Outcome:
The outcome of interest was any cause of death within 1 year after hip fracture. It was determined through telephone interviews. All interviews were conducted after the patient data had been collected.
To ensure a high successful follow-up rate, we made the following efforts.
⒈We developed the principle of telephone interviews by minimizing the content of the interviews as much as possible. The interview content varied according to the condition of the patient. In addition to collecting death and time information, we collected the cause of death and the patient's self-care ability before the fracture and/or after recovery. The purpose was to make the interview easier to accept by the family.
According to the treatment methods in our hospital, patients were divided intotwo categories: surgical and conservative. For the former, if the patient died, we asked about the time of death, the reason, and the self-care situation before the fracture; if the patient survived, we asked about the current self-care situation, whether the patient could take care of himself/herself now, and then ended the interview. For conservatively treated patients, we continued to ask about the self-care situation before the fracture. In this group, they could not simply be classified as conservative treatment because they might go to other places for surgery after leaving our hospital. Therefore, we first had to determine whether they had been following conservative treatment before proceeding with the interview. If not, they were classified as surgical patients and were interviewed like surgery patients in our hospital in addition to questions about the timing of the operation. In this way, at least one question was asked in each interview. For example, those who had recovered their self-care ability after surgery could end the interview after just asking about their current recovery status. At most 5 questions were asked. For example, among those who died after going to other hospitals for surgery, ⑴ whether they were operated on after discharge, ⑵ the operation time, ⑶ the time of death, ⑷ the cause and ⑸ their ability of self-care before the fracture(Fig. 1).
⒉ We set up time reference points to help the patients' families recall when death had occurred. For example, we asking the family members of the patients who had surgery after discharge, "Which day after the discharge or fracture was the surgery was performed". For the patients who had died but their family members could not recall the specific time of death, we used a method of narrowing the time range gradually. For example, "In which season did the death occur? Before or after the Spring Festival? Did it occur after the Lantern Festival?"
⒊ In cases of an incorrect telephone call, the family could not determine the specific time of death, or unwillingness to cooperate, we returned to the original medical record, checked the telephone number, or looked for other telephone numbers that had been recorded and then attempted a re-interview.
⒋ When the original medical records were checked and the interviews were still unsuccessful, we turned to the community medical system, which registered the telephone numbers of all families living in the community. If we were able to obtain a new phone number, then we interviewed them again.
Through the above methods, most of the patients lost to follow-up could successfully be contacted. The rest were regarded as missing data.
Predictors:
Based on the principle of modeling (practicality is preferred to accuracy) and the purpose (to provide a reference for formulating a treatment plan), we determined the principle of selecting candidate predictors: ⒈Simplicity. Predictors were selected from the patient's medical history and the routine preoperative preparations. ⒉Stability. We measured predictors relatively stable across different testers or patients. ⒊Independence. Predictors that could be determined independently by an orthopedic surgeon without consultation with other departments should be preferred. ⒋Rapidity. The results of the predictors need to be determined quickly within 24–48 hours after admission, without long waits. ⒌Quantitative indicators are prioritized over qualitative indicators. ⒍Relevance. Select relevant factors that affect the implementation of surgical treatment. ⒎Subject matter knowledge. Select the indicators that have been shown to be relevant to survival rates.
Initially, 24 indicators were extracted for each patient to provide detailed sample characteristics, including their general characteristics: medical insurance, age, and sex; disease characteristics: fracture site, fracture type, time from the fracture to hospitalization, time from the hospitalization to surgery, and length of stay (LOS); medical history: diabetes, hypertension (HYP), malignancy (MAL), kidney disease (KD), and lung disease (LD) on admission; the ability to live independently (ALI) before the fracture; cardiovascular and cerebrovascular diseases (CCD); test results (all using the first test value after admission): partial pressure of oxygen (PaO2), fasting blood sugar (BS), serum creatinine (SC), hemoglobin (Hb), total protein (TP), albumin (ALB), and mean arterial pressure (MAP); and treatment: skeletal traction or surgery. To understand the impact of surgery (SUR) on survival, SUR was deliberately used as a predictor, although it was not a preoperative indicator.
