Predictive Approaches to Treatment effect Heterogeneity (PATH): A secondary analysis of the HCRN Entry Site Trial

Hydrocephalus is a condition in which excess cerebrospinal fluid (CSF) builds up in the brain or spine. Though some CSF is necessary for the brain to function normally, too much CSF can be harmful. For some, the impacts of this disease are mild, such as headaches or nausea. However, for others, hydrocephalus can reduce brain function or even be fatal.1 For many patients, hydrocephalus is present from birth. Hydrocephalus in infants may be caused by genetic or developmental factors, premature birth, or illness. Meanwhile, hydrocephalus in adults is most often caused by injury or other mechanisms resulting in damage to the brain.

Predictive Approaches to Treatment effect Heterogeneity (PATH): A secondary analysis of the HCRN Entry Site Trial April 30, 2024 Rylee Beckstead Committee: Larry Cook (chair), Ron Reeder, and Jonathan Race Introduction Hydrocephalus is a condition in which excess cerebrospinal fluid (CSF) builds up in the brain or spine. Though some CSF is necessary for the brain to function normally, too much CSF can be harmful. For some, the impacts of this disease are mild, such as headaches or nausea. However, for others, hydrocephalus can reduce brain function or even be fatal.1 For many patients, hydrocephalus is present from birth. Hydrocephalus in infants may be caused by genetic or developmental factors, premature birth, or illness. Meanwhile, hydrocephalus in adults is most often caused by injury or other mechanisms resulting in damage to the brain.1 Hydrocephalus is estimated to affect 84.7 out of 100,000 people, with known cases dating back to medieval times.2,3 There is no known cure for hydrocephalus, but it can be managed with treatment.4 According to the Mayo Clinic, the most common method of treatment for hydrocephalus is the surgical insertion of a ventriculoperitoneal (VP) shunt.5 VP shunts utilize a catheter to drain excess CSF from the ventricles of the brain to another part of the body (usually the abdomen). There are two locations where a VP shunt can be placed; an anterior or posterior entry site. The anterior entry site is located on the top of the head near the front, while the posterior entry site is on the back of the head near the base of the skull (Figure 1).6,7 Figure 1. Anterior and posterior entry site locations7 Despite their common use, VP shunts have a high failure rate, estimated to be 32.5% for adults and 78.2% for pediatric patients. Additionally, the use of VP shunts may result in unwanted post-operative comorbidities including skull fractures, pseudomeningocele (CSF outside of the dura), and seizures.8-10 Consequentially, additional shunts are often needed which require surgical intervention. This repetitive surgical intervention increases the recovery time for patients, adds to medical costs of the patient, introduces the potential for more post-surgical complications, increases costs for insurance companies, and uses more medical resources. HCRN Entry Site Trial In an effort to improve clinical practice related to VP shunts, a recent randomized clinical trial was conducted by the Hydrocephalus Clinical Research Network (HCRN). The purpose of this trial was to assess whether anterior or posterior insertion of VP shunts results in a longer time to shunt failure. Patients were randomized to receive one of the two entry site locations for VP shunt insertion.8 Pediatric patients with clinical hydrocephalus requiring a VP shunt (that had not previously had a shunt) and had imaging-confirmed ventriculomegaly were considered for the study. 8 Patients that needed a complex shunt; had a current infection in the abdomen or CSF; a CSF leak without ventriculomegaly; presence of pseudo-tumor cerebri, hydranencephaly, ventricular loculations, or trigones or bilateral horns in the front of the head; circumstances inhibiting 18-month follow up; or that would be undergoing an intraventricular procedure in conjunction with shunt insertion were excluded.6,10 In total, 467 pediatric participants were enrolled (among 14 facilities) in the study, with 231 assigned to have the shunt inserted anteriorly and 236 posteriorly. A committee blinded to treatment determined 7 patients from each entry site group ineligible, resulting in 224 patients being assigned to the anterior group and 229 to the posterior entry site group. Two patients assigned to the posterior group had the shunt placed anteriorly due to issues found postrandomization. Similarly, one patient in the anterior group had the shunt placed at the posterior entry site.8 Patients were analyzed based on intent to treat. Researchers in the HCRN entry site trial used a log-rank test, which is a common method used to compare two or more survival distributions.11 In particular, researchers used this method to determine if the entry site was a significant predictor of time to shunt failure. As shown in the Kaplan-Meier curves (estimates of survival over time) below, there is a visual difference in the shunt survival for the anterior and posterior entry site groups (Figure 2).12 However, the log-rank test found that the difference in time to shunt failure between the anterior and posterior entry site groups was not significant (p=0.061).8 Though insignificant, this p-value was close to our alpha value of 0.05, raising the question of if there could be a more effective entry site for a given individual. The purpose of this study is to explore the use of Predictive Approaches to Treatment effect Heterogeneity (PATH) to determine the best shunt insertion site for individual patients. Figure 2. Kaplan-Meier curves for probability of VP shunt survival over time Predictive Approaches to Treatment effect Heterogeneity (PATH) PATH is a method that applies heterogeneity (the non-random variation that occurs in the outcome due to one factor) at the patient-level to determine the best route of treatment. Heterogeneity of treatment effects (HTE) considers the impact of a single covariate have on the treatment effect while PATH considers the impact of several covariates simultaneously on the treatment effect. For example, with HTE we may consider how sleep impacts energy, but with PATH can consider how sleep, diet, time of day, etc. collectively impact energy. Because several factors are at play for patients that influence treatment effect, PATH allows for more accurate prediction of the treatment effect for individual patients. 