Statistick modelovn v klinickm vzkumu

Ladislav Pecen

Klinick vzkum = vzkum aplikace novch lk v humnn medicn.

Zjednoduen Fze I - farmakokinemitika* a farmakodynamika** na zdravch dobrovolncch Fze II - innost lk u pacient, pro kter je uren Fze III - vedlej inky lku, jeho tolerabilita Fze IV - post-registran vdeck i komern fze

* Farmakokinetika = osud liva v organismu v asovm prbhu. - vstebvn liva (absorpce)- jeho rozloen v tle (distribuce)- pemna (metabolismus)- vzjemn ovlivovn (interakce)- vylouen z organismu (eliminace - ledvinami, jtry do lui i stolice)

** Farmakodynamika = inek liva na organismus

Nkter milnky souvisejc s biostatistikou a klinickm vzkumem:

epidemie cholery v Londn v roce 1853 - mapovn incidence -> identifikace zvadnho zdroje vody

ped 100 lety - zaloen journlu Biometrics (K.Person, F.Galton, W.F.R.Weldon)

v roce1915 G.W.Snedecor organizoval prvn kurzy biometrie

v roce 1951 A.B.Hill - prvn randomizovan klinick (streoptomycin pi lb tuberkulzy)

Study Designs in Medical Research

1. Observational studies (without intervention)

1.1. Case-series (Descriptive) studies

1.2. Case-Control studies (retrospective - "What happened ?")

1.3. Cross-sectional studies (prevalence - "What is happening ?")

1.4. Cohort studies (prospective - "What will happen ?")

1.5. Historical cohort studies

2. Clinical trials (experimental studies = with intervention)

2.1. Controlled trials

2.1.1. Parallel or concurrent controls

2.1.1.1. Randomized parallel trials *

2.1.1.2. Not randomized parallel trials

2.1.2. Sequential controls

2.1.2.1. Self-controlled design

2.1.2.2. Crossover trial design *

2.1.3. External or historical controls (bias highly probable)

2.2. Studies without controls

* The best selection and the most frequently used designs for treatments (treatment vs. placebo) comparison studies.

Onsetof studyTime With outcomeWithout outcomeCross-Sectional StudiesWhat is happening ?Subjectsselectedfor the study(randomlyfrom studiedpopulation)

Onsetof studyTime With outcome

Without outcomeCohort StudiesWhat will happen?Cohortselectedfor the study(randomlyfrom studiedpopulation)With outcome

Without outcomeExposed or subjectsUnexposed or controls

Onsetof studyTime Exposed

Unexposed Cases ControlsCase - Control Studies Exposed

UnexposedWhat happened ?

Onsetof studyTime With outcome

Without outcomeHistorical Cohort StudiesRecordsselectedfor the studyWith outcome

Without outcomeExposed or subjectsUnexposed or controls

X X X X X XOnsetof studyInterventionTimeExperimentalsubjectsControlsWith outcome

Without outcomeWith outcome

Without outcomeSubjectsmeetingentrycriteriaRandomized Clinical Trial DesignRandomization

X X X X X XOnsetof studyIntervention in subjects onlyTimeSubjectsResults of Controlsfrom previous(historical) studyWith outcome

Without outcomeWith outcome

Without outcomeClinical Trial with External Controls (including historical)

X X X X X XOnsetof studyIntervention InterventionTimeExperimentalsubjectsControls With outcome

Without outcomeSubjectsmeetingentrycriteriaTrial Design with CrossoverRandomization With outcome

Without outcome With outcome

Without outcome With outcome

Without outcomeControlsExperimentalsubjectsWashoutperiod

X X X X X XOnsetof studyIntervention PlaceboTime With outcome

Without outcomeSubjectsmeetingentrycriteriaSelf-controlled Trial Design (intervention -> placebo) With outcome

Without outcomeWashoutperiod

XXX XXX XXX

Onsetof studyIntervention Placebo InterventionTime With outcome

Without outcomeSubjectsmeetingentrycriteriaSelf-controlled Trial Design (intervention->placebo->intervention) With outcome

