January 6, 2021

Pharmac maths

Newshub has a story about a new treatment for Crohn’s disease and some other autoimmune conditions, ustekinumab (brand name Stelara).  This is an artificial antibody that blocks a couple of immune-system signalling chemicals.

The treatment is not funded by Pharmac; that’s the point of the story.  We aren’t told how much it costs, but Matt Nippert looked it up and the US list price is US$12,332 per month.  At that price, Pharmac’s entire annual budget of NZ$1.045 billion would pay for just over 5000 people to receive ustekinumab, or about a quarter of people with Crohn’s or ulcerative colitis in NZ.  Funding it for 630 people would make it Pharmac’s highest single expenditure [to the extent you can tell, because there are secret discounts not included in the published figures]. I think this sort of information is critical to interpreting the call for Pharmac to fund ustekinumab, and it should routinely be part of reporting.

Pharmac obviously isn’t going to fund this at list price, and they could probably get a discount.  Canada seems to pay only about NZ$30,000 per year for the drug. At that price you could fund it over 4000 patients before it got to be Pharmac’s single highest expenditure. That’s still quite a lot of money that would need to be subtracted from expenditures on other drugs. 

New Zealand’s medical system saves a lot of money through Pharmac. Some of this is by negotiating lower prices. Some is by not funding drugs that don’t really work. Another unavoidable component of this saving, though, is not buying effective drugs that are too expensive, and waiting until the price drops.  I’m not going to claim that Pharmac always gets the decisions right, but it actually does pretty well, and every thousand dollars it spends on a more expensive prescription is a thousand dollars it can’t spend on multiple less-expensive prescriptions. We could increase Pharmac’s budget, but if I were going to drop another couple of billion dollars a year on the health system, I think I’d worry about surgery and cancer waiting times first.

Figures that everyone should know (or, at least, everyone with reckons on pharmaceutical subsidies): Pharmac spends about a billion dollars a year.  That’s an average of roughly $200 per person per year, or $16000 per person per lifetime.

 

January 5, 2021

Top 14 Predictions for Round 14

Team Ratings for Round 14

The basic method is described on my Department home page.
Here are the team ratings prior to this week’s games, along with the ratings at the start of the season.

Note that because Lyon is to play Montpellier midweek, there will be a change to those two teams ratings. The changes are likely to be small, but given the closeness of the Brive versus Montpellier match could easily affect that prediction. To deal with this unusual situation, I will post an updated forecast after the Lyon versus Montpellier game, prior to the weekend games.

Current Rating Rating at Season Start Difference
Racing-Metro 92 7.50 6.21 1.30
Stade Toulousain 6.47 4.80 1.70
La Rochelle 5.74 2.32 3.40
Lyon Rugby 4.29 5.61 -1.30
Clermont Auvergne 3.74 3.22 0.50
RC Toulonnais 3.52 3.56 -0.00
Bordeaux-Begles 2.63 2.83 -0.20
Montpellier 1.57 2.30 -0.70
Stade Francais Paris 0.56 -3.22 3.80
Castres Olympique -1.96 -0.47 -1.50
Section Paloise -3.40 -4.48 1.10
Brive -3.90 -3.26 -0.60
Aviron Bayonnais -4.85 -4.13 -0.70
SU Agen -11.33 -4.72 -6.60

 

Performance So Far

So far there have been 83 matches played, 56 of which were correctly predicted, a success rate of 67.5%.
Here are the predictions for last week’s games.

Game Date Score Prediction Correct
1 Bordeaux-Begles vs. RC Toulonnais Jan 02 31 – 18 3.90 TRUE
2 Clermont Auvergne vs. Racing-Metro 92 Jan 02 22 – 24 2.30 FALSE
3 Lyon Rugby vs. Castres Olympique Jan 02 14 – 15 12.70 FALSE
4 Montpellier vs. Stade Toulousain Jan 02 9 – 16 1.30 FALSE
5 Stade Francais Paris vs. Brive Jan 02 51 – 21 8.60 TRUE
6 SU Agen vs. La Rochelle Jan 02 13 – 43 -10.30 TRUE

 

Predictions for Round 14

Here are the predictions for Round 14. The prediction is my estimated expected points difference with a positive margin being a win to the home team, and a negative margin a win to the away team.

