Modelling of multivariate time-to-event data: an ...

Young Statisticians Meeting – March 2010, Liverpool

Annie Herbert Pennine Acute Hospitals NHS Trust [email protected]

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Intended to analyse the data using time-toevent analysis methods, whereby the event is defined as the time to site-reaction.

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Carry out a proportional hazards (Cox) regression, including drug combination and drug dose as a time-varying covariate.

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Perform analyses in Stata to allow for greater flexibility of time-to-event analysis than some other statistical packages.

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Scenario/Definitions

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Clustering - multiple drivers and visits.

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Drug Combinations

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Proportional Hazards Regression – results.

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Further Research

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Syringe drivers: needles used to administer different combinations of drugs at different doses.

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Problem: site reactions, e.g., skin bleed, skin bruise, etc., can occur if driver left in for too long. Inefficient/expensive to change driver too often.

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Research question: How many days should a driver typically be left in for?

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Type/dose of drug combination a potential confounding factor.

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Data were collected prospectively for three years for all patients at two different hospice sites, for each day of their visit.

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Recorded:     

Age, sex and hospice site Date Drug combination and dose of each type of drug Type of needle: ‘Graseby flo-safer’ or ‘Teflon softset’ Whether or not a driver was changed on that day and if so whether it was changed due to a site reaction.

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‘Infusion’ – the period between a new driver being inserted and removed. Includes details of drug combination and dose (uniform for the period of infusion).

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‘Site Change’ – driver is changed (one between each infusion).

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‘Event’ – a site reaction, e.g., skin rash. A site change (and therefore new infusion) is necessary should this occur, but can happen without an event.

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‘Visit’ – continuous amount of time spent at hospice. If patient’s infusion ends and at least one full day passes before a new infusion begins this is assumed to be a new visit.

Visit 1 L E F T

Patient enters hospice site 1 – starts driver containing Diamorphine & Midazolam.

A R M

Driver changed, but not due to a site reaction. Drug combination remains the same.

Drug combination changed to just Diamorphine. Same driver.

Infusion 1

April 1st 2004

Visit 2

SITE CHANGE

Day 2

Patient leaves hospice.

Infusion 2

Day 3

Extra driver inserted on Day 2 to deliver Cyclizine.

A R M

July 2nd 2005

Day 4

Extra driver removed.

Infusion 1 April 1st 2004

April 2nd 2004

April 3rd 2004

Site reaction – bleed. New driver.

Infusion 1 EVENT

Visit 1 R I G H T

Patient re-enters hospice site 1 – starts driver containing Alfentanil, Haloperidol & Midazolam.

April 4th 2004

Day 2

Day 3

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Multiple events per person  Site reaction can occur more than once during the course

of a visit. 

Multiple visits per person 

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Patients can leave the hospice and return. Would return to same hospice site.

Multiple concurrent drivers per person  Can have one in each arm to administer different drug

combinations (so 1-2 drivers per patient at any one time).

23 different possible drugs. Up to 10,902 different possible combinations.

Drugs given at different doses. If drug combination has an effect on whether or not a site reaction occurs, likely that the dose of this drug will too.

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Multiple events per person.  Stata accounts for this.

‘stset time, id(id) failure(reaction)’ 

Multiple visits/driver per person.  Option 1: Shared frailty model. ▪ Visits are the ‘subjects’. ‘...shared(id) failure(reaction)’ ▪ Insert number of driver as covariate/cluster in frailty model.

 Option 2: Sensitivity analysis. ▪ Analyse visit 1 and then all visits pooled as though one visit within a patient. ▪ Analyse driver 1 and then drivers 1 & 2 pooled, as though independent patients.

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Option 1: Calculate the frequencies of drug combinations that occur. For the most frequent, enter into regression as a dummy variable, call all other combinations ‘other’.

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Option 2: Create a dummy variable for most frequent individual drugs, e.g., ‘cyc_any’ would be a dummy variable whereby cyc_any = 1 indicates that the patient has received a combination in that driver that day which includes cyclizine.

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Could also insert drug dose as a ‘time-varying covariate’.

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Breslow (max-likelihood) method for ties (default setting). Other options include:  Efron’s (exact) method – ‘a more accurate

approximation of the exact marginal likelihood than Breslow’s but takes longer to calculate.’1  Exact marginal-likelihood. 