Without outcomeWashoutperiod With outcome

Without outcome

Biostatistics in new treatment development

one-sided non-inferiority test is usually H0: difference in means < -d vs. H1: difference in means >= -d

one-sided superiority test is usually H0: difference in means =0 vs. H1: difference in means >0, (to do power analysis it have to be in reality H1: difference in means >= d).

two-sided equivalence test H0: |difference in means | > d vs. H1: |difference in means |

Studie Fze I

problmy bioequivalence

modely asovho prbhu koncentrace inn ltky v krevn plazm (v zvislosti na dvce, jejm podvn, hmotnosti, pohlav, vku apod.) - obvykle se jedn o parametrick model prbhu kivky a odhaduj s jen parametry v rmci zvolen tdy prbhu kivek

modely asovch zmn v zvislosti na dvce a zpsobu podn nap. tepov frekvence a jej variability u beta-bloktor a antiaritmik EEG u neurofarmak (v pouvanch spektrlnch psmech) EKG

predikn modely na odhad vzniku vedlejch efekt lby (AEs)

BioequivalenceDrug plasmaconcentrationTimeAUCCmaxTmax

Bioequivalencee.g. new treatment formulation - only test on healthy volunteers if time course of concentrations in blood is the same ->Y=ln(AUC) (Area Under the Curve of concentrations)instead of usual H0: E(YT - YR)= = 0 predefined equivalence region (-1,2) is used, typically 1=2, for FDA have to be used exp()=1.25.H0: - or H01: - and H02: vs. HA = HA1 HA2 (HA1 is alternative to H01, HA2 to H02 ) =>two one-sided hypotheses are simultaneously tested 100-2 CI for can be calculated - if completely inside (-, ) H0 - non-equivalence hypothesis is rejected.For =5% => 90% CI for have to be used, p-value is the maximum of p-values of two one-sided hypotheses H01 and H02

Bioequivalence

Standard approach - population bioequivalence - comparejust mean values of AUC (or logarithm of AUC)

New approach H0: - or or T/ R vs. H1: - < < and T/ R < ; variation is also included Testing using maximal likelihood method (Vuorinen J., Turunen J: A simple three-step procedure for parametric and non-parametric assessment of bioequivalence. Drug Information Journal 31, pp.167-180, 1997).

Individual equivalence H0 => more than means and variancesdifferent study design - 3 experiments per person, typically two times reference trt., one new trt., or randomly 2 R + 1 T vs. 1 R + 2 T, order is also random -> method of bootstrap is applied (Schall R., Luus H.G.: On population and individual bioequivalence. Statistics in Medicine 19, pp.2195-2198, 1993).

Fze II

problmy modelovn innosti na pravostrann cenzorovanch datech (onkologie), i oboustrann cenzorovanch datech (AIDS/HIV) - zstupn (surrogate) indentifiktor progrese infekce - podmnn funkce peit (stochastick rizikov funkce)

Response-surface modely pro kvantitativn (dvka) a kvalitativn promnn a jejich kombinace

nejtradinj model je ANCOVA s baseline hodnotou jakou ruivm faktorem z dvodu nejniho relativnho rozptylu (z tdy model ANCOVA, absolutn a relativn zmna)

Synergism Analysis - the synergism definition: joint effect of two treatments being significantly greater than the sum of their effects when administered separately (positive synergism) or the opposite (negative synergism).

Bootstrap technique: An aplication of resampling statistics. It is a data-based simulation method used to estimate variance and bias of an estimator and provide confidence intervals for parameters where it would be difficult to do so in the usual way.

Evolutionary models - the estimation of time-dependence model of primary efficacy parameter during time based on dosages combination

The response surface (Figure 5.3.1-i) and contour plot (Figure 5.3.1-ii) are displayed below:

EMBED Word.Picture.8

Source: Figure 14.2.6.4.1.1

Source: Figure 14.2.7.4.1.1

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Figure 5.3.1-ii

Contour Plot (Full Quadratic Model) for Change in Mean Sitting Diastolic

Blood Pressure (mmHg) at Trough From Baseline to Week 12

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Figure 5.3.1-i

Response Surface (Full Quadratic Model) for Change in Mean Sitting

Diastolic Blood Pressure (mmHg) at Trough From Baseline to Week 12

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Table I:Estimated Response and Optimum Dose Combinations Full Analysis Set Using the Last-observation-carried-forward Method (LOCF)

