Transcript Basic Genetic studies Ladislav Pecen, IMFORM GmbH

Statistické modelování
v klinickém výzkumu
Ladislav Pecen
Klinický výzkum = výzkum aplikace nových léků v humánní
medicíně.
Zjednodušeně
• Fáze I - farmakokinemitika* a farmakodynamika** na zdravých
dobrovolnících
• Fáze II - účinnost léků u pacientů, pro které je určen
• Fáze III - vedlejší účinky léku, jeho tolerabilita
• Fáze IV - post-registrační vědecká či komerční fáze
* Farmakokinetika = osud léčiva v organismu v časovém průběhu.
- vstřebávání léčiva (absorpce)
- jeho rozložení v těle (distribuce)
- přeměna (metabolismus)
- vzájemné ovlivňování (interakce)
- vyloučení z organismu (eliminace - ledvinami, játry do žluči či stolice)
** Farmakodynamika = účinek léčiva na organismus
Některé milníky související s biostatistikou a
klinickým výzkumem:
• epidemie cholery v Londýně v roce 1853 - mapování
incidence -> identifikace závadného zdroje vody
• před 100 lety - založení journálu “Biometrics”
(K.Person, F.Galton, W.F.R.Weldon)
• v roce1915 G.W.Snedecor organizoval první kurzy
biometrie
• v roce 1951 A.B.Hill - první randomizovaný klinický
(streoptomycin při léčbě tuberkulózy)
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.
Cross-Sectional Studies
With outcome
Subjects
selected
for
the study
(randomly
from studied
population)
What is happening ?
Without outcome
Onset
of study
Time
Cohort Studies
With outcome
Exposed or subjects
Cohort
selected
for
the study
(randomly
from studied
population)
Without outcome
With outcome
Unexposed or controls
Onset
of study
What will happen?
Without outcome
Time
Case - Control Studies
Exposed
Cases
Unexposed
Exposed
Controls
Unexposed
What happened ?
Onset
of study
Time
Historical Cohort Studies
With outcome
Exposed or subjects
Records
selected
for
the study
Without outcome
With outcome
Unexposed or controls
Without outcome
Onset
of study
Time
Randomized Clinical Trial Design
Experimental
subjects
Subjects
meeting
entry
criteria
With outcome
Without outcome
Randomization
With outcome
Controls
Onset
of study
Without outcome
XXXXXX
Intervention
Time
Clinical Trial with External Controls (including historical)
With outcome
Subjects
Without outcome
Results of Controls
from previous
(historical) study
Onset
of study
XXXXXX
Intervention in
subjects only
With outcome
Without outcome
Time
Trial Design with Crossover
Experimental
subjects
Subjects
meeting
entry
criteria
With outcome
Experimental
subjects
Without outcome
With outcome
Without outcome
Randomization
With outcome
Controls
With outcome
Controls
Without outcome
XXX
Onset
of study
Intervention
Washout
period
Without outcome
XXX
Intervention
Time
Self-controlled Trial Design (intervention -> placebo)
Subjects
meeting
entry
criteria
With outcome
With outcome
Without outcome
Without outcome
XXX
Onset
of study
Intervention
Washout
period
XXX
Placebo
Time
Self-controlled Trial Design (intervention->placebo->intervention)
Subjects
meeting
entry
criteria
With outcome
With outcome
With outcome
Without outcome
Without outcome
Without outcome
Washout
period
XXX
Onset
of study
Intervention
XXX
Placebo
XXX
Intervention
Time
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 | <= d
• two-sided non-equivalence test H0: |difference in means | <= d
vs. H1: |difference in means | > d.
Studie Fáze I
• problémy bioequivalence
• modely časového průběhu koncentrace účinné látky v krevní
plazmě (v závislosti na dávce, jejím podávání, hmotnosti,
pohlaví, věku apod.) - obvykle se jedná o parametrický model
průběhu křivky a odhadují s jen parametry v rámci zvolené třídy
průběhu křivek
• modely časových změn v závislosti na dávce a způsobu podání
např.
• tepové frekvence a její variability u beta-blokátorů a
antiaritmik
• EEG u neurofarmak (v používaných spektrálních pásmech)
• EKG
• predikční modely na odhad vzniku vedlejších efektů léčby (AEs)
Bioequivalence
Drug plasma
concentration
Cmax
AUC
Tmax
Time
Bioequivalence
e.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 <=> 1002 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 - compare
just 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 variances
different 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).
Fáze II
• problémy modelování účinnosti na pravostranně cenzorovaných
datech (onkologie), či oboustranně cenzorovaných datech
(AIDS/HIV) - zástupný (surrogate) indentifikátor progrese
infekce - podmíněné funkce přežití (stochastické rizikové funkce)
• Response-surface modely pro kvantitativní (dávka) a
kvalitativní proměnné a jejich kombinace
• nejtradičnější model je ANCOVA s baseline hodnotou jakou
rušivým faktorem z důvodu nejnižšího relativního rozptylu
(z třídy modelů ANCOVA, absolutní a relativní změna)
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:
Figure 5.3.1-i
Response Surface (Full Quadratic Model) for Change in Mean
Diastolic Blood Pressure (mmHg) at Trough From Baseline to Week 12
Sitting
40.0
Figure 5.3.1-ii
Contour Plot (Full Quadratic Model) for Change in Mean Sitting
Blood Pressure (mmHg) at Trough From Baseline to Week 12
Diastolic
Reduction
30
30.0
19
20
25
20
C
S
8 20.0
6
6
15
18
10
19
5
17
10.0
0
40.0
18
16
25.0
20.0
30.0
CS-866
(mg)
17
15.0
10.0 HCTZ
5.0
(mg)
20.0
10.0
15
14
0.0
0.0
0.0 0.0
5.0
10.0
15.0
HCTZ
Source: Figure 14.2.6.4.1.1
Table I:
16
Source: Figure 14.2.7.4.1.1
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
20.0
25.0
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 model
Example:
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+ 5X1X2
where 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 nonlinear, 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 model
Smoothing 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 but
95% CI for probability of an event for the patient
is 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 + children
2. Control group - families without occurrence of the particular disease
3. 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
Typical results based LOD score statistical technique:
Particular Disease Related Genes
(Genes mutations)
Particular Disease Protective Genes
(Genes mutations)
BRCA-I and BRCA-II gene mutations and breast cancer incidence