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I would be grateful for your input on the following study:

Research assistants posing as patients called clinics to schedule an appointment with a specialist.  The outcome is the number of days until the appointment (median = 40 days, range 3-208 days).   There are several exposures of interest (some are categorical, some are continuous).  For example, we want to test whether number of days until the appointment is significantly greater for group A than group B after adjusting for confounders. 

About 15% of clinics would not schedule an appointment (10% were not accepting new patients, 5% had a wait list).  We assume that patients would have to wait an excessively long time for an appointment at these clinics, but the number of days they would have to wait is unknown. 

I am considering two analytic approaches:

Approach 1:  include all clinics, treat the 15% of clinics that could not schedule an appointment to be right censored at 210 days (2 days beyond the maximum value observed in the data), and use survival analysis (cox PH model) to analyze the data.

Approach 2:  include only those clinics where the number of days until the appointment is known, and model the data using negative binomial regression (there is overdispersion).

Which approach do you recommend?  Do you have other suggestions about how to analyze this data?

Thank you in advance for your help.

------------------------------
Amy Storfer-Isser
Statistical Research Consultants, LLC
------------------------------

My thought is that you don't want to use survival analysis because it doesn't model the situation well. It's not that each requester is at some risk of having an appointment happen at any given time. Rather, the time-to-appointment is fixed at the time the requester contacts the clinic, with that time being your outcome of interest.

I'm interested in what others have to say; I'd say, first, you want to be sure that not having appointments available truly is independent of requester characteristics (that is, the clinic doesn't pretend to not have appointments for requesters they don't like, or squeeze in those they like). Given that, you can only analyze data from the clinics that in fact could give appointments -- this is your study population, other clinics can't meet your inclusion criteria. Finally, if you want to generalize to more clinics -- including those with wait lists or not accepting new patients -- you have to examine whether this is appropriate. Do full-up clinics tend to serve different populations, offer different types or quality of care, be more popular for various reasons, and so on. And when you generalize, mention how these differences might affect your predictions.

Original Message:
Sent: 06-08-2015 16:28
From: Amy Storfer-Isser
Subject: Survival analysis or negative binomial regression?

I would be grateful for your input on the following study:

Research assistants posing as patients called clinics to schedule an appointment with a specialist.  The outcome is the number of days until the appointment (median = 40 days, range 3-208 days).   There are several exposures of interest (some are categorical, some are continuous).  For example, we want to test whether number of days until the appointment is significantly greater for group A than group B after adjusting for confounders. 

About 15% of clinics would not schedule an appointment (10% were not accepting new patients, 5% had a wait list).  We assume that patients would have to wait an excessively long time for an appointment at these clinics, but the number of days they would have to wait is unknown. 

I am considering two analytic approaches:

Approach 1:  include all clinics, treat the 15% of clinics that could not schedule an appointment to be right censored at 210 days (2 days beyond the maximum value observed in the data), and use survival analysis (cox PH model) to analyze the data.

Approach 2:  include only those clinics where the number of days until the appointment is known, and model the data using negative binomial regression (there is overdispersion).

Which approach do you recommend?  Do you have other suggestions about how to analyze this data?

Thank you in advance for your help.

------------------------------
Amy Storfer-Isser
Statistical Research Consultants, LLC
------------------------------

I would be grateful for your input on the following study:

Research assistants posing as patients called clinics to schedule an appointment with a specialist.  The outcome is the number of days until the appointment (median = 40 days, range 3-208 days).   There are several exposures of interest (some are categorical, some are continuous).  For example, we want to test whether number of days until the appointment is significantly greater for group A than group B after adjusting for confounders. 

About 15% of clinics would not schedule an appointment (10% were not accepting new patients, 5% had a wait list).  We assume that patients would have to wait an excessively long time for an appointment at these clinics, but the number of days they would have to wait is unknown. 

I am considering two analytic approaches:

Approach 1:  include all clinics, treat the 15% of clinics that could not schedule an appointment to be right censored at 210 days (2 days beyond the maximum value observed in the data), and use survival analysis (cox PH model) to analyze the data.

Approach 2:  include only those clinics where the number of days until the appointment is known, and model the data using negative binomial regression (there is overdispersion).

Which approach do you recommend?  Do you have other suggestions about how to analyze this data?

Thank you in advance for your help.

------------------------------
Amy Storfer-Isser
Statistical Research Consultants, LLC
------------------------------

I would be grateful for your input on the following study:

Research assistants posing as patients called clinics to schedule an appointment with a specialist.  The outcome is the number of days until the appointment (median = 40 days, range 3-208 days).   There are several exposures of interest (some are categorical, some are continuous).  For example, we want to test whether number of days until the appointment is significantly greater for group A than group B after adjusting for confounders. 

