@JorgeTeixeira when analyzing data with baseline (pre-treatment) and multiple post-treatment time points, I prefer to use an AR(1) structure as a starting point. It logically/clinically makes sense and is why there is the long standing issue of using lme4. If, for some reason, your actual data do not meet those assumptions, you can then explore alternatives, but if you need to pre-specify these details in an SAP, AR(1) is what I would use. With respect to the older lme() function in the nlme package that is part of Base R + Recommended packages, the description of the “correlation” argument in the documentation is as follows: > an optional corStruct object describing the within-group correlation structure. See the documentation of corClasses for a description of the available `corStruct`classes. Defaults to `NULL`, corresponding to no within-group correlations. Apparently, over time, the last sentence regarding the default has led to confusion, with some interpretations being unstructured and others being independence. Finding what would reasonably be considered the definitive reference from 1998 by Jose and Doug: https://www.stat.cmu.edu/~brian/720-2007-source/week07-08-ideas/pinheiro98mixedeffects-Sguide.pdf on the bottom of page 19 is the following: > The optional argument correlation is used to specify a correlation structure and the optional argument weights is used for variance functions. By default, the within-group errors are assumed to independent and homoscedastic. so that might help to mitigate some of the confusion. It is also why I have never used the default, and prefer to explicitly define these details.

@JorgeTeixeira when analyzing data with baseline (pre-treatment) and multiple post-treatment time points, I prefer to use an AR(1) structure as a starting point. It logically/clinically makes sense and is why there is the long standing issue of using lme4. If, for some reason, your actual data do not meet those assumptions, you can then explore alternatives, but if you need to pre-specify these details in an SAP, AR(1) is what I would use. With respect to the older lme() function in the nlme package that is part of Base R + Recommended packages, the description of the “correlation” argument in the documentation is as follows: > an optional corStruct object describing the within-group correlation structure. See the documentation of corClasses for a description of the available `corStruct`classes. Defaults to `NULL`, corresponding to no within-group correlations. Apparently, over time, the last sentence regarding the default has led to confusion, with some interpretations being unstructured and others being independence. Finding what would reasonably be considered the definitive reference from 1998 by Jose and Doug: https://www.stat.cmu.edu/~brian/720-2007-source/week07-08-ideas/pinheiro98mixedeffects-Sguide.pdf on the bottom of page 19 is the following: > The optional argument correlation is used to specify a correlation structure and the optional argument weights is used for variance functions. By default, the within-group errors are assumed to independent and homoscedastic. so that might help to mitigate some of the confusion. It is also why I have never used the default, and prefer to explicitly define these details.

@JorgeTeixeira when analyzing data with baseline (pre-treatment) and multiple post-treatment time points, I prefer to use an AR(1) structure as a starting point. It logically/clinically makes sense and is why there is the long standing issue of using lme4. If, for some reason, your actual data do not meet those assumptions, you can then explore alternatives, but if you need to pre-specify these details in an SAP, AR(1) is what I would use. With respect to the older lme() function in the nlme package that is part of Base R + Recommended packages, the description of the “correlation” argument in the documentation is as follows: > an optional corStruct object describing the within-group correlation structure. See the documentation of corClasses for a description of the available `corStruct`classes. Defaults to `NULL`, corresponding to no within-group correlations. Apparently, over time, the last sentence regarding the default has led to confusion, with some interpretations being unstructured and others being independence. Finding what would reasonably be considered the definitive reference from 1998 by Jose and Doug: https://www.stat.cmu.edu/~brian/720-2007-source/week07-08-ideas/pinheiro98mixedeffects-Sguide.pdf on the bottom of page 19 is the following: > The optional argument correlation is used to specify a correlation structure and the optional argument weights is used for variance functions. By default, the within-group errors are assumed to independent and homoscedastic. so that might help to mitigate some of the confusion. It is also why I have never used the default, and prefer to explicitly define these details.

