Using Pointwise Mutual Information for Breast Cancer Health Disparities Research With SEER-Medicare Claims

Participants

We used Surveillance Epidemiology and End Results (SEER) data linked to Medicare claims. SEER is maintained by the National Cancer Institute and has long-term data on tumor characteristics and demographics information about incident cancers for over 14% of the United States (https://seer.cancer.gov/registries/). Expansion since 2000 has resulted in more recent data capturing over 28% of the US population. Medicare covers almost all individuals over 65 years old in SEER. Fee-for-service claims from Medicare part A and part B provide a thorough record of treatments and services obtained before and after cancer diagnosis.

We emulated the same exclusion criteria and methods detailed in the supplement of Silber et al. (2013). We primarily examined cases diagnosed from 1992 to 2005 to largely replicate the sample of Silber et al. (2013) which examined cases through 2005. Since we had additional years of data, we repeated the analyses with cases diagnosed 2006 through 2013 and claims through 2014. We restricted our breast cancer case sample to individuals with Medicare Parts A and B over the age of 66. Those with managed care contracts were excluded due to a lack of claims.

We used propensity score matching to match every Black woman to one White woman using sets of potentially confounding variables that mimic those used by Silber et al. (2013). We matched first on demographics, second on demographics and clinical presentation variables, and third on demographic, clinical presentation, and treatment variables. Silber et al. (2013) used this strategy to show that much of the survival differences between Black and White women largely disappeared after controlling for clinical presentation.

Instruments

Demographic variables included age, entered into the propensity score model via restricted cubic splines (Harrell, 2001, Ch. 2), and year of diagnosis and SEER registry, entered as categorical variables. Clinical presentation included tumor size (categorical with centimeter increments to ≥ 4 centimeters and a missing indicator), estrogen receptor positivity (ER+), progesterone receptor positivity (PR+), stage of cancer (Categorical I–IV, unknown), grade (five categories including missing) and 25 comorbidities as detailed in the tables. Many of the comorbidities used corresponded to those in the Charlson Comorbidity Index (Charlson et al., 1987).

Treatment included number of nodes removed and positive, entered via restricted cubic splines with four knots, mastectomy, breast conserving therapy, radiation, surgery, chemotherapy, and particularly whether the chemotherapies were doxorubicin or taxanes. We included all two-way, three-way, and four-way treatment interactions in the propensity score model. We did not adjust for neighborhood level income or education variables, as Silber et al. (2013) did not include those in primary analyses.

Procedure

We identified treatment using two methods. First, we used the ICD-9 and CPT definitions of Silber et al. (2013) directly. We searched for chemotherapy or surgery that occurred within six months of diagnosis, or radiation therapy that occurred within nine months of diagnosis.

The second search method expanded treatment definitions. We developed a machine learning algorithm to identify HCPCS or ICD-9 procedure codes as detailed in Egleston et al. (2021) and Bai et al. (2019) The algorithm allows us to estimate the Pointwise Mutual Information (PMI) statistic that characterizes the strength of relationship between two HCPCS or ICD-9 codes in a Medicare claim (Turney & Pantel, 2010). The PMI relates the joint probability that two codes will be observed in the same claim divided by the probability that the codes will be observed under independence. Software can be accessed at the Supplementary Materials section.

Before presenting the software assistant that implements the algorithm, we define PMI mathematically. Let C represent a multinomial random variable denoting the HCPCS or ICD-9 value of an input code of interest, such as one of the breast cancer procedure codes identified by Silber et al. (2013). Let ${\mathit{C}}^{\mathrm{\prime }}$ be a similar multinomial variable representing codes in the same SEER-Medicare line of a claim of C (i.e., close to C). We assume that the code at each position in the database is an independent and identically distributed variable whether when considered as an input code (C), or a potential claim neighboring code ( ${\mathit{C}}^{\mathrm{\prime }}$). Let subscripts i and $j\in \{\mathrm{1...}K\}$ (i.e., $C_i$ and $C_j^{\prime }$) be index positions of the codes for a total of K codes in the dataset. K represents the total number of codes used in the database, not the number of unique values. Let $D_{ij}$ be a random variable that takes the value 1 if the rule for determining sufficiently close is met for $C_i$ and $C_j^{\prime }$, 0 otherwise. The PMI is the log of the probability that two codes are in neighborhoods of each other conditional on being in the set of codes in neighborhoods of each other (i.e., the set in which $D_{ij}=1$), divided by the probability that the two codes are independent conditional upon being in the set in which $D_{ij}=1$. By Bayes’ theorem, this is also equivalent to the log of the conditional probability that $C_i$ is observed conditional on observing $C_j^{\prime }$ and meeting the rule $D_{ij}=1$ over the conditional probability of observing $C_i$ given meeting the rule. Formally, the PMI is defined as follows.

