Statistical Methods for real-time monitoring of health ...mlpm.eu/static/media/uploads/Summer School 2015/real-time_peter... · Peter J Diggle Statistical Methods for real-time monitoring

Statistical Methods for real-time monitoringof health outcomes

Peter J Diggle

CHICAS, Faculty of Health and Medicine, LancasterUniversity

September 2015

Peter J Diggle Statistical Methods for real-time monitoring of health outcomes

Context

increasing availability of electronically recorded healthoutcome data

community and/or individual level

accruing in “real-time”

often spatially referenced

prediction and/or explanation

case-studies:

monitoring progression towards end-stage renal failurehuman and veterinary surveillance of gastro-enteric illnesslocal-scale malaria prevalence mapping


Chronic renal failure: UK mortality data

2002 2004 2006 2008 2010

8000

1000

012

000

1400

016

000

year

deat

hs

http://www.endoflifecare-intelligence.org.uk


Diagnosis, treatment and survival

Diagnosis

Serum creatinine ⇒ estimated glomerular filtration rate

eGFR = 186×(

SCr

88.4

)−1.154

× age−0.203(×0.742 if female)

progression can be asymptomatic for many years

SCr easy to measure from blood-sample

Treatment and survival

aggressive control of blood-pressure

renal replacement therapy: dialysis and transplantation

early diagnosis can slow rate of progression

Survival rate (%) to year1 2 5 10

Dialysis 79.3 64.7 33.6 10.2Transplant (living) 98.4 96.5 90.0 76.0


Royal Salford Hospital, NW England

Clinical guideline

Loss of > 5% eGFR per year ⇒ refer to secondary care

Data

measurements Yij = log eGFR at times tij,

explanatory variables xi (age, sex)

i = 1, ..., m = 22, 910 “at-risk” primary care patients

j = 1, ..., ni ≤ 305 (median ni = 12)

0 ≤ 10.02 years follow-up (median 4.46)

Hi(t) = {xi, (tij, yij) : tij ≤ t}

Statistical objective

P

(d

dtlog GFR < −0.05|Hi(t)

)= ?


Data: all cross-sectional


Data: all cross-sectional and selected longitudinal


Data: all cross-sectional and selected longitudinal


Dynamic regression model

subjects i = 1, ..., n observed at times tij, j = 1, ...ni

Yij = log(eGFR)

expected value of Yij linear in initial age and time sincerecruitment

rate of progression varies randomly:

between subjects: random effect Ui

within subjects: random effect Ci(tij)


Dynamic Regression Model

Yij = α0 + α1 × I(female)

+ α2 × agei1 + α3 × (ageij − agei1) + α4 ×max(0, ageij − 56.5)

+ Ui + Ci(tij) + Zij

Zij: measurement error, N(0, τ 2)

Ui: between-subject random intercept, N(0, ω2)

Ci(t): within-subject stochastic process

Model Ci(t) as integrated Brownian motion

Ci(t) =

∫ t

0

Bi(u)du

Bi(u)|Bi(s) ∼ N(Bi(u), (u− s)σ2

)Bi(u) is rate of progression for subject i at time t


Maximum likelihood estimates of model parameters

RE(%)= 100(exp(α)− 1) corresponds to estimated annualpercentage change in renal function.

Parameter Estimate SE RE(%)α0 intercept 4.6006 0.0203α1 female -0.0877 0.0048 -8.4α2 age on entry -0.0048 0.0004 -0.5α3 follow-up -0.0232 0.0011 -2.3α4 age>56.5 -0.0075 0.0006 -0.6

ω2 intercept 0.1111 0.0012σ2 signal 0.0141 0.0002τ 2 noise 0.0469 0.0001


Sample data-sequences

0 2 4 6 8 10

2.5

3.0

3.5

4.0

4.5

5.0

5.5

age

log(

eGF

R)


Simulations

0 2 4 6 8 10

34

56

age

log(

eGF

R)


Prediction: classic progression pattern

●

●

●●

●

●●

●●

●

●

●

●

●

●

●●●●●

●

●●

●

0.0 0.5 1.0 1.5 2.0

2.5

3.0

3.5

Follow−up time (in years)

log(

eGF

R)

0.0 0.5 1.0 1.5 2.0

−0.