Game Date Winner Prediction
1 Bordeaux-Begles vs. Lyon Rugby Jan 09 Bordeaux-Begles 3.80
2 Brive vs. Montpellier Jan 09 Brive 0.00
3 Castres Olympique vs. SU Agen Jan 09 Castres Olympique 14.90
4 Racing-Metro 92 vs. La Rochelle Jan 09 Racing-Metro 92 7.30
5 RC Toulonnais vs. Aviron Bayonnais Jan 09 RC Toulonnais 13.90
6 Section Paloise vs. Clermont Auvergne Jan 09 Clermont Auvergne -1.60
7 Stade Toulousain vs. Stade Francais Paris Jan 09 Stade Toulousain 11.40

 

Top 14 Predictions for Postponed Games

Team Ratings for Postponed Games

The basic method is described on my Department home page.
Here are the team ratings prior to this week’s games, along with the ratings at the start of the season.

Current Rating Rating at Season Start Difference
Racing-Metro 92 7.50 6.21 1.30
Stade Toulousain 6.47 4.80 1.70
La Rochelle 5.74 2.32 3.40
Lyon Rugby 4.29 5.61 -1.30
Clermont Auvergne 3.74 3.22 0.50
RC Toulonnais 3.52 3.56 -0.00
Bordeaux-Begles 2.63 2.83 -0.20
Montpellier 1.57 2.30 -0.70
Stade Francais Paris 0.56 -3.22 3.80
Castres Olympique -1.96 -0.47 -1.50
Section Paloise -3.40 -4.48 1.10
Brive -3.90 -3.26 -0.60
Aviron Bayonnais -4.85 -4.13 -0.70
SU Agen -11.33 -4.72 -6.60

 

Performance So Far

So far there have been 83 matches played, 56 of which were correctly predicted, a success rate of 67.5%.
Here are the predictions for last week’s games.

Game Date Score Prediction Correct
1 Bordeaux-Begles vs. RC Toulonnais Jan 02 31 – 18 3.90 TRUE
2 Clermont Auvergne vs. Racing-Metro 92 Jan 02 22 – 24 2.30 FALSE
3 Lyon Rugby vs. Castres Olympique Jan 02 14 – 15 12.70 FALSE
4 Montpellier vs. Stade Toulousain Jan 02 9 – 16 1.30 FALSE
5 Stade Francais Paris vs. Brive Jan 02 51 – 21 8.60 TRUE
6 SU Agen vs. La Rochelle Jan 02 13 – 43 -10.30 TRUE

 

Predictions for Postponed Games

Here are the predictions for Postponed Games. The prediction is my estimated expected points difference with a positive margin being a win to the home team, and a negative margin a win to the away team.

Game Date Winner Prediction
1 Lyon Rugby vs. Montpellier Jan 07 Lyon Rugby 9.30

 

Rugby Premiership Predictions for Round 6

Team Ratings for Round 6

The basic method is described on my Department home page.
Here are the team ratings prior to this week’s games, along with the ratings at the start of the season.

Current Rating Rating at Season Start Difference
Exeter Chiefs 8.47 7.35 1.10
Wasps 4.99 5.66 -0.70
Sale Sharks 3.90 4.96 -1.10
Bristol 1.92 1.28 0.60
Bath 0.08 2.14 -2.10
Harlequins -0.97 -1.08 0.10
Gloucester -1.66 -1.02 -0.60
Northampton Saints -2.37 -2.48 0.10
Leicester Tigers -5.78 -6.14 0.40
Newcastle Falcons -6.77 -10.00 3.20
London Irish -7.17 -8.05 0.90
Worcester Warriors -7.73 -5.71 -2.00

 

Performance So Far

So far there have been 26 matches played, 15 of which were correctly predicted, a success rate of 57.7%.
Here are the predictions for last week’s games.

Game Date Score Prediction Correct
1 Bristol vs. Newcastle Falcons Jan 02 29 – 17 13.40 TRUE
2 Wasps vs. Exeter Chiefs Jan 03 34 – 5 -1.90 FALSE
3 Gloucester vs. Sale Sharks Jan 03 19 – 22 -0.70 TRUE
4 Leicester Tigers vs. Bath Jan 04 36 – 31 -2.20 FALSE

 

Predictions for Round 6

Here are the predictions for Round 6. The prediction is my estimated expected points difference with a positive margin being a win to the home team, and a negative margin a win to the away team.

