The role of stage at diagnosis in colorectal cancer racial/ethnic - - PowerPoint PPT Presentation

The role of stage at diagnosis in colorectal cancer racial/ethnic survival disparities - A causal inference perspective

Linda Valeri Psychiatric Biostatistics Laboratory Harvard Medical School / McLean Hospital June 27th, 2016

Acknowledgments

My collaborators at the Harvard T.H. Chan School of Public Health

• Biostatistics Department

Brent Coull Tyler VanderWeele

• Epidemiology Department

Xabier Garcia-Albeniz

• Social and Behavioral Sciences Department

Jarvis Chen Nancy Krieger

Background

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◮ The identification and elimination of disparities in cancer-related

• utcomes remain among NCI’s highest priorities.

◮ Research in clinical populations and cohort studies have

documented that such disparities exist across the cancer continuum.

◮ However, gaps in knowledge remain as to the extent of cancer

health disparities in the population as a whole and the causes of these disparities.

¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡

Two challenges:

• Formalize relevant questions about mechanism leading to

disparities in cancer outcomes as well as about interventions to eliminate such disparities.

• Inference using big cancer registries and EMR data accounting

for heterogeneities, confounding, and selection bias.

Racial Disparities in CRC Survival

◮ Colorectal cancer (CRC) is the third most common cancer in the

United States, with more than 136,830 new CRC cases and 50,310 CRC deaths in 2014 in the US alone.

◮ CRC is also one cancer that demonstrates widening mortality

disparities between Whites and Blacks.

◮ From the American Cancer Society website: ”African Americans

have the highest colorectal cancer incidence and mortality rates of all racial groups in the United States. The reasons for this are not yet understood.”

Racial Disparities in CRC Survival

Figure :

Trends in Colorectal Cancer Incidence and Mortality Rates by Race/Ethnicity and Gender, 1975-2010 (Source: American Cancer Society, Surveillance Research, 2014).

Racial Disparities in Stage at CRC Diagnosis

◮ Although the determinants are multifactorial, previous studies report

that differences in stage at diagnosis may explain up to 60% of the survival disparity (Grubbs et al., JCO, 2013).

◮ Higher risk of being diagnosed of advanced CRC for Black

individuals is likely due to differences in screening and follow-up rates, which indicates that stage might be a manipulable factor. Figure :

Colorectal Cancer Stage Distribution (%) by Race/Ethnicity, 2003-2009 (Source: American Cancer Society, Surveillance Research, 2014).

Traditional Approaches

Previous studies on mechanisms leading to racial disparities in cancer survival are either flawed or problematic in interpretation.

◮ Difference method1 to assess the importance of mediating

factors have been used extensively but is usually inappropriate.

◮ Micro-simulation2 studies might lack causal interpretations and

might not allow the assessment for particular patients subpopulations.

◮ Causal mediation analysis3 is problematic because assumes an

intervention on racial/ethnic status.

1Baron and Kenny, Psychological Methods, 1986. 2Lansdorp-Vogelaar et al., Cancer Epidemiol Biomarkers Prev, 2012. 3VanderWeele and Robinson, Epidemiology, 2014.

Motivation for a Causal Inference Perspective

◮ Potential outcome framework for causal inference comes to aid in:

◮ Clarifying the scientific questions of interest ◮ Formalizing the causal contrasts and conditions for their

identifiability from observational data

◮ Statistical methods for causal inference come to aid in:

◮ Constructing robust estimators for the estimands of interest ◮ Accounting for potential biases due to the violation of

identifiability assumptions

Question of Interest

To assess the public health relevance of the disparities in stage at diagnosis we propose to estimate To what extent would racial differences in cancer survival be reduced had the distribution of the stage at diagnosis for Black individuals been equal to that of the White individuals.

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Figure : Intervention: shift of cancer stage at diagnosis distribution among black patients to be the same as in white patients.

Notation

Let

• T denote survival time and Y = min(T, τ), where τ is a

pre-specified time point set at month 60 since diagnosis,

• R denote race/ethnicity indicator taking value 0 if the individual is

Non-Hispanic White and 1 if the individual is Non-Hispanic Black.

• M denote a categorical mediator, stage at diagnosis in our case.
• X denote additional covariates.
• Hx(0) denote a random draw of the mediator in the white

population for a fixed level of the covariates X = x.

• Ym denote the counterfactual outcome for a patient had his/her

mediator been set at level m.

• YHx(0) denote the counterfactual outcome for a patient had his/her

mediator been randomly sampled from the distribution of the mediator in the white population.

Estimands of Interest:

• Disparity

D = E(Y |r = 1, x) − E(Y |r = 0, x)

• Residual Disparity

DHx(0) = E(YHx(0)|r = 1, x) − E(Y |r = 0, x)

• Percent Disparity Reduction (%DR)

%DR = (D − DHx(0))/D The residual disparity measure is identifiable from the observed data if: Assumption 1: Ym ⊥ M|R, X (No unmeasured confounding of stage-survival relationship). Assumption 2: Models for the stage and outcome are correctly specified.

