or odds are not interchangable! Regardsing the specific statistical differnces you would have to consult a statistician. But i can try to give you a lay-physician explanation.
Risks refer to absolute numbers of an event (i.e. disease) in a popualation - we have no consideration of time in a risk.
Hazards refers only to the "speed" of specific events in a population. A hazard is therefore a time to event estimate and will never reflect the absolute risk of an event in a population.
Hazard risk and risk ratios are therefor two different measures of events in a population. They are based on two different infernential statistics and most likely also based on two different types of studies (propesctive cohort vs. interventional studies). The statistical question asked in a hazard rate is "does a specific exposure cause outcome quicker than to not being exposed" where the question in a risk ratio is "does exposure cause outcome more often compared to not being exposed".
My advice to you is therefore not to include hazard ratios if you are making a meta analysis based on risks or odds ratios.
More
VOTE
Dear Muhammad Ali,
Risk (hazard) ratios and odds ratios cannot be used interchangeably in meta-analysis. Like euro and pound they have to be converted into the same value e.g. Swedish crowns. You find the formula here:
http://hiv.cochrane.org/sites/hiv.cochrane.org/files/uploads/Ch09_Analysing.pdf
Deeks JJ, Higgins JPT, Altman DG (editors). Chapter 9: Analysing data and undertaking meta-analyses. In: Higgins JPT, Green S (editors).
Cochrane Handbook for Systematic Reviews of Interventions. Version 5.0.1 [updated September 2008]. The Cochrane Collaboration, 2008. Available from www.cochrane-handbook.org.
Dear Muhammad Ali,
Risk (hazard) ratios and odds ratios cannot be used interchangeably in meta-analysis. Like euro and pound they have to be converted into the same value e.g. Swedish crowns. You find the formula here:
http://hiv.cochrane.org/sites/hiv.cochrane.org/files/uploads/Ch09_Analysing.pdf
Deeks JJ, Higgins JPT, Altman DG (editors). Chapter 9: Analysing data and undertaking meta-analyses. In: Higgins JPT, Green S (editors).
Cochrane Handbook for Systematic Reviews of Interventions. Version 5.0.1 [updated September 2008]. The Cochrane Collaboration, 2008. Available from www.cochrane-handbook.org.
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Thank a lot Ali Bhai.
Thank a lot Ali Bhai.
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Dear Mohammed Ali
The answer to your question is no - hazards and risks or odds are not interchangable! Regardsing the specific statistical differnces you would have to consult a statistician. But i can try to give you a lay-physician explanation.
Risks refer to absolute numbers of an event (i.e. disease) in a popualation - we have no consideration of time in a risk.
Hazards refers only to the "speed" of specific events in a population. A hazard is therefore a time to event estimate and will never reflect the absolute risk of an event in a population.
Hazard risk and risk ratios are therefor two different measures of events in a population. They are based on two different infernential statistics and most likely also based on two different types of studies (propesctive cohort vs. interventional studies). The statistical question asked in a hazard rate is "does a specific exposure cause outcome quicker than to not being exposed" where the question in a risk ratio is "does exposure cause outcome more often compared to not being exposed".
My advice to you is therefore not to include hazard ratios if you are making a meta analysis based on risks or odds ratios.
Dear Mohammed Ali
The answer to your question is no - hazards and risks or odds are not interchangable! Regardsing the specific statistical differnces you would have to consult a statistician. But i can try to give you a lay-physician explanation.
Risks refer to absolute numbers of an event (i.e. disease) in a popualation - we have no consideration of time in a risk.
Hazards refers only to the "speed" of specific events in a population. A hazard is therefore a time to event estimate and will never reflect the absolute risk of an event in a population.
Hazard risk and risk ratios are therefor two different measures of events in a population. They are based on two different infernential statistics and most likely also based on two different types of studies (propesctive cohort vs. interventional studies). The statistical question asked in a hazard rate is "does a specific exposure cause outcome quicker than to not being exposed" where the question in a risk ratio is "does exposure cause outcome more often compared to not being exposed".
My advice to you is therefore not to include hazard ratios if you are making a meta analysis based on risks or odds ratios.
More
VOTE
Not really, and without assumption on baseline hazard ( hazards for each group in absolute terms, not just the ratio, and how it changes over time) the answer can be very different. For example, assuming an exponential distribution for survival function (one of the simplest), S(t) = exp(- lambda * t), hazard ratio of 2 would mean that the second group has lambda 2x that of the first. Then, if all population is of the same "age", odds ratio at time t would be [1-S2(t)]/S2(t) / [1-S1(t)/S1(t) ] = (1-exp(-2*L1*t) / (1-exp(-L1*t). So as Mohamad mentioned below, if lambdas are small, this is close to 2L / L, or 2. While playing with this a bit, I found that depending on distribution of age in the population and how prevalent a condition is, hazard of 2 can correspond to odds ratios of anything from 2 till 10 (realistically) and even higher, at the same time risk ratios for very prevalent conditions would be biased towards one if population is rather "old" and close to 2 is young. In short, one can not infer OR from HR without further assumptions, but the smaller OR is the closer these should be
Not really, and without assumption on baseline hazard ( hazards for each group in absolute terms, not just the ratio, and how it changes over time) the answer can be very different. For example, assuming an exponential distribution for survival function (one of the simplest), S(t) = exp(- lambda * t), hazard ratio of 2 would mean that the second group has lambda 2x that of the first. Then, if all population is of the same "age", odds ratio at time t would be [1-S2(t)]/S2(t) / [1-S1(t)/S1(t) ] = (1-exp(-2*L1*t) / (1-exp(-L1*t). So as Mohamad mentioned below, if lambdas are small, this is close to 2L / L, or 2. While playing with this a bit, I found that depending on distribution of age in the population and how prevalent a condition is, hazard of 2 can correspond to odds ratios of anything from 2 till 10 (realistically) and even higher, at the same time risk ratios for very prevalent conditions would be biased towards one if population is rather "old" and close to 2 is young. In short, one can not infer OR from HR without further assumptions, but the smaller OR is the closer these should be
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