Game Date Winner Prediction
1 Bath vs. Wasps Jan 09 Wasps -0.40
2 Sale Sharks vs. Worcester Warriors Jan 09 Sale Sharks 16.10
3 Exeter Chiefs vs. Bristol Jan 10 Exeter Chiefs 11.10
4 Newcastle Falcons vs. Gloucester Jan 10 Gloucester -0.60
5 Northampton Saints vs. Leicester Tigers Jan 10 Northampton Saints 7.90
6 Harlequins vs. London Irish Jan 11 Harlequins 10.70

 

Pro14 Predictions for Round 11

Team Ratings for Round 11

The basic method is described on my Department home page.
Here are the team ratings prior to this week’s games, along with the ratings at the start of the season.

Current Rating Rating at Season Start Difference
Leinster 18.31 16.52 1.80
Munster 10.09 9.90 0.20
Ulster 8.54 4.58 4.00
Edinburgh 3.49 5.49 -2.00
Glasgow Warriors 3.35 5.66 -2.30
Scarlets 2.30 1.98 0.30
Connacht 1.63 0.70 0.90
Cheetahs -0.46 -0.46 0.00
Cardiff Blues -1.27 0.08 -1.30
Ospreys -2.63 -2.82 0.20
Treviso -5.15 -3.50 -1.60
Dragons -7.45 -7.85 0.40
Southern Kings -14.92 -14.92 0.00
Zebre -15.82 -15.37 -0.50

 

Performance So Far

So far there have been 52 matches played, 35 of which were correctly predicted, a success rate of 67.3%.
Here are the predictions for last week’s games.

Game Date Score Prediction Correct
1 Treviso vs. Zebre Jan 03 15 – 24 17.50 FALSE
2 Cardiff Blues vs. Ospreys Jan 03 3 – 17 7.90 FALSE
3 Edinburgh vs. Glasgow Warriors Jan 03 10 – 7 5.60 TRUE
4 Leinster vs. Connacht Jan 03 24 – 35 23.80 FALSE
5 Scarlets vs. Dragons Jan 03 20 – 3 14.30 TRUE
6 Ulster vs. Munster Jan 03 15 – 10 3.10 TRUE

 

Predictions for Round 11

Here are the predictions for Round 11. The prediction is my estimated expected points difference with a positive margin being a win to the home team, and a negative margin a win to the away team.

Game Date Winner Prediction
1 Cardiff Blues vs. Scarlets Jan 10 Cardiff Blues 1.40
2 Connacht vs. Munster Jan 10 Munster -3.50
3 Dragons vs. Ospreys Jan 10 Dragons 0.20
4 Glasgow Warriors vs. Treviso Jan 10 Glasgow Warriors 15.00
5 Leinster vs. Ulster Jan 10 Leinster 14.80
6 Zebre vs. Edinburgh Jan 10 Edinburgh -12.80

 

Currie Cup Predictions for Round 7

Team Ratings for Round 7

The basic method is described on my Department home page.
Here are the team ratings prior to this week’s games, along with the ratings at the start of the season.

Current Rating Rating at Season Start Difference
Bulls 7.63 6.16 1.50
Sharks 4.48 5.63 -1.20
Western Province 4.26 5.26 -1.00
Lions 3.54 1.46 2.10
Cheetahs -2.30 -2.96 0.70
Pumas -8.24 -6.66 -1.60
Griquas -9.37 -8.90 -0.50

 

Performance So Far

So far there have been 16 matches played, 13 of which were correctly predicted, a success rate of 81.2%.
Here are the predictions for last week’s games.

Game Date Score Prediction Correct
1 Pumas vs. Lions Jan 02 25 – 33 -7.10 TRUE
2 Sharks vs. Griquas Jan 02 47 – 19 16.80 TRUE
3 Cheetahs vs. Western Province Jan 02 29 – 31 -2.10 TRUE

 

Predictions for Round 7

Here are the predictions for Round 7. The prediction is my estimated expected points difference with a positive margin being a win to the home team, and a negative margin a win to the away team.

