Statistical Models for Bias and Overdiagnosis in Prostate Cancer Screening

Transcription

1 Statistical Models for Bias and Overdiagnosis in Prostate Cancer Screening Tony Hsiu-Hsi Chen 2007/05/09

2 Evaluation by cumulative mortality curve : Swedish Two-county trial Control Invited (1) RR 0.68 ( ) (2) Lead-time bias problem 200 Years since randomization

3 Evaluation by survival curve Cumulative Surviva C linically- detected cases Screen-detected cases Years of follow-up

4 Lead-time Bias No benefit! Benefit by screening!

5 Length Bias Surface to clinical phase before 1 st screen! Surface to clinical phase before subsequent screen!

6 Survival of Screen- and Clinically-detected Prostate Cancer in a Population-based Screening Trial, Adjusted for Lead-time and Length Bias (Part I)

7 Study Aims To compare survival between cancers detected clinically and at screening Both uncorrected and corrected for major sources of bias To estimate the magnitude of these biases

8 Patients and Methods Data Sources Finnish Prostate Cancer Screening Trial 1 st round: Screening arm: 32,000 men aged Control arm: 48,458 men aged nd round: Prostate cancer cases deriving from Follow-up All patients were followed up until death, migration, or until end of 2002

9 Patients and Methods Case Definition Screen-detected cases: prostate cancers detected In the 1 st round of screening (prevalence) In the 2 nd round of screening (incidence) Clinically-detected cases: Cancers from control arm

10 Uncorrected Survival Analysis Prostate cancer specific survival analysis was performed by life-table method without adjustment for biases The cumulative risk of death from prostate cancer and its 95% CI were calculated

11 Lead-time Bias Adjustment Exponential Weibull Exponential λ ( t) 2 = λ 20 γ t γ 1 λ 20 : scale parameter; γ: shape parameter; t: time of post-lead-time survival Cumulative survival curve after correcting lead-time can be calculated as S() t = exp () t λ 2 s ds 0

12 Lead-time Bias Adjustment-- Likelihood Censored: P 0 ( t) = P ( t) + P ( t) = 11 exp ( t) = dp ( t) = t λ [ ( )] t [ ( ) ] [ ( ) ] γ λˆ λ t λˆ exp λˆ λ s exp λ t s Death from prostate cancer: P P ( t) = dp ( t) 1 12 exp [( ) ] - λˆ + λ s exp[ -λ (t-s)γ] Death from other causes of death: 2 = λ exp [ ( ) ] - ˆ λ + λ t λ γ(t-s) γ- 1 ds ds

13 Adjustment for Length Bias

14 Adjustment for Length Bias (1) (1) Short PCDP: incorporate interval cancer dp tb ( t, t ) λ ( s) S ( t, s) S ( s t ) λ ( t s)ds = b 1 b 02 a b 0 0 a 1, t a dp 02 : derivative of probability of being normal at t a and being diagnosed clinically due to symptoms and signs at t b. t a : age at previous normal screen t b : age at clinical detected as interval cases S 0 : survival functions of staying in state 0 (normal) S 1 : survival function of staying in state 1 (preclinical phase)

15 Adjustment for Length Bias (2) (2) Long PCDP: 1 st screen detected cases has to be conditional on time of surfacing to clinical phase > time to screen 1 st screen: Normal: P 1 st screen: Prostate Cancer: P P ( ) ( ta,t ) t b a,tb = 01 [ P ( t,t ) P ( t, t )] f 1 00 a b + P ( ) ( ta,t ) t b a,tb = 00 [ P ( t,t ) P ( t, t )] f 0 00 a b a a b b

16 Adjustment for Length Bias Weibull(λ 00, γ 0 ) Weibull (λ 10, γ 1 ) Weibull (λ 20, γ 2 ) ( ) ( γ ) 0 γ 0 t, t = λ t λ t P00 a b exp P 01 dp 00 a 00 b t ( ) [ ] ( ) t γ 1 r t t s t s ( 1 v + ) dv 0 γ, exp exp γ λ γ λ λ λ γ λ ds 02 a b b 0 0 = a 00 t a tb γ r tb 0 1 γ r1 1 ( t, t ) [ s ] exp( t s ) γ λ γ λ λ exp ( λ γ v + λ ) dv [ λ γ t ]ds a b = a 00 t s a λ 00, γ 0, λ 10, γ 1, λ 20, and γ 2 can be obtained by MLE 10 s b b

17 Adjustment for Overdiagnosis with a mover-stayer model Mover (M): case with potential for progressing to the symptomatic stage Weibull (λ 20, γ 2 ) Estimate obtained from previous model adjusted for both lead-time and length bias Stayer (S): case has no potential of progressing to the symptomatic stage

18 Further Adjustment for Overdiagnosis Mover (M): Proportion of mover is (1-f) Stayer (S): Proportion of stayer is f Detectable Clinical Prostate Other Causes Preclinical Phase Phase Cancer Death of Death Detectable Preclinical Phase - ( λ ) λ 3 Clinical Phase S = Prostate Cancer Death Other Causes of Death Given f, λ 20 and γ 2 were estimated by MLE method.