@JorgeTeixeira when analyzing data with baseline (pre-treatment) and multiple post-treatment time points, I prefer to use an AR(1) structure as a starting point. It logically/clinically makes sense and is why there is the long standing issue of using lme4. If, for some reason, your actual data do not meet those assumptions, you can then explore alternatives, but if you need to pre-specify these details in an SAP, AR(1) is what I would use. With respect to the older lme() function in the nlme package that is part of Base R + Recommended packages, the description of the “correlation” argument in the documentation is as follows: > an optional corStruct object describing the within-group correlation structure. See the documentation of corClasses for a description of the available `corStruct`classes. Defaults to `NULL`, corresponding to no within-group correlations. Apparently, over time, the last sentence regarding the default has led to confusion, with some interpretations being unstructured and others being independence. Finding what would reasonably be considered the definitive reference from 1998 by Jose and Doug: https://www.stat.cmu.edu/~brian/720-2007-source/week07-08-ideas/pinheiro98mixedeffects-Sguide.pdf on the bottom of page 19 is the following: > The optional argument correlation is used to specify a correlation structure and the optional argument weights is used for variance functions. By default, the within-group errors are assumed to independent and homoscedastic. so that might help to mitigate some of the confusion. It is also why I have never used the default, and prefer to explicitly define these details.

@JorgeTeixeira when analyzing data with baseline (pre-treatment) and multiple post-treatment time points, I prefer to use an AR(1) structure as a starting point. It logically/clinically makes sense and is why there is the long standing issue of using lme4. If, for some reason, your actual data do not meet those assumptions, you can then explore alternatives, but if you need to pre-specify these details in an SAP, AR(1) is what I would use. With respect to the older lme() function in the nlme package that is part of Base R + Recommended packages, the description of the “correlation” argument in the documentation is as follows: > an optional corStruct object describing the within-group correlation structure. See the documentation of corClasses for a description of the available `corStruct`classes. Defaults to `NULL`, corresponding to no within-group correlations. Apparently, over time, the last sentence regarding the default has led to confusion, with some interpretations being unstructured and others being independence. Finding what would reasonably be considered the definitive reference from 1998 by Jose and Doug: https://www.stat.cmu.edu/~brian/720-2007-source/week07-08-ideas/pinheiro98mixedeffects-Sguide.pdf on the bottom of page 19 is the following: > The optional argument correlation is used to specify a correlation structure and the optional argument weights is used for variance functions. By default, the within-group errors are assumed to independent and homoscedastic. so that might help to mitigate some of the confusion. It is also why I have never used the default, and prefer to explicitly define these details.

@JorgeTeixeira when analyzing data with baseline (pre-treatment) and multiple post-treatment time points, I prefer to use an AR(1) structure as a starting point. It logically/clinically makes sense and is why there is the long standing issue of using lme4. If, for some reason, your actual data do not meet those assumptions, you can then explore alternatives, but if you need to pre-specify these details in an SAP, AR(1) is what I would use. With respect to the older lme() function in the nlme package that is part of Base R + Recommended packages, the description of the “correlation” argument in the documentation is as follows: > an optional corStruct object describing the within-group correlation structure. See the documentation of corClasses for a description of the available `corStruct`classes. Defaults to `NULL`, corresponding to no within-group correlations. Apparently, over time, the last sentence regarding the default has led to confusion, with some interpretations being unstructured and others being independence. Finding what would reasonably be considered the definitive reference from 1998 by Jose and Doug: https://www.stat.cmu.edu/~brian/720-2007-source/week07-08-ideas/pinheiro98mixedeffects-Sguide.pdf on the bottom of page 19 is the following: > The optional argument correlation is used to specify a correlation structure and the optional argument weights is used for variance functions. By default, the within-group errors are assumed to independent and homoscedastic. so that might help to mitigate some of the confusion. It is also why I have never used the default, and prefer to explicitly define these details.

@JorgeTeixeira when analyzing data with baseline (pre-treatment) and multiple post-treatment time points, I prefer to use an AR(1) structure as a starting point. It logically/clinically makes sense and is why there is the long standing issue of using lme4. If, for some reason, your actual data do not meet those assumptions, you can then explore alternatives, but if you need to pre-specify these details in an SAP, AR(1) is what I would use. With respect to the older lme() function in the nlme package that is part of Base R + Recommended packages, the description of the “correlation” argument in the documentation is as follows: > an optional corStruct object describing the within-group correlation structure. See the documentation of corClasses for a description of the available `corStruct`classes. Defaults to `NULL`, corresponding to no within-group correlations. Apparently, over time, the last sentence regarding the default has led to confusion, with some interpretations being unstructured and others being independence. Finding what would reasonably be considered the definitive reference from 1998 by Jose and Doug: https://www.stat.cmu.edu/~brian/720-2007-source/week07-08-ideas/pinheiro98mixedeffects-Sguide.pdf on the bottom of page 19 is the following: > The optional argument correlation is used to specify a correlation structure and the optional argument weights is used for variance functions. By default, the within-group errors are assumed to independent and homoscedastic. so that might help to mitigate some of the confusion. It is also why I have never used the default, and prefer to explicitly define these details.