8−

0.6

−0.

4−

0.2

0.0

0.2


B~

0.0 0.5 1.0 1.5 2.0

0.0

0.2

0.4

0.6

0.8

1.0


Pro

babi

lity


Prediction: AKI (Acute Kidney Injury) recovery

● ● ●●

●

●

●●

●

●●

●

●

●

●●

●

●

●

●●● ●

●

●

●

●

●

●

●

●

●

●

●

●●●●

0 1 2 3 4 5

3.8

4.0

4.2

4.4

4.6

4.8

5.0


log(

eGF

R)

0 1 2 3 4 5

−0.

4−

0.2

0.0

0.2

0.4


B~

0 1 2 3 4 5

0.0

0.2

0.4

0.6

0.8

1.0


Pro

babi

lity


Prediction: non-recovery from AKI

●●

●

●

●

●

●●

●

●●

●

●

●

●●●●●

●

●

●●●●

●●

●

●●

●

●●●●●

●

●

●

●

●●

●●●●●●

●

●●

●●

●● ●

●

●

●

●

●●

●

●

●

●

●

●●●●

●●●●●●●

●

●●●

●●●

●

0.0 0.5 1.0 1.5 2.0 2.5

2.5

3.0

3.5

4.0


log(

eGF

R)

0.0 0.5 1.0 1.5 2.0 2.5

−1.

0−

0.5

0.0

0.5


B~

0.0 0.5 1.0 1.5 2.0 2.5

0.0

0.2

0.4

0.6

0.8

1.0


Pro

babi

lity


Work-in-prospect

Field-testing: comparative evaluation against current methods

eye-balling

OLS fit to three most recent values

Informative follow-up: eGFR more likely to be measured whensubject is in poor health

⇒ joint modelling of eGFR measurements and follow-up times

Implementation: in clinical practice...needs informatics expertise


Gastro-intestinal disease

Reported UK annual incidence

Campylobacter 50, 000

Salmonella 10, 000

Cryptosporidium 5, 000

Giardia 3, 000

E Coli,... ?


Real-time spatial surveillance, ca 2003

AEGISS: Ascertainment and Enhancement of

Gastroenteric Infection Surveillance Statistics

largely sporadic incidence pattern

concentration in population centres

occasional “clusters” of cases

Can spatial statistical modelling enable earlier detection of“clusters”?


AEGISS: Cox process model

actual = expected× unexpected

λ(x, t) = λ0(x, t)× R(x, t)

Scientific objective

use incident data up to time t to construct predictivedistribution for current “risk” surface, R(x, t),

hence identify anomalies, for further investigation.


AEGISS model formulation

λ(x, t) = λ0(x, t)R(x, t)

λ0(x, t) = λ0(x)µ0(t)

R(x, t) = exp{S(x, t)}

S(x, t) = spatio-temporal Gaussian process

Conditional on R(x, t), incident cases form an

inhomogeneous Poisson process with intensity λ(x, t)


λ0(x): adaptive kernel smoothing

420 440 460 480

100

120

140

160

Northing (Kilometers)

Eas

ting

(Kilo

met

ers)

00.000720.00140.00220.00290.00360.00430.00510.00580.0065


µ0(t): Poisson log-linear modelav

erag

e ad

just

ed d

aily

cou

nt

46

810

1214

1618

Jan 01 Apr 01 Jul 01 Oct 01 Jan 02 Apr 02 Jul 02 Oct 02 Dec 02


Spatio-temporal covariance

ρ(u, v) = ρx(u)ρt(v)

0.0 0.5 1.0 1.5 2.0

−1

01

23

45

Distance(Kilometers)

Log

Pai

r C

orre

latio

n F

unct

ion

FittedEmpirical

0 2 4 6 8 10 12 14

−1

01

23

4

Time lag(Days)

Aut

ocov

aria

nce

func

tion

FittedEmpirical


Spatial prediction

plug-in for estimated model parameters

MCMC to generate samples from conditionaldistribution of S(x, t) given data up to time t

choose critical threshold value c > 1

map empirical exceedance probabilities,

pt(x) = P (exp{S(x, t)} > c|data)

web-based reporting with daily updates

(www.lancs.ac.uk/staff/diggle/aegiss/)


Spatial prediction: 6 March 2003

c = 2



c = 4



c = 8


Fast-forward to 2015

expand to national coverage

integrate human and small-animal veterinary surveillance

BUT...

replacement of single NHS Direct by multiple NHS111 services

full post-code data no longer available!