Inference on disparity measure: a model-free approach

◮ Conditionally on x, we

estimate the difference in restricted mean survival times (RMST) truncated at 60/mo

• f follow-up between racial

groups5.

◮ This quantity is estimated as

the difference in the areas under the Kaplan-Meier curve for Blacks and Whites truncated at month 60.

◮ The disparity measure in the

• verall population is then
• btained via random effect

meta-analysis across all confounder strata to allow for heterogeneous disparity measures in each stratum.

50 100 150 200 0.0 0.2 0.4 0.6 0.8 1.0 Time (Months) Survival (Probability)

non−Hispanic White non−Hispanic Black

5Uno et al., JCO, 2014.

Inference on residual disparity: a model-free approach

◮ We estimate for White and Black patients, for each confounder and

stage levels, the RMST after 60 months of follow up.

◮ Probability of being diagnosed at a certain stage in the white

population was also empirically estimated.

◮ The estimator for the residual disparity is given by the racial

differences in the RMST, where for the black population the stage specific RMST’s are standardized over the probability of being diagnosed at that stage in the white population: ˆ DHx(0) =

• m

{ E(Y |r = 1, m, x) − E(Y |r = 0, m, x)}ˆ p(m|r = 0, x)

◮ The overall residual disparity measure was then obtained via random

effect meta-analysis.

Population under Study and Data4

◮ Study population consists of a

sample of n = 166, 727 eligible adult White and Black CRC patients diagnosed between 1992 and 2005 and followed up to 2010 from SEER-9 cancer registries.

◮ We included patients diagnosed

at stage I-IV according to the American Joint Committee on Cancer (AJCC) staging criteria.

¡

Figure : SEER Cancer Registries.

4Surveillance, Epidemiology, and End Results (SEER) Program Research

Data (1973-2010), National Cancer Institute, DCCPS, Surveillance Research Program, Surveillance Systems Branch, released April 2013.

Disparities in CRC Survival: The questions of interest

• Y : min(T, τ = 60/mo)
• R: Racial/Ethnic status indicator White vs Black
• M: Stage at Diagnosis (I-IV)
• X: Age and year at diagnosis, gender, grade of tumor

differentiation, tumor site, state, and county median income 1) How much of the disparity in CRC cancer survival would be reduced had stage at diagnosis distribution for the Black had been equal to that of the White? 2) Does stage modify the difference in survival between the racial groups? 3) Is there gender heterogeneity in survival disparities as well as in the impact of the hypothetical shift in stage at diagnosis distribution?

Racial Disparities in CRC Survival: Results

We find evidence of race-stage interaction. M E(Y |r = 1, m) E(Y |r = 0, m) ˆ D I 49.3 52.2

• 2.9 (-4.3, -1.4)

II 45 48.6

• 3.6 (-5.0, -2.2)

III 41.7 43.5

• 1.8 (-3.2, -0.3)

IV 15.9 18.3

• 2.4 (-3.7, -1.1)

Table : Estimates and 95% confidence intervals of RMST in months by race and stage diagnosis and racial differences in RMST (D) by stage at diagnosis.

Racial Disparities in CRC Survival: Results

0.00 0.05 0.10 20 30 40 50

RMST (Months) for Black (count)/sum(count)

0.00 0.05 0.10 20 30 40 50

RMST (Months) for Black percent

0.00 0.05 0.10 20 30 40 50

RMST (Months) for Black percent

0.00 0.05 0.10 0.15 0.20 0.25 20 30 40 50

RMST (Months) for White percent

0.00 0.05 0.10 0.15 20 30 40 50

RMST (Months) for Black after hypothetical intervention percent

Figure : Histograms of restricted mean survival time truncated at month 60 by age at diagnosis for White, Black, and Black after the hypothetical shift in stage at diagnosis distribution to match that of the White.

Racial Disparities in CRC Survival: Results

Under the assumption that all confounders of the mediator-outcome relationship are adjusted for in the analysis: Estimate CI ˆ D

• 4.6

(-5.3, -3.9) ˆ DHx(0)

• 3.2

(-4.2, -2.3) % DR 29% (6%,40%) Table : Estimates and 95% confidence intervals of disparities measures and % disparity reduction. Equalizing stage distribution of the black population to that of the white is estimated to reduce survival disparities in restricted mean survival time truncated at the 60th month since diagnosis by about 30%.

Racial Disparities in CRC Survival: Results

Gender heterogeneities are observed.

Male Estimate CI ˆ D

• 4.8

(-5.8, -3.8) ˆ DHx (0)

• 3.9

(-5.3, -2.5) % DR 20% (1.2%,51%) Female ˆ D

• 4.3

(-5.2, -3.3) ˆ DHx (0)

• 2.6

(-3.8, -1.3) % DR 40% (8%,72%)

Table : Estimates and 95% confidence intervals of disparities measures by gender.