JorgeTeixeira: > The previous software also indicates that when moving from compound symmetry to AR(1), the power actually decreases. I don’t think that is possible without a significant lack of fit of AR(1). JorgeTeixeira: > Regarding questions involving two, three, or four follow-up measurements: if I understood correctly, your preference would be for GLS or Markov models? Yes and if you want to hedge your bets regarding goodness of fit of the correlation structure use Markov models with random intercepts. JorgeTeixeira: > In those models, do you have to manually specify the correlation matrix during analysis, or does the models handle that automatically in the background? For Markov you specify how the current observations depend on past observations from the same subject. For generalized least squares you specify the correlation structure and get maximum likelihood estimates of the parameters of that structure (one parameter for AR(1)). JorgeTeixeira: > Also, out of curiosity, do you believe GEE is better than linear mixed-effects models for parallel RCTs? No. GEE can be inaccurate in estimating regression coefficients by assuming a nonsense working independence model. And GEE requires that dropouts and missing data are missing completely at random. Full modeling methods only require the missing at random assumption.

@JorgeTeixeira when analyzing data with baseline (pre-treatment) and multiple post-treatment time points, I prefer to use an AR(1) structure as a starting point. It logically/clinically makes sense and is why there is the long standing issue of using lme4. If, for some reason, your actual data do not meet those assumptions, you can then explore alternatives, but if you need to pre-specify these details in an SAP, AR(1) is what I would use. With respect to the older lme() function in the nlme package that is part of Base R + Recommended packages, the description of the “correlation” argument in the documentation is as follows: > an optional corStruct object describing the within-group correlation structure. See the documentation of corClasses for a description of the available `corStruct`classes. Defaults to `NULL`, corresponding to no within-group correlations. Apparently, over time, the last sentence regarding the default has led to confusion, with some interpretations being unstructured and others being independence. Finding what would reasonably be considered the definitive reference from 1998 by Jose and Doug: https://www.stat.cmu.edu/~brian/720-2007-source/week07-08-ideas/pinheiro98mixedeffects-Sguide.pdf on the bottom of page 19 is the following: > The optional argument correlation is used to specify a correlation structure and the optional argument weights is used for variance functions. By default, the within-group errors are assumed to independent and homoscedastic. so that might help to mitigate some of the confusion. It is also why I have never used the default, and prefer to explicitly define these details.

JorgeTeixeira: > The previous software also indicates that when moving from compound symmetry to AR(1), the power actually decreases. I don’t think that is possible without a significant lack of fit of AR(1). JorgeTeixeira: > Regarding questions involving two, three, or four follow-up measurements: if I understood correctly, your preference would be for GLS or Markov models? Yes and if you want to hedge your bets regarding goodness of fit of the correlation structure use Markov models with random intercepts. JorgeTeixeira: > In those models, do you have to manually specify the correlation matrix during analysis, or does the models handle that automatically in the background? For Markov you specify how the current observations depend on past observations from the same subject. For generalized least squares you specify the correlation structure and get maximum likelihood estimates of the parameters of that structure (one parameter for AR(1)). JorgeTeixeira: > Also, out of curiosity, do you believe GEE is better than linear mixed-effects models for parallel RCTs? No. GEE can be inaccurate in estimating regression coefficients by assuming a nonsense working independence model. And GEE requires that dropouts and missing data are missing completely at random. Full modeling methods only require the missing at random assumption.