Estimated Response: Decrease of dBP from Baseline to Week 12 [mmHg]

Olmesartan Medoxomil (CS-866)Dose [mg]

HCTZ Dose [mg]

20.45

26.41

24.34

19.25

30.00

25.00

Figure I:Mean Sitting dBP Mean Course by Treatment Group (N = 1471)

Olm = olmesartan medoxomil (dose level 10, 20, 40 mg); HCTZ = hydrochlorothiazide (dose level 12.5, 25 mg); mp = matching placebo

Figure II:Mean Standing dBP Mean Course by Treatment Group (N = 1471)

Olm = olmesartan medoxomil (dose level 10, 20, 40 mg); HCTZ = hydrochlorothiazide (dose level 12.5, 25 mg); mp = matching placebo

Parametric response surface modelExample:The mean change from baseline to week 12 in mean sitting dBP at trough analysed using response-surface methodology. This approach aims to predict an optimum dose combination within the continuous response surface. The relationship between CS-866 and HCTZ and the dose combinations will be examined using the quadratic model:Y = 0 + 1X1 + 2X2 + 3X12 + 4X22+ 5X1X2where Y=mean change from baseline to week 12 in mean sitting dBP at trough; X1=dose of CS-866 and X2=dose of HCTZ. Quadratic and interaction terms that are not statistically significant will be removed from the model in a stepwise fashion until only statistically significant terms remain (p-value 0.05). Response-Surface Model is just special case of polynomial (generally non-linear, in our case polynomial in 2nd power) multidimensional regression model. Adjustment allowing to exclude influence of confounding factor could be used.

Non-parametric response surface modelSmoothing procedure

Oncological Trials-Assessing risk of an event

In oncology the target variable of interest (primary efficacy variable) is usually survival time, disease-free, metastases-free time or a similar time-to-an-event => survival analysis models. Assessing the risk of progression, the risk of occurrence of metastases etc for a given patient and time instant. We are able to quantify the risk of the patient but95% CI for probability of an event for the patientis 0% - 100%. Techniques: Kaplan-Meier estimation of survival function, Cox proportional risk model or Aalen additive risk model,accelerated life model, competing risk model.

HIV/AIDS related studies

The target variable of interest is survival time - the data are left-time censored (time of infection or sero-conversion is unknown) or left-time interval censored (date of last negative and first positive tests are known), right-time censored (death date is sometimes unknown) => survival analysis models with both sides censored data. Using of surrogate indicator of infection progression - e.g., CD4+ T-lymphocytes, No of virus RNA copies Complicated model for many simultaneous treatment effect modeling. New AIDS treatment - Fuzeon produced by Roche Holding (price about 20 000 USD = Euro per year, fuse inhibitor)

Ordinal categorial data

e.g back pain intensity assessed by five-point verbal rating scale (VRS-5) (0= mild, 1= discomforting, 2= distressing, 3= horrible, 4= excrutiating); functional capacity score after performing activity - e.g., putting on a jack, assessed using a four-point scale (1= without pain, 2= with slight pain possible, 3= interrupted pain, 4= impossible because of pain)- 2 test ignore the ordinality of categories - rank tests (e.g. Wilcoxon Rank-Sum test) - small No of categories- ordinal regression models- Proportional Odds ratio (POR) - generalization of binary logistic regression - works with cumulative probabilities - Continuation Ratio (CR) - works with conditional probabilities (hazards) Details Armstrong B., Sloan M.: Ordinal regression models for epidemiologic data, Amer.Jour.of Epidem. 129, pp.191-204,1989

Statistical models based on family tree structure - e.g., for colorectal cancer cases (black below)example of one family tree:For statistical analyses one need:1. Families-tree with hereditary incidence (typically 2 and more cases as a average number at any sub-tree parents + children2. Control group - families without occurrence of the particular disease3. Families with probably random disease occurrence (just one case of the particular disease, or occurrence and not in group 1.)

Used symbols definition:

More difficult family structure

Particular Disease Related Genes(Genes mutations)Particular Disease Protective Genes(Genes mutations)Typical results based LOD score statistical technique:

BRCA-I and BRCA-II gene mutations and breast cancer incidence