13 The PATH methodology was developed by a group of 16 experts with experience in various related fields, such as predictive modeling and patient advocacy. Over a period of several months, researchers consulted with one another and reviewed published literature. At the conclusion of their collaboration, the researchers published a document known as “The PATH Statement”, which outlines how to perform PATH analyses.13 Methods Variable Selection PATH analyses begin with variable selection. Since the goal of PATH is to determine the best treatment, only the covariates available before treatment is determined should be considered. Researchers note that covariates should only be included if they are known or suspected to impact the risk of the outcome.13 Risk Modeling PATH analyses can be performed using risk or effect modeling. In general, risk modeling refers to modeling in which the relationship between the unique combination of covariates and the outcome are considered, rather than the relationship between each individual covariate and the outcome.14 Risk modeling within a PATH analysis is a two-step process. The first step is to create a regression model that quantifies the baseline risk for each patient. It contains all covariates, but excludes the treatment. Modeling the data in this way creates schema that are blinded to treatment. Though any regression model may be used that fits the data well, the equation for logistic regression is shown below as it was used in this PATH analysis.15 Equation 1: 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 𝑜𝑜𝑜𝑜 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 (𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟) = exp(𝛽𝛽0 + 𝛽𝛽1 𝑉𝑉𝑉𝑉𝑉𝑉1 + 𝛽𝛽2 𝑉𝑉𝑉𝑉𝑉𝑉2 + ⋯ + 𝛽𝛽𝑘𝑘 𝑉𝑉𝑉𝑉𝑉𝑉𝑘𝑘 ) 1 + exp(𝛽𝛽0 + 𝛽𝛽1 𝑉𝑉𝑉𝑉𝑉𝑉1 + 𝛽𝛽2 𝑉𝑉𝑉𝑉𝑉𝑉2 + ⋯ + 𝛽𝛽𝑘𝑘 𝑉𝑉𝑉𝑉𝑉𝑉𝑘𝑘 ) The purpose of the second model is to determine the effect of risk and treatment on the outcome of interest. The numeric risk obtained from the first model is included in this second regression model along with treatment and the interaction between risk and treatment. Because a Cox proportional hazards model was used in this PATH analysis, the regression equation below is a Cox proportional hazards model.16 Equation 2: ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = ℎ0 (𝑡𝑡) 𝑒𝑒𝑒𝑒𝑒𝑒(𝛽𝛽1 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 + 𝛽𝛽2 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 + 𝛽𝛽3 (𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅)(𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇)) Although regression models are used in PATH analysis, their use differs in two ways from traditional regression modeling. First, we include one value known as “risk” that represents the unique combination of covariates instead of including all covariates in our final model. Depending on the number of covariates (and the number of levels within each) included, there may be rare combinations that exist. Researchers should consider the number of strata in comparison to sample size. Secondly, the focus is on prediction of the best treatment rather than understanding the relationship between each of the covariates and the outcome. Effect Modeling Effect modeling is a more familiar-feeling approach to PATH analysis. Effect modeling refers to modeling where the relationship between individual covariates and the outcome are measured.17 In effect modeling, a single regression model is created that includes all covariates, the treatment, and interactions between covariates and the treatment.13 Several interactions can be included in the model, but only one is shown in the equation below for simplicity. A Cox proportional hazards model is shown because this type of model was used in our PATH analysis.16 Equation 3: ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = ℎ0 (𝑡𝑡) 𝑒𝑒𝑒𝑒𝑒𝑒(𝛽𝛽1 𝑉𝑉𝑉𝑉𝑉𝑉1 + 𝛽𝛽2 𝑉𝑉𝑉𝑉𝑉𝑉2 + … + 𝛽𝛽𝑘𝑘 𝑉𝑉𝑉𝑉𝑉𝑉𝑘𝑘 + 𝛽𝛽𝑘𝑘+1 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 + 𝛽𝛽𝑘𝑘+2 (𝑉𝑉𝑉𝑉𝑉𝑉𝑖𝑖 )(𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇) Though the equation for effect modeling appears to be the same as in other regression analyses, it differs in consideration of variables and the importance of particular outcomes. As stated before, only variables that are thought to impact the risk of the outcome (and can be measured prior to deciding which treatment to receive) should be included in the model. Outcomes of Interest Since the purpose of PATH is to determine how combinations of covariates impact treatment effect, we will focus on interpreting the interactions between the covariates and treatment. In risk modeling, we will assess the interaction between risk and treatment, while in effect modeling we will assess the interaction between individual covariates and the treatment. PATH Methods Applied to the HCRN Entry Site Trial Study Design The PATH analysis was conducted as a secondary analysis of the data from the entry site trial, which was a prospective cohort. All patients included in the HCRN entry site trial were also included in our study. The University of Utah’s IRB waived the need for approval for this analysis. Additionally, permission was granted by HCRN researchers to access the full data. Variable Selection As in the HCRN study, shunts were considered more effective if they had a longer time to shunt failure. Accordingly, our outcome variable was time to shunt failure (measured in days).8 Since it is important to predict efficacy of a shunt entry site pre-operatively, only measures taken at baseline were considered as potential covariates. A similar study conducted on the efficacy of hydrocephalus treatment found the baseline measures of age and etiology to be significant predictors in determining the most effective method of treatment, so they were included as covariates in the PATH analysis.18 The researchers in the HCRN entry site trial used these variables, along with race, sex, ethnicity, and number of complex chronic conditions (CCCs) in their analysis. For consistency, these variables were also included in the PATH analysis perfomed.8 For both risk and effect modeling, reference levels are indicated with an asterisk below: Table 1. Reference levels for categorical variables Variable Level Corrected age at operation, months < 6 months >= 6 months* Etiology IVH secondary to prematurity* Myelomeningocele Aqueductal stenosis Tumor Congenital Communicating Spontaneous ICH/IVH/SAH (e.g., AVM) Postinfectious Head injury Other Race Black or African American White* Other/unknown Sex Male* Female Ethnicity Hispanic or Latino Not Hispanic or Latino* CCCs 0* 1 2 Data Summaries Initial exploration of the covariates included in the PATH analyses show that most patients (~75% in each entry site group) were less than 6 months old at the time of shunt surgery (Table 2), with most patients being male. Additionally, the most common