@JorgeTeixeira when analyzing data with baseline (pre-treatment) and multiple post-treatment time points, I prefer to use an AR(1) structure as a starting point. It logically/clinically makes sense and is why there is the long standing issue of using lme4. If, for some reason, your actual data do not meet those assumptions, you can then explore alternatives, but if you need to pre-specify these details in an SAP, AR(1) is what I would use. With respect to the older lme() function in the nlme package that is part of Base R + Recommended packages, the description of the “correlation” argument in the documentation is as follows: > an optional corStruct object describing the within-group correlation structure. See the documentation of corClasses for a description of the available `corStruct`classes. Defaults to `NULL`, corresponding to no within-group correlations. Apparently, over time, the last sentence regarding the default has led to confusion, with some interpretations being unstructured and others being independence. Finding what would reasonably be considered the definitive reference from 1998 by Jose and Doug: https://www.stat.cmu.edu/~brian/720-2007-source/week07-08-ideas/pinheiro98mixedeffects-Sguide.pdf on the bottom of page 19 is the following: > The optional argument correlation is used to specify a correlation structure and the optional argument weights is used for variance functions. By default, the within-group errors are assumed to independent and homoscedastic. so that might help to mitigate some of the confusion. It is also why I have never used the default, and prefer to explicitly define these details.

JorgeTeixeira: > The previous software also indicates that when moving from compound symmetry to AR(1), the power actually decreases. I don’t think that is possible without a significant lack of fit of AR(1). JorgeTeixeira: > Regarding questions involving two, three, or four follow-up measurements: if I understood correctly, your preference would be for GLS or Markov models? Yes and if you want to hedge your bets regarding goodness of fit of the correlation structure use Markov models with random intercepts. JorgeTeixeira: > In those models, do you have to manually specify the correlation matrix during analysis, or does the models handle that automatically in the background? For Markov you specify how the current observations depend on past observations from the same subject. For generalized least squares you specify the correlation structure and get maximum likelihood estimates of the parameters of that structure (one parameter for AR(1)). JorgeTeixeira: > Also, out of curiosity, do you believe GEE is better than linear mixed-effects models for parallel RCTs? No. GEE can be inaccurate in estimating regression coefficients by assuming a nonsense working independence model. And GEE requires that dropouts and missing data are missing completely at random. Full modeling methods only require the missing at random assumption.

@JorgeTeixeira when analyzing data with baseline (pre-treatment) and multiple post-treatment time points, I prefer to use an AR(1) structure as a starting point. It logically/clinically makes sense and is why there is the long standing issue of using lme4. If, for some reason, your actual data do not meet those assumptions, you can then explore alternatives, but if you need to pre-specify these details in an SAP, AR(1) is what I would use. With respect to the older lme() function in the nlme package that is part of Base R + Recommended packages, the description of the “correlation” argument in the documentation is as follows: > an optional corStruct object describing the within-group correlation structure. See the documentation of corClasses for a description of the available `corStruct`classes. Defaults to `NULL`, corresponding to no within-group correlations. Apparently, over time, the last sentence regarding the default has led to confusion, with some interpretations being unstructured and others being independence. Finding what would reasonably be considered the definitive reference from 1998 by Jose and Doug: https://www.stat.cmu.edu/~brian/720-2007-source/week07-08-ideas/pinheiro98mixedeffects-Sguide.pdf on the bottom of page 19 is the following: > The optional argument correlation is used to specify a correlation structure and the optional argument weights is used for variance functions. By default, the within-group errors are assumed to independent and homoscedastic. so that might help to mitigate some of the confusion. It is also why I have never used the default, and prefer to explicitly define these details.

JorgeTeixeira: > The previous software also indicates that when moving from compound symmetry to AR(1), the power actually decreases. I don’t think that is possible without a significant lack of fit of AR(1). JorgeTeixeira: > Regarding questions involving two, three, or four follow-up measurements: if I understood correctly, your preference would be for GLS or Markov models? Yes and if you want to hedge your bets regarding goodness of fit of the correlation structure use Markov models with random intercepts. JorgeTeixeira: > In those models, do you have to manually specify the correlation matrix during analysis, or does the models handle that automatically in the background? For Markov you specify how the current observations depend on past observations from the same subject. For generalized least squares you specify the correlation structure and get maximum likelihood estimates of the parameters of that structure (one parameter for AR(1)). JorgeTeixeira: > Also, out of curiosity, do you believe GEE is better than linear mixed-effects models for parallel RCTs? No. GEE can be inaccurate in estimating regression coefficients by assuming a nonsense working independence model. And GEE requires that dropouts and missing data are missing completely at random. Full modeling methods only require the missing at random assumption.

