Propensity Score Analysis to compare effects of radiation and surgery on survival time of lung cancer patients from National Cancer Registry (SEER)

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1 Propensity Score Analysis to compare effects of radiation and surgery on survival time of lung cancer patients from National Cancer Registry (SEER) Yan Wu Advisor: Robert Pruzek Epidemiology and Biostatistics School of Public Health SUNY-Albany December 2009 Abstract: This study used a wide variety of modern propensity score analysis (PSA) methods and graphics to assess survival times following radiation or surgery of lung cancer patients. The data consisted of a sample (n=9474) from the Surveillance, Epidemiology and End Results (SEER) Registry of the National Cancer Institute. Although several different methods were used to define propensity scores, including classification trees and logistic regression, using both stratification and matching, results were generally consistent across methods, showing the following: 1. Lung cancer patients treated with surgery alone had longer survival times than those treated with radiation alone (averaging about ½ year longer). 2. For patients who received no radiation, surgery yielded large mean gains in survival times (almost 1 year longer); among patients who had radiation, the addition of surgery had smaller average effects (roughly ½ year difference). 3. Radiation tended to improve survival of lung cancer patients who did not have surgery (averaging 2-3 months); but radiation tended to have little affect following surgery (adding just over 1 month on average). 1. Introduction 1.1 Data source The Surveillance, Epidemiology, and End Results (SEER) Registry from the National Cancer Institute was used as the data source. This is an authoritative source of information on cancer incidence and survival in the United States (1). The SEER Program is the only comprehensive source of population-based information on cancer in the United States; it includes information for several covariates as well as patient survival data under different treatment conditions. SEER collects information on stage of cancer at the time of diagnosis, incidence, prevalence and survival for patients from specific geographic areas that represent 26 percent of the U.S. population; the reports are compiled to include covariate observations plus cancer mortality for the entire country. The data are available and intended for research for anyone interested in US cancer statistics or cancer surveillance methods. Updated annually and provided as a public service in print and electronic formats, SEER data are used by thousands of researchers, clinicians, public health officials, legislators, policymakers, and community groups. 1

2 1.2 Background of the research Lung cancer is the second most diagnosed cancer in men and women in the U.S. and the number one cause of death from cancer each year in both men and women. Surgical resection (cutting away) of the tumor generally is indicated for cancer that has not spread beyond the lung. This is the principal form of treatment for patients with stage 1 or stage 2 lung cancer. Radiation therapy, or radiotherapy, delivers high-energy x-rays that can destroy rapidly dividing cancer cells. It can shrink the tumor(s) before surgery and eliminate most cancer cells that remain in the treated area after surgery. The SEER data that is analyzed in this report consists of 9474 cases pertaining to the effects of radiation or surgery on survival of patients with lung cancer. 1.3 Literature review of the research Cox regression analysis has predicted long time survival after lung cancer surgery with early preoperative stage, ages below 70 years and normal pulmonary function (2). The Kaplan-Meier method was used to calculate 5-year postoperative survival in all categories of patient s characteristics; it identified significant increases in survival for early stage patients (3). Cox model and Kaplan-Meier curves can more accurately identify patients at risk for lung cancer death after surgery using histologic type and precise size specifications than using conventional tumor-node-metastasis staging, with SEER data (4). Research on the effects of surgery on survival focuses on building up survival models to identify significant variables in survival prediction. No research article on the effects of radiation treatment only on survival of lung cancer patients has been found. No studies seem to have comprehensively compared groups who did vs. did not have surgery or radiation with respect to survival for lung cancer. No comparison seems to have been made by controlling all available covariates, that is, adjusting for the effects of selection bias! The preceding means that an important question still remains to be answered: Do lung cancer patients survive longer with following surgery or radiation, or both of these treatments? Since the observationally defined groups cannot be fairly compared without covariate adjustments, a decision was made to use a wide variety of modern PSA-specific methods and graphics to compare groups after adjusting for selection bias. 1.4 Propensity Score Analysis (PSA) The Propensity Score is the conditional probability that a unit i will receive a treatment (Z i =1), given a set X of observed covariates: e(x i )=pr(z i =1 X i =x i ) (where it is assumed that, given the X s, the Z i [0 or 1] are independent) (5). Given an appropriate (model) or method for computing propensity scores, e(xi), treated and control subjects in the same stratum, or matched set (having nearly the same PS), should have approximately the same distribution for each covariate, or combination of covariates. Given an appropriate choice of covariates, treatment and control groups should differ from one another only by chance if their propensity scores are highly similar. This effect is similar to what happens when randomization is used to assign treatments; it is notable that it can also occur in well-designed observational studies. There are two stages of PSA: Stage 1, 2