cause of hydrocephalus among both entry site groups was intraventricular hemorrhage (IVH) secondary to prematurity.19 A majority of patients did not have the presence of CCCs. Of those participating in the study, the most common race was white with the most observed ethnicity being not Hispanic or Latino. Summaries of the data show that the covariates are approximately equally distributed between the anterior and posterior entry site groups, with the largest standard mean difference (SMD) occurring for sex at 0.189 (Table 2).20 Table 2. Baseline Characteristics Female Race Black or African American White Other/unknown Ethnicity Hispanic or Latino Not Hispanic or Latino Unknown or Not Reported Corrected age at operation, months < 6 months >= 6 months Etiology IVH secondary to prematurity Myelomeningocele Aqueductal stenosis Tumor Congenital communicating Spontaneous ICH/IVH/SAH (e.g., AVM) Postinfectious Head injury Other Complex Chronic Conditions 0 1 >= 2 Risk Modeling Assigned Entry Site Anterior Posterior (n = 224) (n = 229) 80 (35.7%) 103 (45.0%) 40 (17.9%) 136 (60.7%) 48 (21.4%) 35 (15.3%) 150 (65.5%) 44 (19.2%) 40 (17.9%) 147 (65.6%) 37 (16.5%) 46 (20.1%) 153 (66.8%) 30 (13.1%) 167 (74.6%) 57 (25.4%) 171 (74.7%) 58 (25.3%) 79 (35.3%) 36 (16.1%) 22 (9.8%) 21 (9.4%) 20 (8.9%) 13 (5.8%) 8 (3.6%) 5 (2.2%) 20 (8.9%) 69 (30.1%) 40 (17.5%) 27 (11.8%) 14 (6.1%) 20 (8.7%) 22 (9.6%) 13 (5.7%) 3 (1.3%) 21 (9.2%) 132 (58.9%) 58 (25.9%) 34 (15.2%) 135 (59.0%) 63 (27.5%) 31 (13.5%) SMD 0.189 0.053 0.097 0.003 0.084 0.023 The first model, which quantifies risk, was chosen to be a logistic regression model. There were a few plausible options for modeling the risk, including Cox proportional hazards. However, logistic regression provided a more simplistic approach. It is important to note that logistic regression may be impacted by censoring, so shunt failure was limited to the outcome at one year. The model was as follows:15 Equation 4: 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 𝑜𝑜𝑜𝑜 𝑠𝑠ℎ𝑢𝑢𝑢𝑢𝑢𝑢 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 (𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟) = exp(𝛽𝛽0 + 𝛽𝛽1 𝐴𝐴𝐴𝐴𝐴𝐴 + 𝛽𝛽2 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 + 𝛽𝛽3 𝑆𝑆𝑆𝑆𝑆𝑆 + 𝛽𝛽4 𝐸𝐸𝐸𝐸ℎ𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 + 𝛽𝛽5 𝐶𝐶𝐶𝐶𝐶𝐶 + 𝛽𝛽6 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸) 1 + exp(𝛽𝛽0 + 𝛽𝛽1 𝐴𝐴𝐴𝐴𝐴𝐴 + 𝛽𝛽2 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 + 𝛽𝛽3 𝑆𝑆𝑆𝑆𝑆𝑆 + 𝛽𝛽4 𝐸𝐸𝐸𝐸ℎ𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 + 𝛽𝛽5 𝐶𝐶𝐶𝐶𝐶𝐶 + 𝛽𝛽6 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸) The risk produced by the logistic regression model was the probability of shunt survival for each individual, ranging from zero to one. These probabilities obtained from Equation 4 were included in Equation 5 as the risk, which was a Cox proportional hazards model. Since we had time-to-event data, this type of model was a reasonable choice. The model was written as:16 Equation 5: ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = ℎ0 (𝑡𝑡) 𝑒𝑒𝑒𝑒𝑒𝑒(𝛽𝛽1 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 + 𝛽𝛽2 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 + 𝛽𝛽3 (𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅)(𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆)) The two-step risk modeling process resulted in the hazard ratios and p-values shown in Table 3. Though close to the alpha value of 0.05, the p-value for the interaction between risk and entry site was not significant (0.0775). However, interactions are complex relationships that may not be best described with a single hazard ratio and p-value. Figure 3 below shows the probability of shunt survival for each entry site at different percentile risks (p10, p20, p40, p60, p80, and maximum). From this plot, we see that the probability of shunt failure at different percentile risks for anterior and posterior entry sites appears to be quite similar. At the smaller values of baseline risk, probability of shunt failure is much higher for the anterior entry site than for the posterior entry site. However, our model may not predict shunt failure well for outcomes at the most extreme values of risk we observed. Additionally, though the probability of shunt failure appears to decrease as baseline risk increases, the difference appears to be very small and may not be clinically different. We see a slight increase in shunt failure for posterior entry sites over anterior entry sites as risk increases after the 40th percentile, indicating that the anterior entry site may be preferred over the posterior entry site as risk increases. It’s important to note that 50% of the values for risk lie between 0.7068 and 0.8128 (p25=0.7068, median=0.7770, p50=0.8128). Table 3. Risk modeling estimates Risk Posterior Entry Site Risk*Posterior Entry Site Hazard Ratio P-value 1.6103 25.6284 0.0130 0.0259 0.0860 0.0775 Figure 3. Plot of shunt failure for anterior and posterior entry sites at baseline risk with lines for the 10th, 20th, 40th, 60th, 80th, and 100th (maximum) percentiles Figure 4 (below) shows the hazard ratios for posterior and anterior entry site insertion at various risk levels (p10, p20, p40, p60, p80, and maximum). We see that risk increases, so does the hazard ratio for shunt failure. The hazard ratio for all percentiles of risk is greater for the posterior entry site, meaning patients receiving posterior insertion have a higher risk of shunt failure. Though it was noted that the preferred entry site changes around the 40th percentile (looking at the interaction between risk and entry site), the hazard ratios shown below also take into account the relationship between risk and shunt failure and entry site and shunt failure (neither of which was found to be significant). Figure 4. Plot of hazard ratios for anterior and posterior entry sites at baseline risk with lines for the 0th, (minimum), 20th, 40th, 60th, 80th, and 100th (maximum) Effect Modeling Since time to shunt failure is time-to-event data, a Cox proportional hazards model was a more appropriate selection. It is unknown which interactions between individual covariates and the treatment are most likely to occur. For the sake of simplicity, only the interaction between age and entry site was included as shown below: 16 Equation 6: ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = ℎ0 (𝑡𝑡) 𝑒𝑒𝑒𝑒𝑒𝑒(𝛽𝛽1 𝐴𝐴𝐴𝐴𝐴𝐴 + 𝛽𝛽2 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 + 𝛽𝛽3 𝑆𝑆𝑆𝑆𝑆𝑆 + 𝛽𝛽4 𝐸𝐸𝐸𝐸ℎ𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 + 𝛽𝛽5 𝐶𝐶𝐶𝐶𝐶𝐶 + 𝛽𝛽6 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 + 𝛽𝛽7 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 + 𝛽𝛽8 (𝐴𝐴𝐴𝐴𝐴𝐴)(𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆)) As shown in Table 4, the effect model showed no difference in shunt survival for the anterior and posterior groups based on age (p=0.6523). Table 4. Effect modeling estimates Female Race Black or African American White Other/unknown Ethnicity Hispanic or Latino Not Hispanic or Latino Unknown or Not Reported Corrected age at operation, months < 6 months >= 6 months Etiology IVH secondary to prematurity Myelomeningocele Aqueductal stenosis Tumor Congenital communicating Spontaneous ICH/IVH/SAH (e.g., AVM) Postinfectious Head injury Other Complex Chronic Conditions 0 1 >= 2 Posterior Entry Site Corrected Age < 6 months*Posterior Entry Site Hazard Ratio 0.8820 P-value 1.1737 0.7507 0.4764 0.3343 0.8944 1.8247 0.6272 0.0569 1.2557 - 0.5154 - 0.7383 0.8135 0.7243 0.6543 0.6156 0.6841 0.0000 0.8072 0.2248 0.4739 0.4276 0.2190 0.1689 0.3600 0.9715 0.4825 1.1919 1.5632 1.6649 0.8311 0.3642 0.0440 0.1668 0.6523 0.4585 Discussion Risk vs Effect Modeling Risk and effect modeling both make use of regression models. The main difference between these types of modeling is that the combination of covariates (the schema) are blinded to treatment in risk modeling, but not in effect modeling.13 Additionally, in risk modeling, a separate model is created to assess treatment effect over all levels of specified baseline measures. In contrast, effect models evaluate different levels of baseline risk. Researchers who developed PATH methodology noted that effect models are especially prone to low power, which is partially due to the models containing the interaction between the covariates and treatment. Careful steps (such as corrections for overfitting) can be used to mitigate inflated findings, but may still be present. Because of this, researchers who developed the PATH methods noted that risk modeling is preferred to effect modeling. Literature on effect modeling in PATH analyses is also limited.13 Different Applications of PATH Although logistic regression and Cox proportional hazards models were used in the PATH analyses described, other regression models that fit the data well may be used. Depending on the outcome of interest, researchers should consider what model or models fit their data best. In these PATH analyses, we used continuous, linear version of risk. The continuous version of risk may provide a more individualized assessment of risk, but if risk is approximately the same across groups, categories of risk are sufficient.13 Non-linear risk (such as exponential risk) may also be used. If a well-established model for risk exists, researchers may obtain risk from this external model rather than modeling risk on study data. When performing PATH analyses on the HCRN entry site trial data, additional risk and effect models were created exploring some of these applications of PATH. These analyses are provided in the appendix. Strengths A great benefit of PATH analysis is its simplicity in practice. To perform PATH analyses, researchers need to be able to perform basic regression analyses and include appropriate covariates in models. There is potential for wide-spread application of these methods because of their simplicity in practice. Additionally, the interpretation of the outcomes of PATH models are fairly intuitive, which may foster a smooth transition into clinical practice. Limitations Because the purpose of this analysis was to explore PATH methodology rather than produce literature on the treatment of hydrocephalus, clinical knowledge of hydrocephalus was limited. Additional knowledge about hydrocephalus may have resulted in a better selection of covariates and interactions in our models. This informed selection of variables would help to mitigate the biggest limitation of our effect modeling, which was the tendency of the models to result in inflated treatment effects when a difference treatment effect does not actually exist.13 Conclusion The PATH analyses performed showed that there was no difference in time to shunt failure for anterior and posterior sites based on patient’s unique covariates (age, race, sex, ethnicity, CCCs, and etiology). Though there was not a best treatment for patients in our study, PATH methodology has the potential to make a difference in the clinical care of patients. If used correctly (and a best treatment is found), the analyses can produce statistical models that serve as a robust way of determining the most effective treatment for an individual. References 1. Hydrocephalus. National Institute of Neurological Disorders and Stroke. Updated March 8, 2023. Accessed September 19, 2023. https://www.ninds.nih.gov/healthinformation/disorders/hydrocephalus 2. Isaacs AM, Riva-Cambrin J, Yavin D, et al. Age-specific global epidemiology of hydrocephalus: Systematic review, metanalysis and global birth surveillance. PLoS ONE. 2018;13(10): e0204926. doi: 10.1371/journal. pone.0204926 3. Aschoff A, Kremer P, Hashemi B, et al. The scientific history of hydrocephalus and its treatment. Neurosurg Rev. 1999;22:67-93. doi: 10.1007/s101430050035 4. Hydrocephalus Clinical Research Network. Hydrocephalus Clinical Research Network. Accessed April 19, 2024. https://hcrn.org/ 5. Hydrocephalus. Mayo Clinic. Updated September 15, 2023. Accessed December 5, 2023. https://www.mayoclinic.org/diseases-conditions/hydrocephalus/diagnosis-treatment/drc20373609 6. A Randomized Controlled Trial of Anterior versus Posterior Entry Site for CSF Shunt Insertion. Hydrocephalus Clinical Research Network. Updated 2023. Accessed December 5, 2023. http://hcrn.org/research/entry-site/ 7. The CSF Shunt Entry Site Study. Hydrocephalus Association. Accessed April 17, 2024. https://www.hydroassoc.org/the-csf-shunt-entry-site-study-2/ 8. Whitehead WE, Riva-Cambrin J, Wellons, JC, et al. Anterior versus posterior entry site for ventriculoperitoneal shunt insertion: a randomized controlled trial by the Hydrocephalus Clinical Research Network. J Neurosurg Pediatr. 2022;29:257-267. Published online November 19, 2021; doi: 10.3141/2021.9.PEDS21391 9. Solomon P, Sekharappa V, Krishnan V, et al. Spontaneous resolution of postoperative lumbar pseudomeningoceles: A report of four cases. Indian J Orthop. 2013;47(4):417-421. doi: 10.4103/0019-5413.114937 10. Reddy GK, Bollam P, Caldito G. Long-term outcomes of ventriculoperitoneal shunt surgery in patients with hydrocephalus. World Neurosurg. 