@JorgeTeixeira when analyzing data with baseline (pre-treatment) and multiple post-treatment time points, I prefer to use an AR(1) structure as a starting point. It logically/clinically makes sense and is why there is the long standing issue of using lme4. If, for some reason, your actual data do not meet those assumptions, you can then explore alternatives, but if you need to pre-specify these details in an SAP, AR(1) is what I would use. With respect to the older lme() function in the nlme package that is part of Base R + Recommended packages, the description of the “correlation” argument in the documentation is as follows: > an optional corStruct object describing the within-group correlation structure. See the documentation of corClasses for a description of the available `corStruct`classes. Defaults to `NULL`, corresponding to no within-group correlations. Apparently, over time, the last sentence regarding the default has led to confusion, with some interpretations being unstructured and others being independence. Finding what would reasonably be considered the definitive reference from 1998 by Jose and Doug: https://www.stat.cmu.edu/~brian/720-2007-source/week07-08-ideas/pinheiro98mixedeffects-Sguide.pdf on the bottom of page 19 is the following: > The optional argument correlation is used to specify a correlation structure and the optional argument weights is used for variance functions. By default, the within-group errors are assumed to independent and homoscedastic. so that might help to mitigate some of the confusion. It is also why I have never used the default, and prefer to explicitly define these details.

JorgeTeixeira: > The previous software also indicates that when moving from compound symmetry to AR(1), the power actually decreases. I don’t think that is possible without a significant lack of fit of AR(1). JorgeTeixeira: > Regarding questions involving two, three, or four follow-up measurements: if I understood correctly, your preference would be for GLS or Markov models? Yes and if you want to hedge your bets regarding goodness of fit of the correlation structure use Markov models with random intercepts. JorgeTeixeira: > In those models, do you have to manually specify the correlation matrix during analysis, or does the models handle that automatically in the background? For Markov you specify how the current observations depend on past observations from the same subject. For generalized least squares you specify the correlation structure and get maximum likelihood estimates of the parameters of that structure (one parameter for AR(1)). JorgeTeixeira: > Also, out of curiosity, do you believe GEE is better than linear mixed-effects models for parallel RCTs? No. GEE can be inaccurate in estimating regression coefficients by assuming a nonsense working independence model. And GEE requires that dropouts and missing data are missing completely at random. Full modeling methods only require the missing at random assumption.

@JorgeTeixeira when analyzing data with baseline (pre-treatment) and multiple post-treatment time points, I prefer to use an AR(1) structure as a starting point. It logically/clinically makes sense and is why there is the long standing issue of using lme4. If, for some reason, your actual data do not meet those assumptions, you can then explore alternatives, but if you need to pre-specify these details in an SAP, AR(1) is what I would use. With respect to the older lme() function in the nlme package that is part of Base R + Recommended packages, the description of the “correlation” argument in the documentation is as follows: > an optional corStruct object describing the within-group correlation structure. See the documentation of corClasses for a description of the available `corStruct`classes. Defaults to `NULL`, corresponding to no within-group correlations. Apparently, over time, the last sentence regarding the default has led to confusion, with some interpretations being unstructured and others being independence. Finding what would reasonably be considered the definitive reference from 1998 by Jose and Doug: https://www.stat.cmu.edu/~brian/720-2007-source/week07-08-ideas/pinheiro98mixedeffects-Sguide.pdf on the bottom of page 19 is the following: > The optional argument correlation is used to specify a correlation structure and the optional argument weights is used for variance functions. By default, the within-group errors are assumed to independent and homoscedastic. so that might help to mitigate some of the confusion. It is also why I have never used the default, and prefer to explicitly define these details.

JorgeTeixeira: > The previous software also indicates that when moving from compound symmetry to AR(1), the power actually decreases. I don’t think that is possible without a significant lack of fit of AR(1). JorgeTeixeira: > Regarding questions involving two, three, or four follow-up measurements: if I understood correctly, your preference would be for GLS or Markov models? Yes and if you want to hedge your bets regarding goodness of fit of the correlation structure use Markov models with random intercepts. JorgeTeixeira: > In those models, do you have to manually specify the correlation matrix during analysis, or does the models handle that automatically in the background? For Markov you specify how the current observations depend on past observations from the same subject. For generalized least squares you specify the correlation structure and get maximum likelihood estimates of the parameters of that structure (one parameter for AR(1)). JorgeTeixeira: > Also, out of curiosity, do you believe GEE is better than linear mixed-effects models for parallel RCTs? No. GEE can be inaccurate in estimating regression coefficients by assuming a nonsense working independence model. And GEE requires that dropouts and missing data are missing completely at random. Full modeling methods only require the missing at random assumption.