Some of the indicators were defined as follows: ⒈ Medical insurance: this includes employee medical insurance and nonemployee medical insurance. China has achieved full medical insurance coverage since 2011. Nonemployee medical insurance mainly includes new rural cooperative medical insurance, a small number of other types of commercial insurance, and self-paid medical treatment. The type of medication can reflect the economic situation of a patient. ⒉ Fracture site: including the femoral neck, intertrochanteric and subtrochanteric. ⒊ Fracture type: primary and secondary fractures. If there were fragility fractures before this fracture, such as the very common osteoporotic vertebral compression fractures, hip fractures, wrist fractures, and proximal humeral fractures, they were secondary fractures; if not, they were primary fractures. ⒋ Medical history: whether a patient had been diagnosed with diabetes, HYP, MAL or KD was obtained from the medical records, which were provided by the patient and/or their family at the time of admission. ⒌ LD on admission: this can be positive or negative. Various types of pneumonia, tuberculosis, pleural effusion and/or structural changes, such as pulmonary bullae and fibrosis, are positive but do not include locally stable small lesions, such as stable calcifications. They are determined by chest X-ray or chest CT. Otherwise, they are negative. In particular, this indicator did not include lung tumors, which were classified as MALs. ⒍ ALI: positive mainly means that the patient could not walk independently or complete the basic activities of daily life without the help of others before the fracture. This could be due to various reasons, including sequelae of cerebrovascular events, severe hip or knee arthritis, Alzheimer's disease or severe depression. Otherwise, negative. ⒎ CCD: being positive for this indicator means that the patient had been diagnosed with diseases such as myocardial infarction, cerebral infarction, or cerebral hemorrhage; alternatively, CT and/or MRI examination of the head after admission showed the presence of old local infarct changes. In addition, this also includes intravascular thrombosis as shown by vascular ultrasound examination of the extremities but does not include atherosclerotic plaque formation, stenosis or other changes. These examinations are not routine examinations after a patient is admitted. If a patient did not undergo these tests and had no history of a diagnosis of the abovementioned cardiovascular and cerebrovascular diseases, they were regarded as negative. ⒏ PaO2, BS, SC, Hb, TP, ALB: these 6 indicators are routine laboratory test items after admission. Generally, specimens are collected at 7 o'clock in the morning on the second working day after admission, and all of the results are reported in the afternoon. ⒐ MAP: MAP is obtained from the 1/3 systolic blood pressure plus the 2/3 diastolic blood pressure. This value is obtained from the vital signs’ examination of a patient performed immediately after admission. ⒑ Skeletal traction: in general, skeletal traction was considered on the day of admission. If patients refused or if it was decided to perform surgery, bone traction was not applied. Almost all patients given this treatment underwent tibial tuberosity traction.
Through analysis of the above predictors, we reduced the number of candidate predictors. We excluded medical insurance, fracture site, fracture type, time from fracture to hospitalization, time from hospitalization to operation, and skeletal traction. Regardless of the results of these indicators, they did not affect the choice of surgical treatment. According to the principle of priority of quantitative indicators, diabetes, kidney disease, selected BS, and SC were excluded. Although MAP is a quantitative variable, it is easily affected by various factors and has poor stability, so we chose HYP instead. There is some overlap between serum TP and ALB. Previous studies[9, 10] have shown that low ALB is a prognostic factor for death after fracture, so TP was excluded. Based on the principle of stability, PaO2 was excluded. Because many elderly patients are often given oxygen immediately after admission, it was difficult to strictly follow the doctor’s instructions to stop oxygen inhalation two hours before measuring the index, making it very unstable across patients. As a result, 12 candidate predictors were retained, including age, sex, MLA, LD, ALI, CCD, SUR, BS, SC, Hb, ALB and HYP.
Sample Size
We did not specifically calculate the required sample size. The reason for this is that the sample size is affected by many factors, and there is no well-known calculation method[11–13]. Second, in reality, we cannot easily expand a single-center study into a multicenter trial or arbitrarily extend the research time to increase the sample size.
According to widely accepted empirical guidelines, we aimed to achieve at least 10 events per variable (EPV) or at least a total of 100 events in the sample. Fortunately, many empirical studies can provide guidance as to how to develop predictive models based on a small sample[14, 15].
Missing Data
The characteristics of the missing data are shown in Fig. 2.
Among the 14 variables (2 outcome variables, death (Y) and time and 12 covariates), there were 8 variables with missing values, including SUR (containing 9 missing values), BS (9), SC (9), Hb (9), ALB (13), LD (58), Y (11) and time (11). A total of 660 observations had no missing data, and 5 variable values were missing among 5 observations.
Whether the missing data came from covariates or outcomes, we used the mice package for single imputation (SI) in R software. Although multiple imputation (MI) could be used, the reasons why we chose SI are as follows. First, we had relatively little missing data. Among all of the variables with missing values, LD had the highest missing rate, which was 7.9%, and the missing rates of the remaining variables were less than 2%. Second, an SI dataset can be easily created from the first of a series of MI datasets, and it avoids complicated combinations over multiple MI datasets[16]. Third, no method has been found to combine LASSO models derived from multiple MI datasets[17]. Finally, empirical research has shown that the estimation of model regression coefficients is very consistent between the SI dataset and the MI stacked dataset[18].