2014;81(2):404-410. doi: 10.1016/j.wneu.2013.01.096 11. STAT 331 Logrank Test. Accessed April 25, 2024. https://web.stanford.edu/~lutian/coursepdf/unitweek3.pdf 12. Goel M K, Khanna P, Kishore J. Understanding survival analysis: Kaplan-Meier estimate. Int J Ayurveda Res. 2010;1(4):274-278. doi: 10.4103/0974-7788.76794 13. Kent DM, Paulus JK, van Klaveren D, et al. The Predictive Approaches to Treatment effect Heterogeneity (PATH) Statement. Ann Intern Med. 2020;172(1):35-45. doi: 10.7326/M183667 14. Cox L A. Risk Analysis Foundations, Models, and Methods. Springer; 2002. 15. Logistic Regression. Accessed April 25, 2024. http://faculty.cas.usf.edu/mbrannick/regression/Logistic.html 16. stratification in cox model. Stack Exchange. Updated 2023. Accessed April 25, 2024. https://stats.stackexchange.com/questions/256148/stratification-in-cox-model 17. Chiu M M, Joh S W. International Encyclopedia of the Social & Behavioral Sciences, Second Edition. Elsevier; 2015. 18. Kulkarni AV, Drake JM, Kestle JR, et al. Predicting who will benefit from endoscopic third ventriculostomy compared with shunt insertion in childhood hydrocephalus using the ETV Success Score. J Neurosurg Pediatr. 2010;6(4):310-315. doi: 10.3171/2010.8.PEDS103 19. Bu Y, Chen M, et al. Mechanisms of hydrocephalus after intraventricular haemorrhage in adults. Stroke Vasc Neurol. 2016;1(1). doi: 10.1136/syn-2015-000003 20. Andrade C. Mean difference, standardized mean difference (SMD), and their use in metaanalysis: as simple as it gets. J Clin Psychiatry. 2020;81(5). doi: 10.4088/JCP.20f13681 21. ElHafeez S A, D’Arrigo G, et al. Methods to analyze time-to event data: the Cox regression analysis. Oxid Med Cell Longev. 2021;1302811. doi: 10.1155/2021/1302811 22. Klein J P, Moeschberger M L. Survival Analysis: Techniques for Censored and Truncated Data, Second Edition. Springer; 2003. 23. Therneau T M, Grambsch P M. Modeling Survival Data: Extending the Cox Model. Springer; 2000. Appendix Alternate Risk Models Logistic Regression Model with Categorical Risk A model containing categorical risk was also created by classifying the continuous risk into quartiles. We used this quartile risk in place of the continuous risk in our Cox proportional hazards model along with assigned entry site, the interaction between risk and entry site, and previously specified covariates.16 Supplemental Equation 1: ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = ℎ0 (𝑡𝑡) 𝑒𝑒𝑒𝑒𝑒𝑒(𝛽𝛽1 𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 + 𝛽𝛽2 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 + 𝛽𝛽3 (𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅)(𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆)) The two-step risk modeling process resulted in the hazard ratios and p-values shown in Supplemental Table 1. The p-values for the interactions between quartiles of risk and entry site were not significant, indicating that there is no difference in time to shunt failure for anterior and posterior sites based on patient’s unique covariate values (age, race, sex, ethnicity, CCCs, and etiology). Supplemental Table 1. Risk modeling estimates Q2 Risk Q3 Risk Q4 Risk Posterior Entry Site Q2 Risk*Posterior Entry Site Q3 Risk*Posterior Entry Site Q4 Risk*Posterior Entry Site Hazard Ratio 1.5250 3.9802 2.9248 1.5940 0.8764 0.3989 0.4296 P-value 0.3719 0.0029 0.0189 0.3117 0.8226 0.1167 0.1456 Cox Proportional Hazards Models Though risk was modeled with a logistic regression in the main body of the paper, a Cox proportional hazards model may also be a reasonable choice.21 However, when using a Cox proportional hazards model, the survival probability for all patients is 1 at baseline (time zero), so alternate ways of obtaining baseline risk with this type of modeling were considered. 22 According to Therneau and Grambsch, a stratified Cox proportional hazards model produces a different baseline hazard for all groups of strata that are specified. The hazard function for an individual can be written as ℎ𝑖𝑖 (𝑡𝑡) = 𝜆𝜆𝑘𝑘 (𝑡𝑡)𝑒𝑒 𝑋𝑋𝑖𝑖 𝛽𝛽 where i represents the individual patient and k represents the strata.23 Though we can select which variables we want to stratify by, those variables will not be estimated. Because of this, several cox proportional hazards models were produced, with each model being stratified by a different covariate. The risk obtained from this model was then used in a second Cox proportional hazards model as shown in Equation 5 included in the main body of this analysis. Model Stratified by Age. The first variable chosen as the strata was age. The Cox proportional hazards model contained all covariates, as in our initial model. The equations for this model are shown in Supplemental Equation(s) 2.16 Supplemental Equation(s) 2: ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝐴𝐴𝐴𝐴𝐴𝐴 <6 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚ℎ𝑠𝑠 = ℎ0 (𝑡𝑡) 𝑒𝑒𝑒𝑒𝑒𝑒(𝛽𝛽1 𝐴𝐴𝐴𝐴𝐴𝐴 + 𝛽𝛽2 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 + 𝛽𝛽3 𝑆𝑆𝑆𝑆𝑆𝑆 + 𝛽𝛽4 𝐸𝐸𝐸𝐸ℎ𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 + 𝛽𝛽5 𝐶𝐶𝐶𝐶𝐶𝐶 + 𝛽𝛽6 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸)) ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝐴𝐴𝐴𝐴𝐴𝐴 ≥ 6 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚ℎ𝑠𝑠 = ℎ0 (𝑡𝑡) 𝑒𝑒𝑒𝑒𝑒𝑒(𝛽𝛽1 𝐴𝐴𝐴𝐴𝐴𝐴 + 𝛽𝛽2 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 + 𝛽𝛽3 𝑆𝑆𝑆𝑆𝑆𝑆 + 𝛽𝛽4 𝐸𝐸𝐸𝐸ℎ𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 + 𝛽𝛽5 𝐶𝐶𝐶𝐶𝐶𝐶 + 𝛽𝛽6 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸)) As shown in Supplemental Table 2, the p-values for the interactions between risk and entry site in the age stratified model were not significant. This indicates that there is no difference in time to shunt failure for anterior and posterior sites based on patient’s unique covariate values (age, race, sex, ethnicity, CCCs, and etiology). Supplemental Table 2. Risk modeling estimates Hazard Ratio 2.1294 0.3525 4.9850 Risk Posterior Entry Site Risk*Posterior Entry Site P-value <0.0001 0.2687 0.1668 Model Stratified by Race. Next, a Cox proportional hazards model was created that contained all covariates, as in our initial model, but was stratified by race. The equations for this model were:16 Supplemental Equation(s) 3: ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 𝑜𝑜𝑜𝑜 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 = ℎ0 (𝑡𝑡) 𝑒𝑒𝑒𝑒𝑒𝑒(𝛽𝛽1 𝐴𝐴𝐴𝐴𝐴𝐴 + 𝛽𝛽2 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 + 𝛽𝛽3 𝑆𝑆𝑆𝑆𝑆𝑆 + 𝛽𝛽4 𝐸𝐸𝐸𝐸ℎ𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 + 𝛽𝛽5 𝐶𝐶𝐶𝐶𝐶𝐶 + 𝛽𝛽6 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸)) ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑊𝑊ℎ𝑖𝑖𝑖𝑖𝑖𝑖 = ℎ0 (𝑡𝑡) 𝑒𝑒𝑒𝑒𝑒𝑒(𝛽𝛽1 𝐴𝐴𝐴𝐴𝐴𝐴 + 𝛽𝛽2 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 + 𝛽𝛽3 𝑆𝑆𝑆𝑆𝑆𝑆 + 𝛽𝛽4 𝐸𝐸𝐸𝐸ℎ𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 + 𝛽𝛽5 𝐶𝐶𝐶𝐶𝐶𝐶 + 𝛽𝛽6 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸)) ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑂𝑂𝑂𝑂ℎ𝑒𝑒𝑒𝑒/𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈 = ℎ0 (𝑡𝑡) 𝑒𝑒𝑒𝑒𝑒𝑒(𝛽𝛽1 𝐴𝐴𝐴𝐴𝐴𝐴 + 𝛽𝛽2 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 + 𝛽𝛽3 𝑆𝑆𝑆𝑆𝑆𝑆 + 𝛽𝛽4 𝐸𝐸𝐸𝐸ℎ𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 + 𝛽𝛽5 𝐶𝐶𝐶𝐶𝐶𝐶 + 𝛽𝛽6 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸)) The two-step risk modeling process resulted in the hazard ratios and p-values shown in Supplemental Table 3. The p-values for the interactions between risk and entry site in the race stratified model was not significant, indicating that there is no difference in time to shunt failure for anterior and posterior sites based on patient’s unique covariate values (age, race, sex, ethnicity, CCCs, and etiology). Supplemental Table 3. Risk modeling estimates Risk Posterior Entry Site Risk*Posterior Entry Site Hazard Ratio 2.1222 0.3763 4.6363 P-value 0.3719 0.3117 0.8226 Model Stratified by Sex. The next Cox proportional hazards model was stratified by sex. It contained all covariates in our initial model. The equations for this model were: 16 Supplemental Equation(s) 4: ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝑆𝑆𝑆𝑆𝑆𝑆 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 = ℎ0 (𝑡𝑡) 𝑒𝑒𝑒𝑒𝑒𝑒(𝛽𝛽1 𝐴𝐴𝐴𝐴𝐴𝐴 + 𝛽𝛽2 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 + 𝛽𝛽3 𝑆𝑆𝑆𝑆𝑆𝑆 + 𝛽𝛽4 𝐸𝐸𝐸𝐸ℎ𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 + 𝛽𝛽5 𝐶𝐶𝐶𝐶𝐶𝐶 + 𝛽𝛽6 𝐸𝐸𝐸𝐸𝑖𝑖𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜)) ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝑆𝑆𝑆𝑆𝑆𝑆 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 = ℎ0 (𝑡𝑡) 𝑒𝑒𝑒𝑒𝑒𝑒(𝛽𝛽1 𝐴𝐴𝐴𝐴𝐴𝐴 + 𝛽𝛽2 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 + 𝛽𝛽3 𝑆𝑆𝑆𝑆𝑆𝑆 + 𝛽𝛽4 𝐸𝐸𝐸𝐸ℎ𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 + 𝛽𝛽5 𝐶𝐶𝐶𝐶𝐶𝐶 + 𝛽𝛽6 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸)) As shown in Supplemental Table 4, the p-values for the interactions between risk and entry site in the sex stratified model were not significant. This indicates that there is no difference in time to shunt failure for anterior and posterior sites based on patient’s unique covariate values (age, race, sex, ethnicity, CCCs, and etiology). Supplemental Table 4. Risk modeling estimates Hazard Ratio 2.1132 0.3427 5.0992 Risk Posterior Entry Site Risk*Posterior Entry Site P-value <0.0001 0.2984 0.1863 Model Stratified by Ethnicity. Next, the Cox proportional hazards model containing all covariates, was stratified by ethnicity. The equations for this model were:16 Supplemental Equation(s) 5: ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝐸𝐸𝐸𝐸ℎ𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻 𝑜𝑜𝑜𝑜 𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿 = ℎ0 (𝑡𝑡) 𝑒𝑒𝑒𝑒𝑒𝑒(𝛽𝛽1 𝐴𝐴𝐴𝐴𝐴𝐴 + 𝛽𝛽2 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 + 𝛽𝛽3 𝑆𝑆𝑆𝑆𝑆𝑆 + 𝛽𝛽4 𝐸𝐸𝐸𝐸ℎ𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 + 𝛽𝛽5 𝐶𝐶𝐶𝐶𝐶𝐶 + 𝛽𝛽6 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸)) ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝐸𝐸𝐸𝐸ℎ𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 𝑁𝑁𝑁𝑁𝑁𝑁 𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻 𝑜𝑜𝑜𝑜 𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿 = ℎ0 (𝑡𝑡) 𝑒𝑒𝑒𝑒𝑒𝑒(𝛽𝛽1 𝐴𝐴𝐴𝐴𝐴𝐴 + 𝛽𝛽2 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 + 𝛽𝛽3 𝑆𝑆𝑆𝑆𝑆𝑆 + 𝛽𝛽4 𝐸𝐸𝐸𝐸ℎ𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 + 𝛽𝛽5 𝐶𝐶𝐶𝐶𝐶𝐶 + 𝛽𝛽6 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸)) ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝐸𝐸𝐸𝐸ℎ𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈 𝑜𝑜𝑜𝑜 𝑁𝑁𝑁𝑁𝑁𝑁 𝑅𝑅𝑅𝑅𝑅𝑅𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜 = ℎ0 (𝑡𝑡) 𝑒𝑒𝑒𝑒𝑒𝑒(𝛽𝛽1 𝐴𝐴𝐴𝐴𝐴𝐴 + 𝛽𝛽2 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 + 𝛽𝛽3 𝑆𝑆𝑆𝑆𝑆𝑆 + 𝛽𝛽4 𝐸𝐸𝐸𝐸ℎ𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 + 𝛽𝛽5 𝐶𝐶𝐶𝐶𝐶𝐶 + 𝛽𝛽6 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸)) As shown in Supplemental Table 5, the p-values for the interactions between risk and entry site in the ethnicity stratified model were not significant. This indicates that there is no difference in time to shunt failure for anterior and posterior sites based on patient’s unique covariate values (age, race, sex, ethnicity, CCCs, and etiology). Supplemental Table 5. Risk modeling estimates Hazard Ratio 2.0937 0.3335 5.4196 Risk Posterior Entry Site Risk*Posterior Entry Site P-value <0.0001 0.2407 0.1439 Model Stratified by CCCs. Next, a Cox proportional hazards model was created that contained all covariates, as in our initial model, but was stratified by CCCs. The equations for this model were:16 Supplemental Equation(s) 6: ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 0 = ℎ0 (𝑡𝑡) 𝑒𝑒𝑒𝑒𝑒𝑒(𝛽𝛽1 𝐴𝐴𝐴𝐴𝐴𝐴 + 𝛽𝛽2 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 + 𝛽𝛽3 𝑆𝑆𝑆𝑆𝑆𝑆 + 𝛽𝛽4 𝐸𝐸𝐸𝐸ℎ𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 + 𝛽𝛽5 𝐶𝐶𝐶𝐶𝐶𝐶 + 𝛽𝛽6 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸)) ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 1 = ℎ0 (𝑡𝑡) 𝑒𝑒𝑒𝑒𝑒𝑒(𝛽𝛽1 𝐴𝐴𝐴𝐴𝐴𝐴 + 𝛽𝛽2 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 + 𝛽𝛽3 𝑆𝑆𝑆𝑆𝑆𝑆 + 𝛽𝛽4 𝐸𝐸𝐸𝐸ℎ𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 + 𝛽𝛽5 𝐶𝐶𝐶𝐶𝐶𝐶 + 𝛽𝛽6 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸)) ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 ≥ 2 = ℎ0 (𝑡𝑡) 𝑒𝑒𝑒𝑒𝑒𝑒(𝛽𝛽1 𝐴𝐴𝐴𝐴𝐴𝐴 + 𝛽𝛽2 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 + 𝛽𝛽3 𝑆𝑆𝑆𝑆𝑆𝑆 + 𝛽𝛽4 𝐸𝐸𝐸𝐸ℎ𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 + 𝛽𝛽5 𝐶𝐶𝐶𝐶𝐶𝐶 + 𝛽𝛽6 𝐸𝐸𝐸𝐸𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖)) The two-step risk modeling process resulted in the hazard ratios and p-values shown in Supplemental Table 6. The p-values for the interactions between risk and entry site in the CCC stratified model was not significant, indicating that there is no difference in time to shunt failure for anterior and posterior sites based on patient’s unique covariate values (age, race, sex, ethnicity, CCCs, and etiology). Supplemental Table 6. Risk modeling estimates Hazard Ratio 2.1221 0.3549 5.0169 Risk Posterior Entry Site Risk*Posterior Entry Site P-value <0.0001 0.2731 0.1670 Model Stratified by Etiology. The next Cox proportional hazards model contained all covariates, as in our initial model, but was stratified by etiology. The equations for this model were: 16 Supplemental Equation(s) 7: ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝐼𝐼𝐼𝐼𝐼𝐼 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 𝑡𝑡𝑡𝑡 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 = ℎ0 (𝑡𝑡) 𝑒𝑒𝑒𝑒𝑒𝑒(𝛽𝛽1 𝐴𝐴𝐴𝐴𝐴𝐴 + 𝛽𝛽2 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 + 𝛽𝛽3 𝑆𝑆𝑆𝑆𝑆𝑆 + 𝛽𝛽4 𝐸𝐸𝐸𝐸ℎ𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 + 𝛽𝛽5 𝐶𝐶𝐶𝐶𝐶𝐶 + 𝛽𝛽6 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸)) ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 = ℎ0 (𝑡𝑡) 𝑒𝑒𝑒𝑒𝑒𝑒(𝛽𝛽1 𝐴𝐴𝐴𝐴𝐴𝐴 + 𝛽𝛽2 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 + 𝛽𝛽3 𝑆𝑆𝑆𝑆𝑆𝑆 + 𝛽𝛽4 𝐸𝐸𝐸𝐸ℎ𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 + 𝛽𝛽5 𝐶𝐶𝐶𝐶𝐶𝐶 + 𝛽𝛽6 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸)) ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 = ℎ0 (𝑡𝑡) 𝑒𝑒𝑒𝑒𝑒𝑒(𝛽𝛽1 𝐴𝐴𝐴𝐴𝐴𝐴 + 𝛽𝛽2 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 + 𝛽𝛽3 𝑆𝑆𝑆𝑆𝑆𝑆 + 𝛽𝛽4 𝐸𝐸𝐸𝐸ℎ𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 + 𝛽𝛽5 𝐶𝐶𝐶𝐶𝐶𝐶 + 𝛽𝛽6 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸)) ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 = ℎ0 (𝑡𝑡) 𝑒𝑒𝑒𝑒𝑒𝑒(𝛽𝛽1 𝐴𝐴𝐴𝐴𝐴𝐴 + 𝛽𝛽2 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 + 𝛽𝛽3 𝑆𝑆𝑆𝑆𝑆𝑆 + 𝛽𝛽4 𝐸𝐸𝐸𝐸ℎ𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 + 𝛽𝛽5 𝐶𝐶𝐶𝐶𝐶𝐶 + 𝛽𝛽6 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸)) ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝐶𝐶𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 = ℎ0 (𝑡𝑡) 𝑒𝑒𝑒𝑒𝑒𝑒(𝛽𝛽1 𝐴𝐴𝐴𝐴𝐴𝐴 + 𝛽𝛽2 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 + 𝛽𝛽3 𝑆𝑆𝑆𝑆𝑆𝑆 + 𝛽𝛽4 𝐸𝐸𝐸𝐸ℎ𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 + 𝛽𝛽5 𝐶𝐶𝐶𝐶𝐶𝐶 + 𝛽𝛽6 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸)) ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 𝐼𝐼𝐼𝐼𝐼𝐼,𝐼𝐼𝐼𝐼𝐼𝐼,𝑆𝑆𝑆𝑆𝑆𝑆 (𝑒𝑒.𝑔𝑔.,𝐴𝐴𝐴𝐴𝐴𝐴) = ℎ0 (𝑡𝑡) 𝑒𝑒𝑒𝑒𝑒𝑒(𝛽𝛽1 𝐴𝐴𝐴𝐴𝐴𝐴 + 𝛽𝛽2 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 + 𝛽𝛽3 𝑆𝑆𝑆𝑆𝑆𝑆 + 𝛽𝛽4 𝐸𝐸𝐸𝐸ℎ𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 + 𝛽𝛽5 𝐶𝐶𝐶𝐶𝐶𝐶 + 𝛽𝛽6 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸)) ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 = ℎ0 (𝑡𝑡) 𝑒𝑒𝑒𝑒𝑒𝑒(𝛽𝛽1 𝐴𝐴𝐴𝐴𝐴𝐴 + 𝛽𝛽2 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 + 𝛽𝛽3 𝑆𝑆𝑆𝑆𝑆𝑆 + 𝛽𝛽4 𝐸𝐸𝐸𝐸ℎ𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 + 𝛽𝛽5 𝐶𝐶𝐶𝐶𝐶𝐶 + 𝛽𝛽6 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸)) ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝐻𝐻𝑒𝑒𝑎𝑎𝑎𝑎 𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼 = ℎ0 (𝑡𝑡) 𝑒𝑒𝑒𝑒𝑒𝑒(𝛽𝛽1 𝐴𝐴𝐴𝐴𝐴𝐴 + 𝛽𝛽2 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 + 𝛽𝛽3 𝑆𝑆𝑆𝑆𝑆𝑆 + 𝛽𝛽4 𝐸𝐸𝐸𝐸ℎ𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 + 𝛽𝛽5 𝐶𝐶𝐶𝐶𝐶𝐶 + 𝛽𝛽6 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸)) ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝑂𝑂𝑂𝑂ℎ𝑒𝑒𝑒𝑒 = ℎ0 (𝑡𝑡) 𝑒𝑒𝑒𝑒𝑒𝑒(𝛽𝛽1 𝐴𝐴𝐴𝐴𝐴𝐴 + 𝛽𝛽2 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 + 𝛽𝛽3 𝑆𝑆𝑆𝑆𝑆𝑆 + 𝛽𝛽4 𝐸𝐸𝐸𝐸ℎ𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 + 𝛽𝛽5 𝐶𝐶𝐶𝐶𝐶𝐶 + 𝛽𝛽6 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝑔𝑔𝑦𝑦)) The two-step risk modeling process resulted in the hazard ratios and p-values shown in Supplemental Table 7. The p-values for the interactions between risk and entry site in the etiology stratified model was not significant, indicating that there is no difference in time to shunt failure for anterior and posterior sites based on patient’s unique covariate values (age, race, sex, ethnicity, CCCs, and etiology). Supplemental Table 7. Risk modeling estimates Risk Posterior Entry Site Risk*Posterior Entry Site Hazard Ratio 2.0168 0.3605 4.7293 P-value <0.0001 0.2848 0.1908 Alternate Effect Models As stated in the section on applying effect modeling to the HCRN entry site trial data, our knowledge is limited regarding known interactions between the covariates and the entry site. The effect model containing the interaction between entry site and age was included in the main body of the paper. The models including the interaction between entry site and the other covariates are given below (Supplemental Table 8 through Supplemental Table 12). Interaction Between Entry Site and Race The first effect model contained the interaction between entry site and race as shown in the following equation:16 Supplemental Equation 8: ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = ℎ0 (𝑡𝑡) 𝑒𝑒𝑒𝑒𝑒𝑒(𝛽𝛽1 𝐴𝐴𝐴𝐴𝐴𝐴 + 𝛽𝛽2 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 + 𝛽𝛽3 𝑆𝑆𝑆𝑆𝑆𝑆 + 𝛽𝛽4 𝐸𝐸𝐸𝐸ℎ𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 + 𝛽𝛽5 𝐶𝐶𝐶𝐶𝐶𝐶 + 𝛽𝛽6 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 + 𝛽𝛽7 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 + 𝛽𝛽8 (𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅)(𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆) As shown in Supplemental Table 8, the p-values for the interactions between race and entry site were not significant. This indicates that there is no difference in time to shunt failure for anterior and posterior sites based on patient’s race. Supplemental Table 8. Effect modeling estimates Female Race Black or African American White Other/unknown Ethnicity Hispanic or Latino Not Hispanic or Latino Unknown or Not Reported Corrected age at operation, months < 6 months >= 6 months Etiology IVH secondary to prematurity Myelomeningocele Aqueductal stenosis Tumor Congenital communicating Spontaneous ICH/IVH/SAH (e.g., AVM) Postinfectious Head injury Other Hazard Ratio 0.8828 P-value 0.9589 0.7689 0.8998 0.4944 0.9029 1.8237 0.6575 0.0597 1.1054 - 0.6716 - 0.7326 0.8209 0.6958 0.6548 0.6237 0.7028 0.0000 0.7956 0.2127 0.4967 0.3703 0.2208 0.1815 0.3968 0.9716 0.4526 0.4630 Complex Chronic Conditions 0 1 >= 2 Posterior Entry Site Black or African American*Posterior Entry Site Other/Unknown Race*Posterior Entry Site 1.2158 1.5777 1.3528 1.4311 0.3105 0.0400 0.1586 0.3995 0.9458 0.8916 Interaction Between Entry Site and Sex The next model created contained the interaction between sex and entry site as shown:16 Supplemental Equation 9: ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = ℎ0 (𝑡𝑡) 𝑒𝑒𝑒𝑒𝑒𝑒(𝛽𝛽1 𝐴𝐴𝐴𝐴𝐴𝐴 + 𝛽𝛽2 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 + 𝛽𝛽3 𝑆𝑆𝑆𝑆𝑆𝑆 + 𝛽𝛽4 𝐸𝐸𝐸𝐸ℎ𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 + 𝛽𝛽5 𝐶𝐶𝐶𝐶𝐶𝐶 + 𝛽𝛽6 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 + 𝛽𝛽7 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 + 𝛽𝛽8 (𝑆𝑆𝑆𝑆𝑆𝑆)(𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆) As shown in Supplemental Table 9, the p-values for the interactions between sex and entry site were not significant. This indicates that there is no difference in time to shunt failure for anterior and posterior sites based on patient’s sex. Supplemental Table 9. Effect modeling estimates Female Race Black or African American White Other/unknown Hazard Ratio 1.1390 P-value 1.1684 0.7590 0.4881 0.3494 0.6157 Ethnicity Hispanic or Latino Not Hispanic or Latino Unknown or Not Reported Corrected age at operation, months < 6 months >= 6 months Etiology IVH secondary to prematurity Myelomeningocele Aqueductal stenosis Tumor Congenital communicating Spontaneous ICH/IVH/SAH (e.g., AVM) Postinfectious Head injury Other Complex Chronic Conditions 0 1 >= 2 Posterior Entry Site Female*Posterior Entry Site 0.9041 1.8357 0.6605 