SAVSNET: real-time data-feed from network of small-animal vetpractices:

practice location

species (cat or dog)

diagnosis

http://www.savsnet.co.uk/realtimedata/


Work-in-prospect

re-calibration of AEGISS model

coarser spatial resolution...fitting spatially continuous modelsto spatially discrete data

joint modelling of human and animal incidence

implementation as part of routine surveillance systems


Malaria prevalence mapping


Prevalence mapping 1

Single prevalence survey

Sample n individuals, observe Y positives

Y ∼ Bin(n, p)

Multiple prevalence surveys

Sample ni individuals, observe Yi positives, i = 1, ...,m

Yi ∼ Bin(ni, pi) ?


Prevalence mapping 2

Extra-binomial variation

Sample ni individuals, observe Yi positives, i = 1, ...,m

Yi|di,Ui ∼ Bin(ni, pi) log{pi/(1− pi)} = d′iβ + Ui

Question: What to do if the di and/or the Ui are spatiallystructured


Geostatistical model for prevalence data

Latent spatially correlated process

S(x) ∼ SGP{0, σ2, ρ(u))} ρ(u) = exp(−|u|/φ)

Latent spatially independent random effects

Ui ∼ iidN(0, ν2)

Linear predictor (regression model)

d(x) = environmental variables at location xη(xi) = d(xi)′β + S(xi) + Ui

p(xi) = log[η(xi)/{1− η(xi)}]

Conditional distribution for positive proportion Yi/ni

Yi|S(·) ∼ Bin{ni, p(xi)} (binomial sampling)


Multiple surveys (Giorgi et al, 2015)

Surveys: i = 1, . . . , r locations xij : j = 1, . . . , ni

ηij = d(xij)>β1 + Si(xij) + I(i ∈ B)[Bi(xij) + d(xij)

′βi] + Uij

1

S1

2*

B2

2

S2


Malaria mapping, Chikhwawa district, Malawi(Giorgi et al, 2015): rMIS individual locations

34.72 34.74 34.76 34.78 34.80 34.82 34.84

-16.10

-16.05

-16.00

(a)

Longitude

Latitude


Malaria mapping, Chikhwawa district, Malawi(Giorgi et al, 2015): eMIS individual locations

34.72 34.74 34.76 34.78 34.80 34.82 34.84

-16.10

-16.05

-16.00

(b)

Longitude

Latitude


Malaria mapping, Chikhwawa district, Malawi(Giorgi et al, 2015): EAG village locations and prevalences

34.70 34.75 34.80 34.85 34.90

-16.10

-16.05

-16.00

-15.95

(c)

Longitude

Latitude


Continuous time: rolling malaria indicator surveys

Hotspots: P(prevalence > 20%)


Continuous time: rolling malaria indicator surveys

Coldspots: P(prevalence < 5%)


Work-in-prospect: Majete national park project, Malawi

adaptive design strategies

embedded RCT of community-level interventions


Closing remarks

Operational issues

predictive probability of exceedance over intervention threshold

to inform, but not to over-ride, clinical judgement

Methodological issues:

observational studies vs trials

long series with irregular follow-up times

informative follow-up...marked point process models


References

Monitoring renal function

Diggle, P.J., Sousa, I. and Asar, O. (2014). Real-time monitoring ofprogression towards renal failure in primary care patients. (submitted)

Gastro-enteric surveillance

Diggle, P.J., Rowlingson, B. and Su, T-L. (2005). Point processmethodology for on-line spatio-temporal disease surveillance.Environmetrics, 16, 423–34.

Malaria prevalence mapping

Giorgi, E., Sesay, S.S., Terlouw, D.J. and Diggle, P.J. (2015). Combiningdata from multiple spatially referenced prevalence surveys usinggeneralized linear geostatistical models. Journal of the Royal StatisticalSociety A 178, 445–464.


Documents

Statistical Methods for real-time monitoring of health ...mlpm.eu/static/media/uploads/Summer School 2015/real-time_peter... · Peter J Diggle Statistical Methods for real-time monitoring