Game Date Winner Prediction
1 Pumas vs. Bulls Jan 08 Bulls -11.40
2 Griquas vs. Cheetahs Jan 09 Cheetahs -2.60
3 Western Province vs. Sharks Jan 09 Western Province 4.30

 

December 29, 2020

Top 14 Predictions for Round 13

Team Ratings for Round 13

The basic method is described on my Department home page.
Here are the team ratings prior to this week’s games, along with the ratings at the start of the season.

Current Rating Rating at Season Start Difference
Racing-Metro 92 7.20 6.21 1.00
Stade Toulousain 6.13 4.80 1.30
La Rochelle 5.08 2.32 2.80
Lyon Rugby 4.79 5.61 -0.80
Clermont Auvergne 4.04 3.22 0.80
RC Toulonnais 3.89 3.56 0.30
Bordeaux-Begles 2.26 2.83 -0.60
Montpellier 1.91 2.30 -0.40
Stade Francais Paris -0.14 -3.22 3.10
Castres Olympique -2.46 -0.47 -2.00
Brive -3.21 -3.26 0.10
Section Paloise -3.40 -4.48 1.10
Aviron Bayonnais -4.85 -4.13 -0.70
SU Agen -10.68 -4.72 -6.00

 

Performance So Far

So far there have been 77 matches played, 53 of which were correctly predicted, a success rate of 68.8%.
Here are the predictions for last week’s games.

Game Date Score Prediction Correct
1 Brive vs. Lyon Rugby Dec 27 12 – 8 -3.50 FALSE
2 La Rochelle vs. Montpellier Dec 27 22 – 9 8.00 TRUE
3 Racing-Metro 92 vs. SU Agen Dec 27 45 – 10 22.40 TRUE
4 RC Toulonnais vs. Clermont Auvergne Dec 27 27 – 9 4.40 TRUE
5 Section Paloise vs. Stade Francais Paris Dec 27 29 – 27 2.30 TRUE
6 Stade Toulousain vs. Bordeaux-Begles Dec 27 45 – 23 8.40 TRUE

 

Predictions for Round 13

Here are the predictions for Round 13. The prediction is my estimated expected points difference with a positive margin being a win to the home team, and a negative margin a win to the away team.

Game Date Winner Prediction
1 Aviron Bayonnais vs. Section Paloise Jan 02 Aviron Bayonnais 4.00
2 Bordeaux-Begles vs. RC Toulonnais Jan 02 Bordeaux-Begles 3.90
3 Clermont Auvergne vs. Racing-Metro 92 Jan 02 Clermont Auvergne 2.30
4 Lyon Rugby vs. Castres Olympique Jan 02 Lyon Rugby 12.70
5 Montpellier vs. Stade Toulousain Jan 02 Montpellier 1.30
6 Stade Francais Paris vs. Brive Jan 02 Stade Francais Paris 8.60
7 SU Agen vs. La Rochelle Jan 02 La Rochelle -10.30

 

Rugby Premiership Predictions for Round 5

Team Ratings for Round 5

The basic method is described on my Department home page.
Here are the team ratings prior to this week’s games, along with the ratings at the start of the season.

Current Rating Rating at Season Start Difference
Exeter Chiefs 9.95 7.35 2.60
Sale Sharks 3.71 4.96 -1.30
Wasps 3.51 5.66 -2.20
Bristol 2.03 1.28 0.70
Bath 0.50 2.14 -1.60
Harlequins -0.97 -1.08 0.10
Gloucester -1.48 -1.02 -0.50
Northampton Saints -2.37 -2.48 0.10
Leicester Tigers -6.21 -6.14 -0.10
Newcastle Falcons -6.89 -10.00 3.10
London Irish -7.17 -8.05 0.90
Worcester Warriors -7.73 -5.71 -2.00

 

Performance So Far

So far there have been 22 matches played, 13 of which were correctly predicted, a success rate of 59.1%.
Here are the predictions for last week’s games.