0.000 0.025 0.050 0.075 0.100 −30 −20 −10 10 20

Disparity (Months) density

name D D_Hx(0)

Male

0.000 0.025 0.050 0.075 −30 −20 −10 10 20

Disparity (Months) density

name D D_Hx(0)

Female

Racial Disparities in CRC Survival: Conclusions

◮ Analyses show that eliminating disparities in stage at diagnosis

might reduce survival disparities in CRC survival by ∼ 30%.

◮ Difference method approach applied to our sample over-estimates

the %DR.

◮ Model-free analyses reveal race-stage interactions as well as gender

and age heterogeneities.

◮ The assumption of no un-measured confounding might not hold. ◮ Sensitivity analyses reveal that residual confounding might explain

part of the disparity reduction.

◮ Lead-time bias might also lead to over-estimation of the role of

stage at diagnosis.

Discussion

◮ By endorsing the potential outcome framework we propose a causal

estimand to investigate determinants of racial disparities.

◮ The approach is robust to model mis-specification and gives a

clinically meaningful and interpretable measure of disparity.

◮ Sensitivity analyses for violation of identifiability assumptions should

become routine practice in health disparity studies.

◮ The non-parametric approach adopted is viable in very large

samples (code available). For studies with smaller sample sizes parametric approaches are recommended.

◮ SAS macro to estimate residual disparity is available. 5

5 Valeri and VanderWeele, Epidemiology (2015)

Thank You! Questions?

lvaleri@mclean.harvard.edu

Traditional Approach: Difference Method

• Let Y denote a health outcome
• R denote racial/ethnic status indicator
• M denote the hypothesized determinant of racial/ethnic disparities
• n the pathway between race and the health outcome (i.e.

mediator)

• X denote additional covariates,

E(Y |R = r, X = x) = θ

†

0 + θ† 1r + θ

′†

2 x

(1) E(Y |R = r, M = m, X = x) = θ0 + θ1r + θ2m + θ

′

3x

(2) Disparity = θ

†

1

Residual Disparity = θ1

Limitations of Difference Method Approach:

◮ Definition of ”residual disparity” is model driven and has merely a

statistical interpretation (i.e. residual effect of race after adjustment for the putative determinant).

◮ However, analyses based on the difference method claim to study

”determinants” of the disparity, giving a causal interpretation.

◮ Difference method approach has causal interpretation under

stringent assumptions of multivariate normality and no unmeasured confounding.

◮ These assumptions are not met when the outcome is survival time. 6 ◮ Effects are estimated on the hazard ratio scale, however estimation

• f difference in expected survival time is more meaningful for public

health considerations.

◮ Statistical approaches ignore interactions between race and the

hypothesized determinant as well heterogeneities across baseline patients’ characteristics.

◮ Issues of confounding and selection bias are overlooked.

6VanderWeele, Epidemiology, 2013.

Eligibility Criteria

◮ Age at diagnosis > 18 ◮ non-Hispanic Origin ◮ CRC primary site ◮ Diagnosis microscopically confirmed ◮ Adenocarcinoma histology

Patients with diagnosis of cancer in situ and with diagnosis reporting source in nursing homes, hospice or via autopsy or death certificate were excluded from the study. Patients from Hawaii registry were excluded due to low percentage of non-Hispanic Black.

Characteristics of our Sample of Patients

Two Potential Sources of Bias

Let U denote an unmeasured confounder of the mediator-outcome relationship (Comment, Coull, and Valeri, 2015). Let S denote the missing data indicator for the mediating variable dependent of both the mediator and the outcome (Valeri and Coull, 2015).

¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡R ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡M ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡Y ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡U ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡R ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡M ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡Y ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡S=1 ¡

Issues of Confounding and Selection in Our Study

◮ The assumption of unmeasured confounding is likely violated in this

study.

◮ Information on genetic predisposition, comorbidities and lifestyle

factors was not available.

◮ In particular obesity status is an important determinant of cancer

stage and survival.

◮ Stage information was missing for 8% of the sample. ◮ Although this percentage is not very high we observe a difference

RMSE of 10 months between individuals who have vs don’t have stage information recorded.

Racial Disparities in CRC Survival: Sensitivity Analyses Results

◮ Sensitivity analyses for selection bias reveal a slight

under-estimation of the reduction in disparity.

◮ When we account for unmeasured confounding for obesity the

disparity reduction appears over-estimated. Estimate (CI) Naive ˆ DHx(0)

• 3.2 (-4.2, -2.3)

Naive % DR 29% (6%,40%) Selection adjusted ˆ DHx(0)

• 3.1 (-4.2, -2.2)

Selection adjusted %DR 32% (0.3%, 42%) Confounding adjusted ˆ DHx(0)

• 3.6 (-4.6, -2.6)

Confounding adjusted %DR 21% (0.5%, 33%) Table : Naive and bias corrected estimates and 95% confidence intervals

• f disparities measures and % disparity reduction.