About 15% of clinics would not schedule an appointment (10% were not accepting new patients, 5% had a wait list).  We assume that patients would have to wait an excessively long time for an appointment at these clinics, but the number of days they would have to wait is unknown. 

I am considering two analytic approaches:

Approach 1:  include all clinics, treat the 15% of clinics that could not schedule an appointment to be right censored at 210 days (2 days beyond the maximum value observed in the data), and use survival analysis (cox PH model) to analyze the data.

Approach 2:  include only those clinics where the number of days until the appointment is known, and model the data using negative binomial regression (there is overdispersion).

Which approach do you recommend?  Do you have other suggestions about how to analyze this data?

Thank you in advance for your help.

------------------------------
Amy Storfer-Isser
Statistical Research Consultants, LLC
------------------------------

I would be grateful for your input on the following study:

Research assistants posing as patients called clinics to schedule an appointment with a specialist.  The outcome is the number of days until the appointment (median = 40 days, range 3-208 days).   There are several exposures of interest (some are categorical, some are continuous).  For example, we want to test whether number of days until the appointment is significantly greater for group A than group B after adjusting for confounders. 

About 15% of clinics would not schedule an appointment (10% were not accepting new patients, 5% had a wait list).  We assume that patients would have to wait an excessively long time for an appointment at these clinics, but the number of days they would have to wait is unknown. 

I am considering two analytic approaches:

Approach 1:  include all clinics, treat the 15% of clinics that could not schedule an appointment to be right censored at 210 days (2 days beyond the maximum value observed in the data), and use survival analysis (cox PH model) to analyze the data.

Approach 2:  include only those clinics where the number of days until the appointment is known, and model the data using negative binomial regression (there is overdispersion).

Which approach do you recommend?  Do you have other suggestions about how to analyze this data?

Thank you in advance for your help.

------------------------------
Amy Storfer-Isser
Statistical Research Consultants, LLC
------------------------------

I would be grateful for your input on the following study:

Research assistants posing as patients called clinics to schedule an appointment with a specialist.  The outcome is the number of days until the appointment (median = 40 days, range 3-208 days).   There are several exposures of interest (some are categorical, some are continuous).  For example, we want to test whether number of days until the appointment is significantly greater for group A than group B after adjusting for confounders. 

About 15% of clinics would not schedule an appointment (10% were not accepting new patients, 5% had a wait list).  We assume that patients would have to wait an excessively long time for an appointment at these clinics, but the number of days they would have to wait is unknown. 

I am considering two analytic approaches:

Approach 1:  include all clinics, treat the 15% of clinics that could not schedule an appointment to be right censored at 210 days (2 days beyond the maximum value observed in the data), and use survival analysis (cox PH model) to analyze the data.

Approach 2:  include only those clinics where the number of days until the appointment is known, and model the data using negative binomial regression (there is overdispersion).

Which approach do you recommend?  Do you have other suggestions about how to analyze this data?

Thank you in advance for your help.

------------------------------
Amy Storfer-Isser
Statistical Research Consultants, LLC
------------------------------

I would be grateful for your input on the following study:

Research assistants posing as patients called clinics to schedule an appointment with a specialist.  The outcome is the number of days until the appointment (median = 40 days, range 3-208 days).   There are several exposures of interest (some are categorical, some are continuous).  For example, we want to test whether number of days until the appointment is significantly greater for group A than group B after adjusting for confounders. 

About 15% of clinics would not schedule an appointment (10% were not accepting new patients, 5% had a wait list).  We assume that patients would have to wait an excessively long time for an appointment at these clinics, but the number of days they would have to wait is unknown. 

I am considering two analytic approaches:

Approach 1:  include all clinics, treat the 15% of clinics that could not schedule an appointment to be right censored at 210 days (2 days beyond the maximum value observed in the data), and use survival analysis (cox PH model) to analyze the data.

Approach 2:  include only those clinics where the number of days until the appointment is known, and model the data using negative binomial regression (there is overdispersion).

Which approach do you recommend?  Do you have other suggestions about how to analyze this data?

Thank you in advance for your help.

------------------------------
Amy Storfer-Isser
Statistical Research Consultants, LLC
------------------------------

This discussion (or I, at least) would benefit from a careful explanation of why the data are more appropriately analyzed as time-to-event data.