19 Results 1,784 prostate cancer cases were ascertained in Intervention arm: 987 cases Control arm: 797 cases Follow-up time Average: 2.7 years ( SD 1.8) Median: 2.5 years ±

20 Uncorrected RR=0.17 ( ) Cumulative Survival Clinical-detected cases Screen-detected cases Adjusted for lead-time bias Adjusted for bothe length bias and lead-time bias Adjusted for length bias and lead-time bias given 40% overdiagnosis Years of follow-up *Taking the average age at diagnosis among screen-detected cases, 64 years old, as example.

21 Relative death rate after correcting lead-time, length-bias, and overdiagnosis Lead-time Adjustment Both length bias and lead-time adjustment Length bias and lead-time adjustment, given 40% overdiagnosis Years of follow-up RR 95% CI RR 95% CI RR 95% CI *RR, relative risk; CI, confidence interval. Taking the average age at diagnosis among screen-detected cases, 64 years old, as example.

22 Final Remark In the Finnish PSA-based trial, the crude estimate of 83% benefit was reduced to non-significant 6% gain after correcting for lead-time and length bias as well as overdiagnosis. It seems too early to show the benefit of PSA screening

23 A Markov Model for Over-diagnosis in Prostate Cancer Screening With PSA: Finnish Prostate Cancer Screening Trial (Part II)

24 Stop screen design-- Overdiagnosis Stop Stop Screen arm control arm 250 Screen arm control arm Incidence rate Incidence rate Time (Year since trial) T ime (Years since trial) Stop screening at 7 th year Catch-up time=mean sojourn time =average duration of tumour staying in the preclinical phase

25 A thorny issue in estimating the magnitude of over-diagnosis in prostate cancer screening Crude CI: 1.95 Cumulative Incidence Control Screen Time since randomization Month (month)

26 Factors related to over-diagnosis Age at screening Mean sojourn time Sensitivity for progressive and nonprogressive tumour

27 Study aim The aim of the current study is to quantify overdiagnosis in the Finnish Prostate Cancer Screening Trial using a novel stochastic model of prostate cancer by taking related factors mentioned above.

28 Patients and Methods Data source Finnish prostate cancer screening trial. During 1996 to 1999, 80,458 men aged 55, 59,63, and 67 years entered the trial. 32,000 in the screening group. 4 years inter-screening interval until age 71 years. Follow-up We followed the subjects till end of 2002 or till they received their second screen

29 Patients and Methods Case Definition Screen-detected cases: PSA 4:consisting of a DRE, TRUS and prostate biopsy. 3.0 PSA 3.9: suspicious finding Control group The remaining 48,458 men comprise the control group Cancers which occurred between two screening rounds and the clinical cancers in the control group: =>Identified by record linkage with the Finnish Cancer Registry.

30 A four-state Markov Model

31 Sensitivity parameter The likelihood for each event or mode of observation can be expressed by the transition probability, P ij (t), and taking into account the program sensitivity (S).

32 Likelihood function False Negative of Progressive Non-Progressive

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34 Progressive tumour with data from control arm ˆ + 1 ˆλ 2 ( i 1) ( i) λ

35 Expectation-Maximum (E-M) Algorithm Maximum Likelihood- estimated the maximum likelihood estimates for λ 2 and λ 3 and S in the four-state Markov model (Figure 1). Expectation: λ 1 was obtained by using the expected equation from control arm that non-progressive tumour would not be observed.

36 Expectation Step Expected (E CN ) = E CN : the expected number of prostate cancers in the control arm given time t N CN : the total number of subjects in the control arm C CN : the observed number of prostate cancers in the control arm given time t Then we obtained the estimated λ 1 (1) from this equation and re-estimated λ 2 (2),λ 3 (2), and S (2) Repeat the procedure of M-E steps until the convergence of parameters.

37 Model Validation The model goodness of fit was evaluated based on the Pearson s chi-square test using the formula as follow.

38 Proportion of overdiagnosis P _ over where () t = P P14 ( t) sen () t + P12 () t + P14 () t P14 () t sen P11() t + P12 () t + P14 () t P11( t) () t + [ P12 () t + P14 () t ] ( 1 sen) P12 ( t) ( 1 sen) () t + [ P () t + P () t ] ( 1 sen) 11 f1 = and P f 2 = 11 P f 1 P 13 ( 4) + f 2 P ( 4) 13 P_over(t): The proportion of over-diagnosed prostate cancers, varies with time (age or inter-screening interval),

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41 Proportion of Overdiagnosis by sensitivity, age, and round of screen Sensitivity Age First Second Sensitivity Age First Second 30% % 45.3% 90% % 20.7% % 51.1% % 23.1% % 56.0% % 25.4% % 60.1% % 27.7% % 63.6% 80 Crude CI: % 29.9% 60% % 42.9% 47.9% 52.2% 36.6% 41.7% 46.2% 50.2% Cumulative Incide Control Screen % 53.7% 0.01 Month

42 Future work Modeling the sensitivity as a function of age, PSA level at baseline, or other markers-identify an individual with high potential of overdiagnosis By taking over-diagnosis into account, extend the model to elucidate the natural history defined by gleason score and stage do Cost-effectiveness analysis for PSA screening