3 Estimation of Propensity Scores (PS); Stage 2a, PS matching and 2b, treatment comparisons. 2. Methods 2.1 Data creation and cleaning The SEER archive starts since Quite a few of the data elements are outdated and some of them have different coding, most of which standardized in Thus, we extracted patients who were diagnosed with lung cancer in 2004 and used the data elements with coding consistent from 2004 to There are no missing data for outcome variable or treatment variables, which are surgery and radiation. About 40% records with any missing data elements were deleted from the final dataset which has 9474 cases. The survival time is measured by month and the cutoff is in Thus, the data is censored and about 30% people were still alive with survival time equaling to 35 months. The description of the data elements is in the table 1. The following Table provides a brief description of all SEER covariates as well as the response variable, survival, in the form of a data dictionary: Variable survival surgery radiation laterality size marital race sex age grade histg diag_confirm node exten stage site mets malignant number_pri vitalr lymph Description # of months 0 35 (All cases diagnosed in 2004 and cutoff is in If survive at the end of 3 years, survival=35) Surgery is performed or not Radiation is performed or not Which side the tumor originated The diameter of the primary tumor recorded in millimeters marital status patient race patient gender patient age Grading and differentiation codes Grouped histological type The method used to confirm the presence of cancer (histology or cytology) Exact number of regional lymph nodes containing metastases Contiguous growth of the primary tumor Describes the extent of the cancer the site in which the primary tumor originated the distant site(s) of metastatic involvement First malignant primary indicator the actual number of primaries Whether patient dies from the cancer the regional lymph nodes involved with cancer Table 1. Data dictionary of the studying dataset. 3

4 2.2 Comparison design To answer the question: Do lung cancer patients survive longer following surgery or radiation, or both, five binary group comparisons were made, using a 2 x 2 table to show how a total of five comparisons were made in three groups. See Figure 1. The first comparison, for Group I compared the effects of the surgery alone vs. radiation alone with respect to survival times (Figure 1a). Two comparisons were defined for Group II (by rows): for these, the effects of surgery on survival were assessed with and without radiation (Figure 1b). For Group III (by columns): the effects of radiation were compared with or without surgery (Figure 1c) PSA stages Stage 1: Estimation of PS. Both classification tree and logistic regression (LR) methods were used to estimate propensity scores. The classification tree algorithm is not model-based; rather it is algorithmic. Binary recursive partitioning is used to form splits; the bottom of the tree identifies leaves. Covariates and cut points are chosen to ensure the best splits; interactions of covariates are therefore automatically detected. Strata were formed naturally using leaves of a tree; strata sizes were unconstrained and the number of terminal leaves/strata chosen was based on prior experience with logistic regression, especially some results of Rosenbaum and Rubin (6). Propensity Scores were derived as (# in treatment group) / (# of units), within each stratum; the number of strata equaled the number of leaves (bottom of tree). All individuals were assigned the same estimated PS within each stratum. For the LR, Z i = binary variable (1 = treatment, 0 = control) and X i = vector of independent variables (explanatory covariates). PS= Prob(Z i =1 X). Fitted values are used to estimate PS s, e(x i ), for each observation, based on the available covariates. When propensity scores are estimated from the X i ; the estimation method should generally consider product functions, or interactions. The goal of LR is to use all covariates that appear to relate to treatment and outcome to improve prediction. Overfitting in phase I of PSA is not problematic since there are no concerns about external validity of PS estimation model. To the extent that there is selection bias (for which adjustments are needed) this can be seen in discrimination reflected in an ROC curve associated with the model. (But many of the best PSA studies show little discrimination.) 4