Under independence, $P(C_i=c|C_j^{\prime }=c^{\prime },D_{ij}=1)$ would be equal to $P(C_i=c|D_{ij}=1)$, so PMI = $\log (1)=0$. If the two codes are commonly observed together, then $P(C_i=c|C_j^{\prime }=c^{\prime },D_{ij}=1)>P(C_i=c|D_{ij}=1)$ and the ratio will be greater than one, so on the log scale, PMI > 0. One can tokenize the data and then use counts within the tokenized data to estimate the PMI via the component numerators and denominators, or use a logistic regression model detailed in Bai et al. (2019) and Egleston et al. (2021).

Our programs calculate the PMI and cosine similarity statistics for comparing two codes in claims data. The algorithms can be tested using one’s own data or synthetic Medicare claims (Center for Medicare Medicaid Services., 2021). In Figure 1, we demonstrate the assistant interface. The software estimates the PMI using code counts of tokenized data and uses the word2vec method found in the python package Gensim (Řehůřek & Sojka, 2010) to find vector representations of codes based on word2vec embeddings (Bai et al., 2019). These vectors are then used to estimate the cosine similarity statistics. In Bai et al. (2019) we previously validated the methods using SEER-Medicare data in which we compared our empirically found codes to those from a clinical paper in which the expert curated codes were published in an appendix (Bleicher et al., 2012). We found that the empirical method identified many of the same codes, but also found three codes that were not listed in the curated set.

In the SEER-Medicare breast cancer data used for this project, we had 67,332,516 lines of claims, 240,150,032 codes, and 36,566 unique ICD-9 and HCPCS code values. Codes were used an average of 6,567 times (SD = 118,945). In estimation (i.e., “training”), we excluded infrequent codes used fewer than 50 times in the claims to reduce the computational burden due to high dimensional matrices. This removed 21,215 unique values, but only 218,341 codes from the total (218,341/240,150,032 = 0.1% of total). The codes of most interest were used much more than 50 times. The ICD-9 Code 85.95 (“Operations on the breast//Other operations on the breast//Insertion of breast tissue expander”), for example, was used 7,197 times in the dataset. After removing infrequent codes, each line of a claim had 239,931,691/67,332,516 = 3.56 codes on average. We considered claims to be close to each other, and thus possibly related, if they were on the same line of the claim. This gives approximately 3.56 choose 2 times 67,332,516 = 306,820,808 pairings of codes when not considering order.

After using our programs to estimate the PMI and cosine similarity statistics, one inputs a SEER-Medicare ICD or HCPCS code, and then the related codes with the top PMIs will be displayed. For the time period of our current work, ICD-9 codes were in common use; the assistant will also work with ICD-10 codes. We show an example for an Input Code 85.42, which indicates bilateral simple mastectomy. The ICD-9 Code 85.95 had the highest PMI of 5.34. The assistant will also display related codes with the largest cosine similarity statistics (Huang, 2008). In our case, 85.95 also had the highest word2vec cosine similarity of 0.647.

For each code that Silber et al. (2013) identified, we searched for ICD-9 procedure and HCPCS codes with the largest PMI similarities and used the results to augment breast conserving therapy, mastectomy, and radiation definitions. For chemotherapy receipt in general, as opposed to specific types of chemotherapy, we repeated the process, but only used CPT codes as Silber et al. (2013) had. Then, in an augmented analysis, if a case had a code for mastectomy using either Silber et al. (2013)’s definitions or the augmented definition, we classified that case as having a mastectomy. We did not augment Silber et al. (2013)’s definitions of taxane or doxorubicin chemotherapy as the codes for these are very specific. For surgery, we used the most extensive treatment received in six months. If a woman received breast conserving therapy followed by mastectomy, then we deterministically coded surgery as mastectomy. This algorithm acknowledges that many women may have multiple procedures due to reasons such as positive surgical margins on the first lumpectomy.

A rationale for using expanded and empirically derived definitions to capture treatment is that there is heterogeneity in the codes providers use for reimbursement. For example, a lumpectomy could be billed as an excisional biopsy. By deriving an empirical method of finding treatment codes, we may better identify novel or unusual billing patterns. From a causal inference perspective, the use of empirically derived coding schemes could provide better control of potential confounders. We only controlled for the traditionally identified treatment variables or the augmented variables separately, not together.

Data Analysis

After forming the matched sample, we examined overall survival using Cox Proportional Hazards regressions and breast cancer specific survival using Fine and Gray (1999) proportional hazards regressions.