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P-values from random effects linear regression models

This post was originally published here

lme4::lmer

 is a useful frequentist approach to hierarchical/multilevel linear regression modelling. For good reason, the model output only includes t-values and doesn’t include p-values (partly due to the difficulty in estimating the degrees of freedom, as discussed here).

Yes, p-values are evil and we should continue to try and expunge them from our analyses. But I keep getting asked about this. So here is a simple bootstrap method to generate two-sided parametric p-values on the fixed effects coefficients. Interpret with caution.

library(lme4)

# Run model with lme4 example data
fit = lmer(angle ~ recipe + temp + (1|recipe:replicate), cake)

# Model summary
summary(fit)

# lme4 profile method confidence intervals
confint(fit)

# Bootstrapped parametric p-values
boot.out = bootMer(fit, fixef, nsim=1000) #nsim determines p-value decimal places 
p = rbind(
  (1-apply(boot.out$t<0, 2, mean))*2,
  (1-apply(boot.out$t>0, 2, mean))*2)
apply(p, 2, min)

# Alternative "pipe" syntax
library(magrittr)

lmer(angle ~ recipe + temp + (1|recipe:replicate), cake) %>% 
  bootMer(fixef, nsim=100) %$% 
  rbind(
  (1-apply(t<0, 2, mean))*2,
  (1-apply(t>0, 2, mean))*2) %>% 
  apply(2, min)

 

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Effect of day of the week on mortality after emergency general surgery

This post was originally published here

Out latest paper published in the BJS describes short- and long-term outcomes after emergency surgery in Scotland. We looked for a weekend effect and didn’t find one.

  • In around 50,000 emergency general surgery patients, we didn’t find an association between day of surgery or day of admission and death rates;
  • In around 100,000 emergency surgery patients including orthopaedic and gynaecology procedures, we didn’t find an association between day of surgery or day of admission and death rates;
  • In around 500,000 emergency and planned surgery patients, we didn’t find an association between day of surgery or day of admission and death rates.

We also found that emergency surgery performed at weekends, or in those admitted at weekends, was performed a little quicker compared with weekdays.

More details can be found here:

Effect of day of the week on short- and long-term mortality after emergency general surgery
http://onlinelibrary.wiley.com/doi/10.1002/bjs.10507/full

bjs_dow-100

bjs_dow2-100

Press coverage

Broadcast: BBC GOOD MORNING SCOTLAND, HEART FM,

Print: DAILY TELEGRAPH, DAILY MIRROR, METRO, HERALD, HERALD (Leader), SCOTSMAN, THE NATIONAL, YORKSHIRE POST, GLASGOW EVENING TIMES

Online: BBC NEWS ONLINE, DAILY MAIL, EXPRESS.CO.UK, MIRROR.CO.UK, HERALD SCOTLAND, THE COURIER, WEBMD.BOOTS.COM, NEWS-MEDICAL.NET, NEW KERALA (India), BUSINESS STANDARD, YAHOO NEWS, ABERDEEN EVENING EXPRESS, BT.COM, MEDICAL XPRESS.

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Publishing mortality rates for individual surgeons

This post was originally published here

This is our new analysis of an old topic.In Scotland, individual surgeon outcomes were published as far back as 2006. It wasn’t pursued in Scotland, but has been mandated for surgeons in England since 2013.

This new analysis took the current mortality data and sought to answer a simple question: how useful is this information in detecting differences in outcome at the individual surgeon level?

Well the answer, in short, is not very useful.

We looked at mortality after planned bowel and gullet cancer surgery, hip replacement, and thyroid, obesity and aneurysm surgery. Death rates are relatively low after planned surgery which is testament to hard working NHS teams up and down the country. This together with the fact that individual surgeons perform a relatively small proportion of all these procedures means that death rates are not a good way to detect under performance.

At the mortality rates reported for thyroid (0.08%) and obesity (0.07%) surgery, it is unlikely a surgeon would perform a sufficient number of procedures in his/her entire career to stand a good chance of detecting a mortality rate 5 times the national average.

Surgeon death rates are problematic in more fundamental ways. It is the 21st century and much of surgical care is delivered by teams of surgeons, other doctors, nurses, physiotherapists, pharmacists, dieticians etc. In liver transplantation it is common for one surgeon to choose the donor/recipient pair, for a second surgeon to do the transplant, and for a third surgeon to look after the patient after the operation. Does it make sense to look at the results of individuals? Why not of the team?

It is also important to ensure that analyses adequately account for the increased risk faced by some patients undergoing surgery. If my granny has had a heart attack and has a bad chest, I don’t want her to be deprived of much needed surgery because a surgeon is worried that her high risk might impact on the public perception of their competence. As Harry Burns the former Chief Medical Officer of Scotland said, those with the highest mortality rates may be the heroes of the health service, taking on patients with difficult disease that no one else will face.

We are only now beginning to understand the results of surgery using measures that are more meaningful to patients. These sometimes get called patient-centred outcome measures. Take a planned hip replacement, the aim of the operation is to remove pain and increase mobility. If after 3 months a patient still has significant pain and can’t get out for the groceries, the operation has not been a success. Thankfully death after planned hip replacement is relatively rare and in any case, might have little to do with the quality of the surgery.

Transparency in the results of surgery is paramount and publishing death rates may be a step towards this, even if they may in fact be falsely reassuring. We must use these data as part of a much wider initiative to capture the success and failures of surgery. Only by doing this will we improve the results of surgery and ensure every patient receives the highest quality of care.

Read the full article for free here.

Press coverage

Radio: LBC, Radio Forth

Print:

  • New Scientist
  • Scotsman
  • Daily Mail
  • Express
  • the I

Online:

ONMEDICA, SHROPSHIRESTAR.COM, THE BOLTON NEWS, EXPRESSANDSTAR.COM, BELFAST TELEGRAPH, AOL UK, MEDICAL XPRESS, BT.COM, EXPRESS.CO.UK

Individual surgery mortality press clippingsDownload