5 2.3.2 Stage 2: PS matching and treatments comparison. Nearest neighbor 1:1 matching (NNM) was used, without replacement: this method selects the m comparison (control) units whose propensity cores are closest to those of the corresponding treated unit. Propensity scores were ranked from high to low. The highest ranked unit was matched first and the matched comparison unit was removed from further matching; then the next highest ranked unit, etc., until all matches were made. Given the matched pairs, a paired sample comparison was used to analyze and display the data pairs and difference scores; confidence intervals for the population mean difference were used for each such comparison. Stratification was also used; this entailed use of loess regression and Five (nearly equally sized) strata from stratification-based comparison of outcomes across derived strata were generally sufficient to remove 90% of removable bias. Means of treatment and control group were compared within each stratum and the DAE-Direct Adjustment Estimator (weighted mean difference between control and treatment response across strata) was calculated. The LOESS-based comparison of treatment to control groups for response was based on LR results. Local nonlinear regression curves were obtained for treatment and control groups. The span argument in the R function loess was used to control smoothness. The vertical distance between curves across PS range provides an index of the treatment effect weighted according to the density of the PS distribution ignoring groups. 3. Results 3.1 Preliminary comparison of survival time distribution. The survival time histograms from total, no surgery and no radiation, surgery alone, radiation alone, and surgery and radiation groups were compared side by side in figure 2. These histograms suggested several questions about survival for certain 5

6 groups that would be worthy of deeper analysis, but they required detailed knowledge of archive and so were not considered here. 3.2 Classification tree stratification 6

7 In the classification tree graphics, each leaf (at the bottom) shows numerical values of the derived propensity scores and number of observations with such PS. The circ.psa function in PSAgraphics R package was used for these comparisons. In the circ.psa plots, a circle is plotted for each stratum, centered on the means for the treatments groups (for the X and Y axes) respectively. The size of the circle corresponds to the size of the stratum. A diagonal line from lower left to upper right shows the identity where X=Y, so that circles on, say, the lower side of this line show that the corresponding X mean is larger than the Y mean for that stratum, and vice-versa. Parallel projections are made from the centers of the stratumcircles to difference scores that are plotted on a line segment on the lower-left corner of the graphic; the average difference, which corresponds to the direct adjustment estimator (DAE) for the overall treatment effect, is plotted as the blue heavy dashed line parallel to the identity diagonal. Rug plots are shown on the upper and right margins of the graphic, for the X and Y marginal distributions. A 95% confidence interval (green solid bar) 7

8 for the overall effect is plotted to the left of the distribution of the stratadefined difference scores, centered on the DAE. In the comparison of surgery alone vs. radiation alone (Figure 3), the grand mean difference is 6.56 and the 95% C.I. ranges from 5.38 to In Figure 4, we assess the effects of surgery on survival time with or without radiation. For the patients without radiation, surgery led to average months longer survivals compared to no surgery (95% CI =10.28, 12.76). For patients who had had radiation, surgery led to average 6.68 months longer survival compared to no surgery (95% CI = 4.04,9.32). In Figure 5, we assess the effects of radiation on survival time with or without surgery. For the patients without surgery, radiation led on average to 2.89 months longer survival than no surgery (95% CI =2.06, 3.71). For patients with surgery, radiation led to a mean of 0.78 months longer survival than no radiation (95% CI = -2.3, 0.74). 3.3 LR to estimate the PS LR was used to estimate the PS of treatment for each comparison. The covariates in red with very small p values contribute most 8

9 to the PS, compared to covariates in black. In Figure 6, race, sex, age, site, grade, diag_confirm, exten, lymph, mets, stage and number_pri had stronger roles in defining the estimated PS of surgery alone vs. radiation alone. In Figure 7, in no radiation group, marital, age, site, laterality, grade, diag_confirm, exten, lymph, mets, stage and number_pri had strong roles in determining the estimated PS fpr comparing surgery with no surgery. In the radiation group, race, age, site, 9

10 laterality, grade, diag_confirm, exten, lymph, mets, stage, number_pri and malignant had strong roles in determining the estimated PS for comparing surgery to no surgery. In Figure 8, the no surgery group, marital, age, site, grade, diag_confirm, exten, lymph, mets, stage and malignant had strong roles in determining the estimated PS for radiation vs. no radiation. In the surgery group, marital, age, site, grade, diag_confirm, exten, lymph, mets and stage had strong roles in determining the estimated PS for comparing surgery with no surgery :1 nearest neighbor matching (NNM) Nearest neighbor 1:1 matching (NNM) was used without replacement; we compared the distribution of estimated probabilities for each treatment before and after matching using histograms. The gray histograms correspond to before matching; these 10