An important advantage of methods of survival analysis is that they can handle censored data. In this example, I do not see an observation on a specialist who is not accepting new patients as censored. Instead, one could regard the number of days for that observation as infinite.  I am reminded of the New Yorker cartoon that shows a man on the phone with someone who is trying to make an appointment; the caption is "How about never? Is never good for you?"  Treating such observations as infinite has worked well in some analyses that transformed the data to a reciprocal scale, replacing time with "speed."  Paul Velleman has an impressive example in which the observation is the time required to complete a task. Some children did not complete the task and hence had zero "speed." In principle, it might have been possible to treat their observations as censored at the time allotted for them to complete the task, but transforming to the reciprocal scale produced an effective analysis for the relation of the outcome to the predictors in those data.  The present example seems not to have an analogous censoring time for the specialists who are not accepting new patients.

If methods for handling censoring are not needed, the analysis of the number of days until the appointment takes the form of a regression.  Then a key part of the task is to find a suitable model, including the random component.  If a negative-binomial distribution is not satisfactory, other choices are available, including "continuous" distributions (some of which are used in survival analysis).

------------------------------
David Hoaglin
------------------------------

This discussion (or I, at least) would benefit from a careful explanation of why the data are more appropriately analyzed as time-to-event data.

An important advantage of methods of survival analysis is that they can handle censored data. In this example, I do not see an observation on a specialist who is not accepting new patients as censored. Instead, one could regard the number of days for that observation as infinite.  I am reminded of the New Yorker cartoon that shows a man on the phone with someone who is trying to make an appointment; the caption is "How about never? Is never good for you?"  Treating such observations as infinite has worked well in some analyses that transformed the data to a reciprocal scale, replacing time with "speed."  Paul Velleman has an impressive example in which the observation is the time required to complete a task. Some children did not complete the task and hence had zero "speed." In principle, it might have been possible to treat their observations as censored at the time allotted for them to complete the task, but transforming to the reciprocal scale produced an effective analysis for the relation of the outcome to the predictors in those data.  The present example seems not to have an analogous censoring time for the specialists who are not accepting new patients.

If methods for handling censoring are not needed, the analysis of the number of days until the appointment takes the form of a regression.  Then a key part of the task is to find a suitable model, including the random component.  If a negative-binomial distribution is not satisfactory, other choices are available, including "continuous" distributions (some of which are used in survival analysis).

------------------------------
David Hoaglin
------------------------------

I do not see this as drawing patients. With each call you are sampling practices.

Each practice is a cluster, with a distribution of appointment times. Each time you call a particular practice you are sampling from that distribution.

The means (medians) of all these practice-specific distributions have a distribution themselves and it is the hyperparameter of this distribution that you are interested in (in the Bayesian sense).

I would go with survival analyses with random effects (frailty).

If you have multiple calls per practice, great. But if you only have one call per practice, then you only have 1 draw from each cluster and this reduces the analyses to the usual survival analyses modeling.

I would NOT include practices that do not take new patients. They have no distribution of time-to-appointment (for new patients) so to speak. Conceptually, they are not even eligible when we estimate time to appointment for new patients. Practices w/ wait list are unclear, but I view them similarly to those that do not take new patients.

But that is only if you are interested in time to appointment for NEW patients. If you are interested in time to appointment of any patient (including established patients), things are different. But your design is probably not quite right for that objective.

Finally, I strongly favor survival analyses over negative binomial. In practice, In the past, I have had trouble fitting negative binomial models that fit the data well (I have used Stata which has a fairly flexible implementation of those models). Also I can assess the fit better w/ survival models and have a better handle on what to do to improve the fit.

Disclaimer: I am neither a survival expert nor a Bayesian, so I may be off in a lot of these things.

------------------------------
Constantine Daskalakis
Thomas Jefferson University, Philadelphia, PA
------------------------------


Original Message:
Sent: 06-08-2015 16:28
From: Amy Storfer-Isser
Subject: Survival analysis or negative binomial regression?

I would be grateful for your input on the following study:

Research assistants posing as patients called clinics to schedule an appointment with a specialist.  The outcome is the number of days until the appointment (median = 40 days, range 3-208 days).   There are several exposures of interest (some are categorical, some are continuous).  For example, we want to test whether number of days until the appointment is significantly greater for group A than group B after adjusting for confounders. 

About 15% of clinics would not schedule an appointment (10% were not accepting new patients, 5% had a wait list).  We assume that patients would have to wait an excessively long time for an appointment at these clinics, but the number of days they would have to wait is unknown. 

I am considering two analytic approaches:

Approach 1:  include all clinics, treat the 15% of clinics that could not schedule an appointment to be right censored at 210 days (2 days beyond the maximum value observed in the data), and use survival analysis (cox PH model) to analyze the data.