Because our SI dataset came from the first of the MI data series, we also analyzed the missing mechanisms of the data and explained the method of generating the MI data series. The missing data were mainly related to the choice of treatment methods for the patients. When patients and their families were not actively involved or were skeptical about surgical treatment, they often refused any routine preoperative preparations. In this case, several variable values were often missing together. Therefore, missing data were often seen among patients who took conservative treatment. This is a "missing at random" (MAR) situation, and MI can effectively address this problem[19–21]. The 12 candidate predictors and the outcome of event and time were all included in the imputation procedure. In this way, 8 variables, LD, SUR, BS, SC, Hb, ALB, Y and time, were imputed. Among them, the two factor variables, LD and SUR, were imputed using the logistic regression (logreg) method, while the remaining 6 variables were imputed using the predictive mean matching (pmm) method. No interaction terms were introduced during the MI procedure.
Statistical Analysis Methods
The distributions of the 5 continuous variables Age, BS, SC, Hb and ALB of the 12 candidate predictors were checked for extreme values. After excluding input errors, only SC was found to have obvious extreme values. The extreme values of SC were winsorized to avoid excessive leverage effects. This was done by shifting the values above the 99th centile (8 values, and among them the maximum was 860 µmol/L) to the truncation points (99th centile, 190.75 µmol/L).
To make full use of the information, we did not categorize any continuous variables, and all kept their original scales. For all continuous variables, linear and nonlinear relationships with the outcome were fitted. The nonlinearity was fitted by using restricted cubic splines (RCSs), and 3, 4, and 5 knots were compared for each variable. In particular, we also checked the log transformation for SC. In addition, we plotted the relationship between the fitted variables and the outcome to check the biological rationality. Based on a higher Waldχ2 value but a lower degree of freedom (df) and biological rationality, the final coding of each number variable in the model was determined (Table 1). The optimal coding for each predictor was as follows: age: linear; BS: nonlinear (RCS, 3
Table 1
Optimal coding exploration for continuous predictors (complete case analysis)
Predictor | coding | Waldχ2 | df | p value |
Age | Linear | 24.96 | 1 | < .0001 |
RCS (3) | 22.03 | 2 | < .0001 |
RCS (4) | 23.90 | 3 | < .0001 |
RCS (5) | 23.62 | 4 | 0.0001 |
BS | Linear | 0.61 | 1 | 0.4345 |
RCS (3) | 0.77 | 2 | 0.6798 |
RCS (4) | 5.66 | 3 | 0.1291 |
RCS (5) | 6.39 | 4 | 0.1719 |
SC | Linear | 13.27 | 1 | 0.0003 |
RCS (3) | 12.77 | 2 | 0.0017 |
RCS (4) | 13.94 | 3 | 0.0030 |
RCS (5) | 13.96 | 4 | 0.0074 |
Log | 11.25 | 1 | 0.0008 |
Hb | Linear | 10.19 | 1 | 0.0014 |
RCS (3) | 15.14 | 2 | 0.0005 |
RCS (4) | 14.65 | 3 | 0.0021 |
RCS (5) | 15.36 | 4 | 0.0040 |
ALB | Linear | 33.97 | 1 | < .0001 |
RCS (3) | 31.76 | 2 | < .0001 |
RCS (4) | 31.30 | 3 | < .0001 |
RCS (5) | 32.07 | 4 | < .0001 |
Note: Bold represents the optimal coding. |
knots); SC: linear; Hb: nonlinear (RCS, 3 knots); ALB: linear. |
According to the principle of simplicity of modeling, all seven categorical variables of SEX, MLA, LD, ALI, CCD, HYP and |
SUR, were coded as binary variables.
1. Type of model
Because our goal was a 1-year survival rate, a time-to-event outcome, we chose the Cox proportional hazards model.
2. Predictor selection during modeling
Based on our small sample and empirical studies[14, 15, 22, 23] showing that stepwise selection deteriorates the predictive quality of the model in small datasets, we chose to build a full model that included all 12 candidate predictors. We further refined the full model using the LASSO method, where selection was achieved through shrinking regression coefficients to zero[24, 25]. Therefore, we developed a LASSO model.
3. Interaction terms
To avoid the type I statistical error of multiple repeated detections of interactions[26], we tested the overall interactions of age with the other remaining predictors[27]; the same test was also performed for sex. If there was statistical significance as a whole, then we introduced the statistically significant interaction terms; otherwise, the possibility was excluded. We also tested the proportional hazards assumption.
4. Model performance
Overall performance measures of Nagelkerke’s R2 are presented.
The concordance (c) statistic is given as the LASSO model’s discrimination measure, which was further illustrated by dividing the predictions into 3 groups and plotting the Kaplan–Meier curves of each group.
We did not evaluate the calibration because the “assessment of calibration” makes little sense in the development data, while it is essential for external validation”[28].
5. Internal Validation
Then, we assessed the internal validity with a bootstrapping procedure of 1 000 repetitions for a realistic estimate of the performance of the LASSO and full model in similar future patients.