11 generally showed strong PS differences between treatments for all comparisons. After NNM, the green histograms show that the estimated PS s were nearly identical for the paired treatments in each five comparisons (Figures 9, 10 and 11). 3.5 Paired dependent sample comparison After 1:1 NNM, we used the function granova.ds from the granova R package to compare the matched (paired) dependent data. Paired X & Y values (survival times) were plotted as scatterplot where the identity reference line (for Y=X) is drawn. All data points are plotted relative to the identity line, and summary results are shown graphically. Parallel projections of data points to (a lower-left) line segment show how each point relates to its X-Y = D difference score; blue 'crosses' are used to display the distribution of difference scores and the mean difference is displayed as a red heavy dashed line, parallel to the identity reference line. Means for X and Y are also plotted as thin dashed vertical and horizontal lines to form rug plots for the distributions of X (at the top of graphic) and Y (on the right side). The 95% confidence interval for the population mean difference is also shown graphically (the green solid bar at the lower left side). In the comparison of surgery alone vs. radiation alone (Figure 12), the grand mean difference between the paired groups is 5.12 and the C.I. is from 4.44 to In Figure 13, we access the effects of surgery on survival time with or without radiation. For the patients without radiation, surgery led to 9.12 months longer average survivals compared to no surgery (95% CI = 7.87,10.38). For patients with radiation, 11

12 surgery led to a mean of 5.51 months longer survival compared to no surgery (95% CI = 4.19, 6.84). In Figure 14, we assess the effects of radiation on survival time with or without surgery. For the patients without surgery, radiation led to an average of 2.59 months longer survival than no surgery (95% CI =2.05, 3.12). For the patients with surgery, radiation led to an average of 0.29 months shorter survival than no radiation (95% CI = , 1.02). 3.6 Stratification-based comparison After estimation of PS by LR, stratification-based comparisons were made using quintiles of the PS distribution, to follow the logic of Rosenbaum and Rubin (1983), i.e, 5 strata eliminate 90 % of selection bias. We stratified the observations into 5 equal sized strata according to their PSs. The cbal.psa R function (from the not-yet posted PSAgraphics package) was used to check the balance of covariates in treatment and control groups with and without PS adjustment. In the cbal.psa plot, the standardized effect size (stes) is defined as difference of means divided by pooled standard deviation. Both unadjusted ESs (stesuna) and the adjusted counterparts (stes-adj) are computed and plotted. For stes-adj, d is 12

13 computed using denominator based on pooling variances in all subgroups for each covariate. stes-adj corresponds to the stes adjusted using PS values, while stes-una does not entail PS adjustment. The horizontal scale corresponds to differences of stes between treatment and control groups. The blue letters show results for individual propensity score stratum, while the larger filled (blue) squares show the average standardized effect sizes across strata. The filled (red) circles show standardized effect size differences between the treatment and control groups before covariate adjustment; that is, these are stes-una differences. Covariates are listed on the vertical scale, and they are ordered on the basis of the sizes of unadjusted stes differences. From the balance plot, we see that the PS adjustment helped to balance the covariates between the treatment and control groups (Figure 15 17). 13

14 Then we used the circ.psa function from PSAgraphics R for further comparisons. The circles are equal sized as we used quintiles so that all 5 circles have the same area. We also computed the grand mean of difference from the blue heavy dash line along with the C.I. from the green solid bar. In the comparison of surgery alone vs. radiation alone (Figure 15), the grand mean difference between the paired groups is 5.7 months and the 95% C.I. is from 3.36 to 6.9. In Figure 16, we assess the effects of surgery on survival time with or without radiation. For the patients without radiation, surgery led to an average of 10.7 months longer survival than no surgery (95% CI = 7.95, 13.53). For the patients with radiation, 14