Game Date Score Prediction Correct
1 Harlequins vs. Bristol Dec 27 19 – 27 2.70 FALSE
2 Exeter Chiefs vs. Gloucester Dec 27 28 – 20 17.00 TRUE
3 Northampton Saints vs. Worcester Warriors Dec 27 29 – 10 8.70 TRUE
4 Sale Sharks vs. Wasps Dec 28 23 – 26 5.70 FALSE

 

Predictions for Round 5

Here are the predictions for Round 5. The prediction is my estimated expected points difference with a positive margin being a win to the home team, and a negative margin a win to the away team.

Game Date Winner Prediction
1 Bristol vs. Newcastle Falcons Jan 02 Bristol 13.40
2 Worcester Warriors vs. Harlequins Jan 02 Harlequins -2.30
3 Wasps vs. Exeter Chiefs Jan 03 Exeter Chiefs -1.90
4 Gloucester vs. Sale Sharks Jan 03 Sale Sharks -0.70
5 London Irish vs. Northampton Saints Jan 04 Northampton Saints -0.30
6 Leicester Tigers vs. Bath Jan 04 Bath -2.20

 

Pro14 Predictions for Round 10

Team Ratings for Round 10

The basic method is described on my Department home page.
Here are the team ratings prior to this week’s games, along with the ratings at the start of the season.

Current Rating Rating at Season Start Difference
Leinster 19.39 16.52 2.90
Munster 10.26 9.90 0.40
Ulster 8.37 4.58 3.80
Edinburgh 3.72 5.49 -1.80
Glasgow Warriors 3.12 5.66 -2.50
Scarlets 2.05 1.98 0.10
Connacht 0.55 0.70 -0.20
Cheetahs -0.46 -0.46 0.00
Cardiff Blues -0.49 0.08 -0.60
Ospreys -3.42 -2.82 -0.60
Treviso -4.26 -3.50 -0.80
Dragons -7.20 -7.85 0.70
Southern Kings -14.92 -14.92 0.00
Zebre -16.71 -15.37 -1.30

 

Performance So Far

So far there have been 46 matches played, 32 of which were correctly predicted, a success rate of 69.6%.
Here are the predictions for last week’s games.

Game Date Score Prediction Correct
1 Connacht vs. Ulster Dec 27 19 – 32 -1.80 TRUE
2 Dragons vs. Cardiff Blues Dec 27 12 – 13 -1.90 TRUE
3 Ospreys vs. Scarlets Dec 27 14 – 16 -0.10 TRUE

 

Predictions for Round 10

Here are the predictions for Round 10. The prediction is my estimated expected points difference with a positive margin being a win to the home team, and a negative margin a win to the away team.

Game Date Winner Prediction
1 Treviso vs. Zebre Jan 03 Treviso 17.50
2 Cardiff Blues vs. Ospreys Jan 03 Cardiff Blues 7.90
3 Edinburgh vs. Glasgow Warriors Jan 03 Edinburgh 5.60
4 Leinster vs. Connacht Jan 03 Leinster 23.80
5 Scarlets vs. Dragons Jan 03 Scarlets 14.30
6 Ulster vs. Munster Jan 03 Ulster 3.10

 

Currie Cup Predictions for Round 6

Team Ratings for Round 6

The basic method is described on my Department home page.
Here are the team ratings prior to this week’s games, along with the ratings at the start of the season.

Current Rating Rating at Season Start Difference
Bulls 7.63 6.16 1.50
Western Province 4.27 5.26 -1.00
Sharks 3.69 5.63 -1.90
Lions 3.46 1.46 2.00
Cheetahs -2.31 -2.96 0.60
Pumas -8.16 -6.66 -1.50
Griquas -8.58 -8.90 0.30

 

Performance So Far

So far there have been 13 matches played, 10 of which were correctly predicted, a success rate of 76.9%.
Here are the predictions for last week’s games.

Game Date Score Prediction Correct
1 Western Province vs. Griquas Dec 26 34 – 17 17.40 TRUE
2 Cheetahs vs. Sharks Dec 27 37 – 10 -5.60 FALSE

 

Predictions for Round 6

Here are the predictions for Round 6. The prediction is my estimated expected points difference with a positive margin being a win to the home team, and a negative margin a win to the away team.

Game Date Winner Prediction
1 Pumas vs. Lions Jan 02 Lions -7.10
2 Sharks vs. Griquas Jan 02 Sharks 16.80
3 Cheetahs vs. Western Province Jan 02 Western Province -2.10