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standardizing p_max
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Cliff AB
Cliff AB
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In short, as long as none of the observations dominate the estimation of the regression coefficients, or none of the covariate effects are too extreme (i.e. binary covariates that perfectly sort outcomes), then the estimated coefficients should be approximately normally distributed. This same rule of thumb applies to the unweighted Cox-PH model.

With the probability weights, the new aspect of potential "observation domination" can come in the form a small number of observations having the majority of the probability weights. This is very conservative, but if $p_{max}$ = maximum probability assigned to a single observation$p_{max} = \arg \max_j \frac{p_j}{\sum p_i}$, then you can think of the effective sample size as $\tilde n = \frac{1}{p_{max}}$. Better yet, you can use bootstrapping to get an idea of whether the estimator is approximately normal.

In short, as long as none of the observations dominate the estimation of the regression coefficients, or none of the covariate effects are too extreme (i.e. binary covariates that perfectly sort outcomes), then the estimated coefficients should be approximately normally distributed. This same rule of thumb applies to the unweighted Cox-PH model.

With the probability weights, the new aspect of potential "observation domination" can come in the form a small number of observations having the majority of the probability weights. This is very conservative, but if $p_{max}$ = maximum probability assigned to a single observation, then you can think of the effective sample size as $\tilde n = \frac{1}{p_{max}}$. Better yet, you can use bootstrapping to get an idea of whether the estimator is approximately normal.

In short, as long as none of the observations dominate the estimation of the regression coefficients, or none of the covariate effects are too extreme (i.e. binary covariates that perfectly sort outcomes), then the estimated coefficients should be approximately normally distributed. This same rule of thumb applies to the unweighted Cox-PH model.

With the probability weights, the new aspect of potential "observation domination" can come in the form a small number of observations having the majority of the probability weights. This is very conservative, but if $p_{max} = \arg \max_j \frac{p_j}{\sum p_i}$, then you can think of the effective sample size as $\tilde n = \frac{1}{p_{max}}$. Better yet, you can use bootstrapping to get an idea of whether the estimator is approximately normal.

grammar
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Cliff AB
Cliff AB
  • 21.6k
  • 1
  • 51
  • 104

In short, as long as none of the observations dominate the estimation of the regression coefficients, or none of the covariate effects are too extreme (i.e. binary covariates that perfectly sort outcomes), then the estimated coefficients should be approximately normally distributed. This same rule of thumb applies to the unweighted Cox-PH model.

With the probability weights, the new aspect of potential "observation domination" can come in the form a small number of observations having the majority of the probability weights. This is very conservative, but if $p_{max}$ = maximum probability assigned to a single observation, thanthen you can think of the effective sample size as $\tilde n = \frac{1}{p_{max}}$. Better yet, you can use bootstrapping to get an idea of whether the estimator is approximately normal.

In short, as long as none of the observations dominate the estimation of the regression coefficients, or none of the covariate effects are too extreme (i.e. binary covariates that perfectly sort outcomes), then the estimated coefficients should be approximately normally distributed. This same rule of thumb applies to the unweighted Cox-PH model.

With the probability weights, the new aspect of potential "observation domination" can come in the form a small number of observations having the majority of the probability weights. This is very conservative, but if $p_{max}$ = maximum probability assigned to single observation, than you can think of the effective sample size as $\tilde n = \frac{1}{p_{max}}$. Better yet, you can use bootstrapping to get an idea of whether the estimator is approximately normal.

In short, as long as none of the observations dominate the estimation of the regression coefficients, or none of the covariate effects are too extreme (i.e. binary covariates that perfectly sort outcomes), then the estimated coefficients should be approximately normally distributed. This same rule of thumb applies to the unweighted Cox-PH model.

With the probability weights, the new aspect of potential "observation domination" can come in the form a small number of observations having the majority of the probability weights. This is very conservative, but if $p_{max}$ = maximum probability assigned to a single observation, then you can think of the effective sample size as $\tilde n = \frac{1}{p_{max}}$. Better yet, you can use bootstrapping to get an idea of whether the estimator is approximately normal.

Source Link
Cliff AB
Cliff AB
  • 21.6k
  • 1
  • 51
  • 104

In short, as long as none of the observations dominate the estimation of the regression coefficients, or none of the covariate effects are too extreme (i.e. binary covariates that perfectly sort outcomes), then the estimated coefficients should be approximately normally distributed. This same rule of thumb applies to the unweighted Cox-PH model.

With the probability weights, the new aspect of potential "observation domination" can come in the form a small number of observations having the majority of the probability weights. This is very conservative, but if $p_{max}$ = maximum probability assigned to single observation, than you can think of the effective sample size as $\tilde n = \frac{1}{p_{max}}$. Better yet, you can use bootstrapping to get an idea of whether the estimator is approximately normal.