15 surgery led to an average of 5.99 months longer survival than no surgery (95% CI = 4.18, 7.79). In Figure 17, we assess the effects of radiation on survival time with or without surgery. For the patients without surgery, radiation led to an average of 2.68 months longer survival than no surgery (95% CI = 2.19, 3.17). For the patients with surgery, radiation led to an average of 1.21 months longer survival than no radiation (95% CI = , 2.44). To see more details about the distribution of each observation, we used the LOESS graph (loess.psa, from PSAgraphics) to assess treatment effects across the full range of each PS distribution. Data points are plotted using propensity scores against the survival response, separately for treatment and control groups, and distinguished by both symbol and color for both groups (the green is for control and the blue is for treatment). Non-linear, loess-based regression curves for both groups are also plotted to show the estimates of effects across the range of PS scores; the vertical differences between these regression curves are weighted by the density of the PS distribution (where the red line is for the treatment group and the black line is for the control group). 15

16 In the comparison of surgery alone (black line) vs. radiation alone (red line in Figure 15), the grand mean difference between the two groups is 6.63 months and the 95% C.I. is (4.82, 8.45). In Figure 16, we assess the effects of surgery on survival time with versus without radiation. For patients without radiation, surgery led to a mean of 10.5 months longer survival than no surgery (95% CI = 9.05, 11.85); for patients who had had radiation, surgery led to an average of 5.8 months longer survival than no surgery (95% CI = 4.01, 7.58). In Figure 17, we assess the effects of radiation on survival time with or without surgery. For the patients without surgery, radiation led to an average of 2.6 months longer survival than no surgery (95% CI =2.09, 3.1). For patients with surgery, radiation led to a mean of 1.42 months longer survival than no radiation (95% CI = -0.16, 2.67). 4. Summary and discussion All four kinds of PSA-related methods and graphics consistently showed similar inferential results for all five comparisons, after adjusting for selection bias. These results are summarized in Figure 18 using 95% confidence intervals; they generally suggest that surgery offers longer survival than radiation, and surgery leads to longer average survival times than no surgery, with or without radiation, while radiation does so only without surgery but not with surgery. This is a relatively thorough comparison of lung cancer patients survival times following radiation or surgery treatments after adjusting for all available covariates in SEER. It has been based on modern methods of covariate adjustment using propensity scores so that the interpretations require fewer qualifications than are needed when covariates adjustments are not used; and it has demonstrated use of different PSA methods and several graphics (using R). This study has helped quantify mean differences (expressed as months of survival) between various treatments, after adjusting for covariate differences. Future steps: PSA can only adjust for observable covariates, which leads to the question of how large the effects of unknown or unobserved confounders would have to be to explain the effects. This question might be answered to some extent using Sensitivity Analysis, as suggested by Rosenbaum. There were missing values for some covariates; these records were removed from study data set. Multiple imputation may provide a useful strategy for dealing with this issue in future analyses. 16

17 References: Predictors of long time survival after lung cancer surgery: A retrospective cohort study. Kjetil Roth et al. BMC Pulmonary Medicine 2008, 8:22 3. Surgery for non-small cell lung cancer: postoperative survival based on the revised tumor-node-metastasis classification and its time trend. Fumihiro Tanaka et al. European Journal of Cardio-thoracic Surgery 18 (2000) Survival after Surgery in Stage IA and IB Non Small Cell Lung Cancer David Ost et al. Am J Respir Crit Care Med Vol 177. pp , Propensity score methods for bias reduction in the comparison of a treatment to a non-randomized control group. Ralph Doagostino. Statist. Med. 17, (1998) 6. The central role of the propensity score in observational studies for causal effects. PAUL R. ROSENBAUM and DONALD B. RUBIN. Biometrika (1): Enhancing Dependent Sample Analyses with Graphics. Robert M. Pruzek, James E. Helmreich. Journal of Statistics Education Volume 17, Number 1, 2009 ( 8. PSAgraphics: An R package to Support Propensity Score Analysis. Helmreich, J & Pruzek, R.M. Jour. of Stat. Software, 29, ( 9. R Granova package. Robert M. Pruzek, James E. Helmreich. 10. R PSAgraphics package. Robert M. Pruzek, James E. Helmreich. 11. R cbal-es function. Kuannan Xiong, Robert M. Pruzek. (unpublished) 17