0.0528 1.0977 - 0.6922 - 0.7282 0.7781 0.6801 0.6256 0.6040 0.6574 0.0000 0.7860 0.2041 0.3883 0.3415 0.1761 0.1533 0.3126 0.9715 0.4295 1.1933 1.5671 1.6813 0.6519 0.3586 0.0428 0.0122 0.2073 Interaction Between Entry Site and Ethnicity Another model was created that contained the interaction between ethnicity and entry site as shown below:16 Supplemental Equation 10: ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = ℎ0 (𝑡𝑡) 𝑒𝑒𝑒𝑒𝑒𝑒(𝛽𝛽1 𝐴𝐴𝐴𝐴𝐴𝐴 + 𝛽𝛽2 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 + 𝛽𝛽3 𝑆𝑆𝑆𝑆𝑆𝑆 + 𝛽𝛽4 𝐸𝐸𝐸𝐸ℎ𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 + 𝛽𝛽5 𝐶𝐶𝐶𝐶𝐶𝐶 + 𝛽𝛽6 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 + 𝛽𝛽7 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 + 𝛽𝛽8 (𝐸𝐸𝐸𝐸ℎ𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛)(𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆) As shown in Supplemental Table 10, the p-values for the interactions between ethnicity and entry site were not significant. This indicates that there is no difference in time to shunt failure for anterior and posterior sites based on patient’s ethnicity. Supplemental Table 10. Effect modeling estimates Female Race Black or African American White Other/unknown Ethnicity Hispanic or Latino Not Hispanic or Latino Unknown or Not Reported Corrected age at operation, months < 6 months >= 6 months Etiology IVH secondary to prematurity Myelomeningocele Aqueductal stenosis Tumor Congenital communicating Spontaneous ICH/IVH/SAH (e.g., AVM) Postinfectious Head injury Other Complex Chronic Conditions 0 1 >= 2 Posterior Entry Site Hispanic or Latino*Posterior Entry Site Unknown or Not Reported Ethnicity*Posterior Entry Site Hazard Ratio 0.8883 P-value 1.1527 0.7592 0.5269 0.3537 1.2026 2.2180 0.5750 0.0339 1.1429 - 0.5727 - 0.7040 0.8398 0.7266 0.6778 0.6189 0.7380 0.0000 0.7799 0.1665 0.5483 0.4298 0.2629 0.1756 0.4675 0.9715 0.4140 1.1905 1.5410 1.6997 0.5843 0.6451 0.3652 0.0519 0.0102 0.2353 0.3176 0.4859 Interaction Between Entry Site and CCCs Next, a model was created that contained the interaction between CCCs and entry site as shown below:16 Supplemental Equation 11: ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = ℎ0 (𝑡𝑡) 𝑒𝑒𝑒𝑒𝑒𝑒(𝛽𝛽1 𝐴𝐴𝐴𝐴𝐴𝐴 + 𝛽𝛽2 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 + 𝛽𝛽3 𝑆𝑆𝑆𝑆𝑆𝑆 + 𝛽𝛽4 𝐸𝐸𝐸𝐸ℎ𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 + 𝛽𝛽5 𝐶𝐶𝐶𝐶𝐶𝐶 + 𝛽𝛽6 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 + 𝛽𝛽7 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 + 𝛽𝛽8 (𝐶𝐶𝐶𝐶𝐶𝐶)(𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆) As shown in Supplemental Table 11, the p-values for the interactions between CCCs and entry site were not significant. This indicates that there is no difference in time to shunt failure for anterior and posterior sites based on patient’s number of CCCs. Supplemental Table 11. Effect modeling estimates Female Race Black or African American White Other/unknown Ethnicity Hispanic or Latino Not Hispanic or Latino Unknown or Not Reported Corrected age at operation, months < 6 months >= 6 months Etiology IVH secondary to prematurity Myelomeningocele Aqueductal stenosis Tumor Congenital communicating Spontaneous ICH/IVH/SAH (e.g., AVM) Postinfectious Head injury Other Complex Chronic Conditions 0 1 >= 2 Hazard Ratio 0.8828 P-value 1.1802 0.7377 0.4611 0.3062 0.9010 1.8675 0.6500 0.0484 1.1287 - 0.6075 - 0.7377 0.8174 0.6972 0.6460 0.6236 0.6907 0.0000 0.7872 0.2244 0.4842 0.3720 0.2055 0.1807 0.3715 0.9716 0.4332 1.0369 1.3474 0.9013 0.3624 0.4623 Posterior Entry Site 1 CCC*Posterior Entry Site >= 2 CCCs*Posterior Entry Site 1.2670 1.2973 1.3175 0.2923 0.4921 0.5369 Interaction Between Entry Site and Etiology The last effect model created contained the interaction between etiology and entry site as shown in the following equation: 16 Supplemental Equation 12: ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = ℎ0 (𝑡𝑡) 𝑒𝑒𝑒𝑒𝑒𝑒(𝛽𝛽1 𝐴𝐴𝐴𝐴𝐴𝐴 + 𝛽𝛽2 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 + 𝛽𝛽3 𝑆𝑆𝑆𝑆𝑆𝑆 + 𝛽𝛽4 𝐸𝐸𝐸𝐸ℎ𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 + 𝛽𝛽5 𝐶𝐶𝐶𝐶𝐶𝐶 + 𝛽𝛽6 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 + 𝛽𝛽7 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 + 𝛽𝛽8 (𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸)(𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆) As shown in Supplemental Table 12, the p-values for the interactions between all but one etiology and entry site were not significant, indicating that there is no difference in time to shunt failure for anterior and posterior sites based on patient’s etiology (aside from aqueductal stenosis). However, the interaction between posterior entry site and aqueductal stenosis was significant (p=0.0298), indicating that there is a difference in time to shunt failure based on entry site for those with aqueductal stenosis compared to those with IVH secondary to prematurity. If a patient’s shunt was placed at the posterior entry site and their known cause of hydrocephalus was aqueductal stenosis, the risk of shunt failure increased by 432.84% compared to those who received the anterior shunt placementand had IVH secondary to maturity-casued hydrocephalus. The risk is calculated by adding the risk for aqueductal stenosis, posterior entry site, and their interaction together (0.3522 + 0.9953 + 3.9809 = 5.3284). To obtain the increase in risk, we subtract one from this number and convert it to a percentage to get 432.84%. For patients with aqueductal stenosis, the anterior entry site results in a longer time to shunt failure. Supplemental Table 12. Effect modeling estimates Female Race Black or African American White Other/unknown Ethnicity Hispanic or Latino Not Hispanic or Latino Unknown or Not Reported Corrected age at operation, months < 6 months >= 6 months Etiology IVH secondary to prematurity Myelomeningocele Aqueductal stenosis Tumor Congenital communicating Spontaneous ICH/IVH/SAH (e.g., AVM) Postinfectious Head injury Other Complex Chronic Conditions 0 1 >= 2 Posterior Entry Site Myelomeningocele*Posterior Entry Site Aqueductal stenosis *Posterior Entry Site Tumor *Posterior Entry Site Congenital communicating *Posterior Entry Site Spontaneous ICH/IVH/SAH (e.g., AVM)*Posterior Entry Site Postinfectious*Posterior Entry Site Head injury *Posterior Entry Site Hazard Ratio 0.9227 P-value 1.1528 0.7705 0.5280 0.3767 0.9238 1.6745 0.7361 0.1022 1.1169 - 0.6409 - 0.5070 0.3522 0.5713 0.6030 0.4793 0.5785 0.0000 0.6917 0.0795 0.0521 0.2940 0.3030 0.2258 0.4575 0.9783 0.4181 1.2077 1.6002 0.9953 1.9653 3.9809 1.5346 1.2403 0.3314 0.0365 0.9857 0.1749 0.0298 0.5327 0.7474 1.6369 0.5041 1.4237 1.1638 0.6888 0.9998 0.6388 Other Etiology*Posterior Entry Site 1.3335 0.6332