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Uncertainty Analyses

Latin hypercube method implemented in POHEM

Tamoxifen example

Bill FlanaganPhilippe FinèsFeb 9, 2010

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Generating lognormal deviate

• 1) Computation of sigmafor ( i = 0; i < SIZE( TAMOXIFEN_RR_AGE_GROUP ); i++ ) {

for ( j = 0; j < SIZE( TAMOXIFEN_RELATED_DISEASES ); j++ ) {if ( TAMOXIFEN_CALCULATE_SIGMA )

{mTamoxifen_RR_STD_LN[i][j] = (( log( TAMOXIFEN_RRISK[i][j][2] ) - log( TAMOXIFEN_RRISK[i][j]

[1] ) ) / TAMOXIFEN_RR_CI ) / 2;

ex: (UCI-LCI) /1.96/2}else

{mTamoxifen_RR_STD_LN[i][j] = TAMOXIFEN_RR_SIGMA[i][j];}}}• 2) Generation of a lognormal random variable

/* The RR is assumed to be lognormal. When calculating the mean for the lognormalfrom a normal there is an adjustment factor of exp(sigma^2 / 2) */mTamoxifen_RR[s][i][j] = TAMOXIFEN_RRISK[i][j][0] / exp( pow( mTamoxifen_RR_STD_LN[i][j], 2) / 2 )

* exp( mTamoxifen_RR_STD_LN[i][j] * dRand );

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Generating lognormal deviate

• Normal distribution– mean= , sd=– draw Z ~ N(0,1)

X = +Z* ~ N(,²)• Lognormal distribution

– Y ~ lognormal(,²) ln(Y)~N(,²) – mean=exp(²/2)=exp() exp(²/2) , – sd=sqrt[(exp(²)-1)(exp(2²))] – draw Z ~ N(0,1)

X = exp(+Z*)/exp(²/2) = exp() exp(Z*)/exp(²/2)~ lognormal(,²)

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Interpreting and Using RCT results

• RCT tamoxifen trial– control vs tamoxifen

• TAMOXIFEN_RRISK – by age, disease and estimate (mean, lci, uci)– model generated rTamoxifen_RR

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Using Subsamples

• Subsamples– when a person is first created in POHEM they are randomly

assigned to a subsample– subsamples generated automatically by Modgen– user picks the total number in Scenario Settings ( eg 40)

• Presimulation– generate a vector of RR for each subsample

• RR from lognormal distribution defined by RCT mean and CI – by age group and disease

• CaseSimulation– during code execution of an individual simulated life course– the risk equation for each disease is multiplied by the RR given

the person’s subsample (and age)– use GetCaseSample() in code to know person’s subsample

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Looking in the code

• Presimulation code– can be in any mpp– see Otherhealth.mpp

• starts in line 18 but important part in line 369

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Presimulation codefor ( s = 0; s < SIZE( MAX_SUBSAMPLES ); s++ ) {

for ( i = 0; i < SIZE( TAMOXIFEN_RR_AGE_GROUP ); i++ ) { for ( j = 0; j < SIZE( TAMOXIFEN_RELATED_DISEASES ); j++ ) {

/* The RR is assumed to be lognormal. When calculating the mean for the lognormalfrom a normal there is an adjustment factor of sigma^2 / 2The reference for this is the Handbook of the Normal DistributionPatel and Read page 24.*/// We further decided to limit to the 95% confidence interval to avoid outliersdo { dRand = RandDeviate(7); } while ( fabs( dRand ) > 1.96 );

mTamoxifen_RR[s][i][j] = TAMOXIFEN_RRISK[i][j][0]/ exp( pow( mTamoxifen_RR_STD_LN[i][j], 2) / 2 )* exp( mTamoxifen_RR_STD_LN[i][j] * dRand );

}}

}

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CaseSimulationvoid Person::StartTamoxifen(){...

for ( i = 0; i < SIZE( TAMOXIFEN_RELATED_DISEASES ); i++ ){

s = GetCaseSample();rr_tamoxifen[i]=mTamoxifen_RR[s][tamoxifen_rr_age_index][i];

}}void Person::BreastCancerCheck(){ ...

bc_relative_risk= ... * rr_tamoxifen[TAM_BREAST];

nProb_breast_incidence = Breast_prob[curtate_age] * bc_relative_risk;

...}

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Output

• Export Tables to Excel– in the Output contents window, check each of

the subsamples– one workbook per subsample for each table

• naming convention SUB#_<table name>• plus one series of new tables called trun,

SUB#_trun

– analyse differences in outcomes (e.g. life expectancy) between subsamples in each workbook (manual calculations)

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Example: Results on HUI in POHEM-OA from perturbations of

the parametersPhilippe Finès

August 2009

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Average HUI, original values and values from 10 realisations of parameters, females

Females

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

OA has not yet been diagnosed

Diagnosis of OA

First Visit to an orthopaedic surgeon(OS)

Second Visit to an orthopaedicsurgeon (OS)

Third+ Visit to an orthopaedicsurgeon (OS)

Primary surgery for OA (max 4)

Revision surgery for OA (max 4?)

All

Orig Sub0 Sub1 Sub2 Sub3 Sub4 Sub5 Sub6 Sub7 Sub8 Sub9 Sub10

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Average HUI, original values and values from 10 realisations of parameters, males

Males

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

OA has not yet been diagnosed

Diagnosis of OA

First Visit to an orthopaedic surgeon(OS)

Second Visit to an orthopaedicsurgeon (OS)

Third+ Visit to an orthopaedicsurgeon (OS)

Primary surgery for OA (max 4)

Revision surgery for OA (max 4?)

All

Orig Sub0 Sub1 Sub2 Sub3 Sub4 Sub5 Sub6 Sub7 Sub8 Sub9 Sub10

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Average HUI in 2020, original values and some statistics on the values, females

Females, 2020

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

OA has not yetbeen diagnosed

Diagnosis of OA First Visit to anorthopaedic

surgeon (OS)

Second Visit toan orthopaedicsurgeon (OS)

Third+ Visit to anorthopaedic

surgeon (OS)

Primary surgeryfor OA (max 4)

Revision surgeryfor OA (max 4?)

All

Orig Min 5% Mean Median 95% Max

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Average HUI in 2020, original values and some statistics on the values, males

Males, 2020

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

OA has not yetbeen diagnosed

Diagnosis of OA First Visit to anorthopaedic

surgeon (OS)

Second Visit toan orthopaedicsurgeon (OS)

Third+ Visit to anorthopaedic

surgeon (OS)

Primary surgeryfor OA (max 4)

Revision surgeryfor OA (max 4?)

All

Orig Min 5% Mean Median 95% Max

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Average HUI in 2020, original values, mean and median, females

Females, 2020

0.85

0.68

0.49 0.48 0.49

0.69

0.64

0.820.85

0.68

0.49 0.48 0.49

0.69

0.65

0.82

0.82

0.64

0.85

0.68

0.49 0.48 0.49

0.69

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

OA has not yetbeen diagnosed

Diagnosis of OA First Visit to anorthopaedic

surgeon (OS)

Second Visit toan orthopaedicsurgeon (OS)

Third+ Visit to anorthopaedic

surgeon (OS)

Primary surgeryfor OA (max 4)

Revision surgeryfor OA (max 4?)

All

Orig Mean Median