@JorgeTeixeira when analyzing data with baseline (pre-treatment) and multiple post-treatment time points, I prefer to use an AR(1) structure as a starting point. It logically/clinically makes sense and is why there is the long standing issue of using lme4. If, for some reason, your actual data do not meet those assumptions, you can then explore alternatives, but if you need to pre-specify these details in an SAP, AR(1) is what I would use. With respect to the older lme() function in the nlme package that is part of Base R + Recommended packages, the description of the “correlation” argument in the documentation is as follows: > an optional corStruct object describing the within-group correlation structure. See the documentation of corClasses for a description of the available `corStruct`classes. Defaults to `NULL`, corresponding to no within-group correlations. Apparently, over time, the last sentence regarding the default has led to confusion, with some interpretations being unstructured and others being independence. Finding what would reasonably be considered the definitive reference from 1998 by Jose and Doug: https://www.stat.cmu.edu/~brian/720-2007-source/week07-08-ideas/pinheiro98mixedeffects-Sguide.pdf on the bottom of page 19 is the following: > The optional argument correlation is used to specify a correlation structure and the optional argument weights is used for variance functions. By default, the within-group errors are assumed to independent and homoscedastic. so that might help to mitigate some of the confusion. It is also why I have never used the default, and prefer to explicitly define these details.

JorgeTeixeira: > The previous software also indicates that when moving from compound symmetry to AR(1), the power actually decreases. I don’t think that is possible without a significant lack of fit of AR(1). JorgeTeixeira: > Regarding questions involving two, three, or four follow-up measurements: if I understood correctly, your preference would be for GLS or Markov models? Yes and if you want to hedge your bets regarding goodness of fit of the correlation structure use Markov models with random intercepts. JorgeTeixeira: > In those models, do you have to manually specify the correlation matrix during analysis, or does the models handle that automatically in the background? For Markov you specify how the current observations depend on past observations from the same subject. For generalized least squares you specify the correlation structure and get maximum likelihood estimates of the parameters of that structure (one parameter for AR(1)). JorgeTeixeira: > Also, out of curiosity, do you believe GEE is better than linear mixed-effects models for parallel RCTs? No. GEE can be inaccurate in estimating regression coefficients by assuming a nonsense working independence model. And GEE requires that dropouts and missing data are missing completely at random. Full modeling methods only require the missing at random assumption.

@JorgeTeixeira when analyzing data with baseline (pre-treatment) and multiple post-treatment time points, I prefer to use an AR(1) structure as a starting point. It logically/clinically makes sense and is why there is the long standing issue of using lme4. If, for some reason, your actual data do not meet those assumptions, you can then explore alternatives, but if you need to pre-specify these details in an SAP, AR(1) is what I would use. With respect to the older lme() function in the nlme package that is part of Base R + Recommended packages, the description of the “correlation” argument in the documentation is as follows: > an optional corStruct object describing the within-group correlation structure. See the documentation of corClasses for a description of the available `corStruct`classes. Defaults to `NULL`, corresponding to no within-group correlations. Apparently, over time, the last sentence regarding the default has led to confusion, with some interpretations being unstructured and others being independence. Finding what would reasonably be considered the definitive reference from 1998 by Jose and Doug: https://www.stat.cmu.edu/~brian/720-2007-source/week07-08-ideas/pinheiro98mixedeffects-Sguide.pdf on the bottom of page 19 is the following: > The optional argument correlation is used to specify a correlation structure and the optional argument weights is used for variance functions. By default, the within-group errors are assumed to independent and homoscedastic. so that might help to mitigate some of the confusion. It is also why I have never used the default, and prefer to explicitly define these details.