Approach 2:  include only those clinics where the number of days until the appointment is known, and model the data using negative binomial regression (there is overdispersion).

Which approach do you recommend?  Do you have other suggestions about how to analyze this data?

Thank you in advance for your help.

------------------------------
Amy Storfer-Isser
Statistical Research Consultants, LLC
------------------------------

I suggest that you investigate models from queuing theory.

i am not particularly well versed in these, but it seems that the assumptions of some of these models apply to your research assumptions.

------------------------------
Gretchen Donahue
------------------------------


Original Message:
Sent: 06-09-2015 13:31
From: Constantine Daskalakis
Subject: Survival analysis or negative binomial regression?

I do not see this as drawing patients. With each call you are sampling practices.

Each practice is a cluster, with a distribution of appointment times. Each time you call a particular practice you are sampling from that distribution.

The means (medians) of all these practice-specific distributions have a distribution themselves and it is the hyperparameter of this distribution that you are interested in (in the Bayesian sense).

I would go with survival analyses with random effects (frailty).

If you have multiple calls per practice, great. But if you only have one call per practice, then you only have 1 draw from each cluster and this reduces the analyses to the usual survival analyses modeling.

I would NOT include practices that do not take new patients. They have no distribution of time-to-appointment (for new patients) so to speak. Conceptually, they are not even eligible when we estimate time to appointment for new patients. Practices w/ wait list are unclear, but I view them similarly to those that do not take new patients.

But that is only if you are interested in time to appointment for NEW patients. If you are interested in time to appointment of any patient (including established patients), things are different. But your design is probably not quite right for that objective.

Finally, I strongly favor survival analyses over negative binomial. In practice, In the past, I have had trouble fitting negative binomial models that fit the data well (I have used Stata which has a fairly flexible implementation of those models). Also I can assess the fit better w/ survival models and have a better handle on what to do to improve the fit.

Disclaimer: I am neither a survival expert nor a Bayesian, so I may be off in a lot of these things.

------------------------------
Constantine Daskalakis
Thomas Jefferson University, Philadelphia, PA
------------------------------


Original Message:
Sent: 06-08-2015 16:28
From: Amy Storfer-Isser
Subject: Survival analysis or negative binomial regression?

I would be grateful for your input on the following study:

Research assistants posing as patients called clinics to schedule an appointment with a specialist.  The outcome is the number of days until the appointment (median = 40 days, range 3-208 days).   There are several exposures of interest (some are categorical, some are continuous).  For example, we want to test whether number of days until the appointment is significantly greater for group A than group B after adjusting for confounders. 

About 15% of clinics would not schedule an appointment (10% were not accepting new patients, 5% had a wait list).  We assume that patients would have to wait an excessively long time for an appointment at these clinics, but the number of days they would have to wait is unknown. 

I am considering two analytic approaches:

Approach 1:  include all clinics, treat the 15% of clinics that could not schedule an appointment to be right censored at 210 days (2 days beyond the maximum value observed in the data), and use survival analysis (cox PH model) to analyze the data.

Approach 2:  include only those clinics where the number of days until the appointment is known, and model the data using negative binomial regression (there is overdispersion).

Which approach do you recommend?  Do you have other suggestions about how to analyze this data?

Thank you in advance for your help.

------------------------------
Amy Storfer-Isser
Statistical Research Consultants, LLC
------------------------------

I would be grateful for your input on the following study:

Research assistants posing as patients called clinics to schedule an appointment with a specialist.  The outcome is the number of days until the appointment (median = 40 days, range 3-208 days).   There are several exposures of interest (some are categorical, some are continuous).  For example, we want to test whether number of days until the appointment is significantly greater for group A than group B after adjusting for confounders. 

About 15% of clinics would not schedule an appointment (10% were not accepting new patients, 5% had a wait list).  We assume that patients would have to wait an excessively long time for an appointment at these clinics, but the number of days they would have to wait is unknown. 

I am considering two analytic approaches:

Approach 1:  include all clinics, treat the 15% of clinics that could not schedule an appointment to be right censored at 210 days (2 days beyond the maximum value observed in the data), and use survival analysis (cox PH model) to analyze the data.

Approach 2:  include only those clinics where the number of days until the appointment is known, and model the data using negative binomial regression (there is overdispersion).

Which approach do you recommend?  Do you have other suggestions about how to analyze this data?

Thank you in advance for your help.

------------------------------
Amy Storfer-Isser
Statistical Research Consultants, LLC
------------------------------