Chose Efron.

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Robust standard errors/shared frailty.

1. Stata Release 11, Survival Analysis & Epidemiological Tables, Stata Press 2009. Page 129.

Site 1, n = 97

Site 2, n = 74 Total, N = 171

Male: n (%)

56 (58)

38 (51)

94 (55)

Age: Median (IQR)

71 (60 - 78)

73 (63 – 80)

72 (61 - 79)

Teflon: n (%)

1 (1)

65 (88)

66 (39)

Graseby: n(%)

92 (95)

6 (8)

98 (57)

N = 171, 890 observations No. of days on a driver per patient: Median (IQR)

4 (2 to 7)

No. of patients with 2nd driver: n (%)

14 (8)

No. of patients with 2 visits: n(%) No. of patients with 3 visits: n (%)

11 (7) 1 (0.6)

No. of site reactions observed: n

62

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Use 10th percentile to recommend time before change.

Time to Site-Reaction: 10th Percentile (95% CI)

First visit, first driver

First visit, both drivers

All visits, first driver

3 (3 to 4)

3 (3 to 4)

3 (3 to 4)

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Calculating frequencies of all drug combinations – data too sparse. For each combinations mostly 1 and at most 3 occurrences.

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Inserted 4 drug dummy variables, for any cyclizine, levomapromazine, morphine and haloperidol.

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Checked proportionality of hazards of sex and site on the first visit-first driver data. Complimentary log-log plot of time-to-reaction, by site

4 3 2 1

0

0

1

2

3

4

-ln[-ln(Survival Probability)]

5

5

Complimentary log-log plot of time-to-reaction, by sex

0

1

2 ln(analysis time)

sex = Female

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3

0

1

2

3

ln(analysis time) sex = Male

site = HG

site = LH

Drug combinations – as time varying covariate, wasn’t sure how to check this.

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Inserting driver as a cluster: “option cluster(driverno) not allowed for shared frailty models”

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Inserting driver as a covariate: “194 records at same instant”... “PROBABLE ERROR”

Hazard Ratio (95% CI)

First visit, first driver

First visit, both drivers

Both visits, first driver

First driver, visit no. as covariate

First visit, driver no. inserted as covariate

Driver No.

N/A

N/A

N/A

N/A

1.27 x 10-9 (0 to .)

Visit No.

N/A

N/A

N/A

0.11 (0.01 to 1.51)

N/A

Site

4.05 (0.95 to 17.34)

5.44 (1.37 to 21.64)

3.63 (0.95 to 13.91)

3.82 (0.97 to 15.03)

5.84 (1.29 to 26.45)

Sex

1.65 (0.66 to 4.14)

1.86 (0.75 to 4.65)

1.98 (0.85 to 4.62)

2.05 (0.85 to 4.91)

1.73 (0.69 to 4.35)

Cyclizine (any)

3.02 x 10-19 (. To .)

7.22 x 10-9 (0 to .)

0.31 (0.034 to 2.85)

0.073 (0.003 to 1.77)

1.11 x 10-8 (0 to .)

Haloperidol (any)

2.96 x 10-20 (. To .)

1.13 x 10-9 (0 to .)

1.85 x 10-19 (0 to .)

2.52 x 10-20 (. to .)

5.57 x 10-10 (0 to .)

Morphine (any)

1.17 (0.32 to 4.28)

1.15 (0.33 to 3.99)

1.29 (0.37 to 4.44)

1.27 (0.54 to 2.96)

1.45 (0.38 to 5.57)

Levomepromazaine (any)

1.45 (0.59 to 3.54)

1.91 (0.81 to 4.54)

1.33 (0.57 to 3.12)

0.11 (0.009 to 1.51)

1.94 (0.82 to 4.60)

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Considered stratifying by site to allow for baseline hazard functions to differ between the two, but had planned to investigate if site had an effect on typical time to site-reaction.

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Appears that there’s a difference, but is this because of a difference in a measurable characteristic such as needle type or a latent variable such as patient-clinician interaction?

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Conclusion: Recommend 2-3 days before each site change.

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Any questions or suggestions?

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How could the data be utilised more efficiently?

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How to deal with drug groupings/doses?

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Suggestions for further research?  E.g., RCT of Graseby vs. Teflon.