JorgeTeixeira: > The previous software also indicates that when moving from compound symmetry to AR(1), the power actually decreases. I don’t think that is possible without a significant lack of fit of AR(1). JorgeTeixeira: > Regarding questions involving two, three, or four follow-up measurements: if I understood correctly, your preference would be for GLS or Markov models? Yes and if you want to hedge your bets regarding goodness of fit of the correlation structure use Markov models with random intercepts. JorgeTeixeira: > In those models, do you have to manually specify the correlation matrix during analysis, or does the models handle that automatically in the background? For Markov you specify how the current observations depend on past observations from the same subject. For generalized least squares you specify the correlation structure and get maximum likelihood estimates of the parameters of that structure (one parameter for AR(1)). JorgeTeixeira: > Also, out of curiosity, do you believe GEE is better than linear mixed-effects models for parallel RCTs? No. GEE can be inaccurate in estimating regression coefficients by assuming a nonsense working independence model. And GEE requires that dropouts and missing data are missing completely at random. Full modeling methods only require the missing at random assumption.

@JorgeTeixeira when analyzing data with baseline (pre-treatment) and multiple post-treatment time points, I prefer to use an AR(1) structure as a starting point. It logically/clinically makes sense and is why there is the long standing issue of using lme4. If, for some reason, your actual data do not meet those assumptions, you can then explore alternatives, but if you need to pre-specify these details in an SAP, AR(1) is what I would use. With respect to the older lme() function in the nlme package that is part of Base R + Recommended packages, the description of the “correlation” argument in the documentation is as follows: > an optional corStruct object describing the within-group correlation structure. See the documentation of corClasses for a description of the available `corStruct`classes. Defaults to `NULL`, corresponding to no within-group correlations. Apparently, over time, the last sentence regarding the default has led to confusion, with some interpretations being unstructured and others being independence. Finding what would reasonably be considered the definitive reference from 1998 by Jose and Doug: https://www.stat.cmu.edu/~brian/720-2007-source/week07-08-ideas/pinheiro98mixedeffects-Sguide.pdf on the bottom of page 19 is the following: > The optional argument correlation is used to specify a correlation structure and the optional argument weights is used for variance functions. By default, the within-group errors are assumed to independent and homoscedastic. so that might help to mitigate some of the confusion. It is also why I have never used the default, and prefer to explicitly define these details.

JorgeTeixeira: > The previous software also indicates that when moving from compound symmetry to AR(1), the power actually decreases. I don’t think that is possible without a significant lack of fit of AR(1). JorgeTeixeira: > Regarding questions involving two, three, or four follow-up measurements: if I understood correctly, your preference would be for GLS or Markov models? Yes and if you want to hedge your bets regarding goodness of fit of the correlation structure use Markov models with random intercepts. JorgeTeixeira: > In those models, do you have to manually specify the correlation matrix during analysis, or does the models handle that automatically in the background? For Markov you specify how the current observations depend on past observations from the same subject. For generalized least squares you specify the correlation structure and get maximum likelihood estimates of the parameters of that structure (one parameter for AR(1)). JorgeTeixeira: > Also, out of curiosity, do you believe GEE is better than linear mixed-effects models for parallel RCTs? No. GEE can be inaccurate in estimating regression coefficients by assuming a nonsense working independence model. And GEE requires that dropouts and missing data are missing completely at random. Full modeling methods only require the missing at random assumption.

@JorgeTeixeira when analyzing data with baseline (pre-treatment) and multiple post-treatment time points, I prefer to use an AR(1) structure as a starting point. It logically/clinically makes sense and is why there is the long standing issue of using lme4. If, for some reason, your actual data do not meet those assumptions, you can then explore alternatives, but if you need to pre-specify these details in an SAP, AR(1) is what I would use. With respect to the older lme() function in the nlme package that is part of Base R + Recommended packages, the description of the “correlation” argument in the documentation is as follows: > an optional corStruct object describing the within-group correlation structure. See the documentation of corClasses for a description of the available `corStruct`classes. Defaults to `NULL`, corresponding to no within-group correlations. Apparently, over time, the last sentence regarding the default has led to confusion, with some interpretations being unstructured and others being independence. Finding what would reasonably be considered the definitive reference from 1998 by Jose and Doug: https://www.stat.cmu.edu/~brian/720-2007-source/week07-08-ideas/pinheiro98mixedeffects-Sguide.pdf on the bottom of page 19 is the following: > The optional argument correlation is used to specify a correlation structure and the optional argument weights is used for variance functions. By default, the within-group errors are assumed to independent and homoscedastic. so that might help to mitigate some of the confusion. It is also why I have never used the default, and prefer to explicitly define these details.