Comparison of prediction ability of two extended Cox models in nonlinear survival data analysis / 南方医科大学学报

OBJECTIVE@#To compare the predictive ability of two extended Cox models in nonlinear survival data analysis.@*METHODS@#Through Monte Carlo simulation and empirical study and with the conventional Cox Proportional Hazards model and Random Survival Forests as the reference models, we compared restricted cubic spline Cox model (Cox_RCS) and DeepSurv neural network Cox model (Cox_DNN) for their prediction ability in nonlinear survival data analysis. Concordance index was used to evaluate the differentiation of the prediction results (a larger concordance index indicates a better prediction ability of the model). Integrated Brier Score was used to evaluate the calibration degree of the prediction (a smaller index indicates a better prediction ability).@*RESULTS@#For data that met requirement of the proportion risk, the Cox_RCS model had the best prediction ability regardless of the sample size or deletion rate. For data that failed to meet the proportion risk, the prediction ability of Cox_DNN was optimal for a large sample size (≥500) with a low deletion (< 40%); the prediction ability of Cox_RCS was superior to those of other models in all other scenarios. For example data, the Cox_RCS model showed the best performance.@*CONCLUSION@#In analysis of nonlinear low maintenance data, Cox_RCS and Cox_DNN have their respective advantages and disadvantages in prediction. The conventional survival analysis methods are not inferior to machine learning or deep learning methods under certain conditions.

Modelo de Cox para análise da sobrevida das empresas de plano de saúde no Brasil / Cox model for survival analysis of health insurance companies in Brazil

Objetivo: No Brasil, estudos sobre o tempo de vida das operadoras de planos de saúde são escassos. Assim, o artigo tem o objetivo de investigar fatores econômicos que explicam a sobrevida de empresas de plano de saúde. Métodos: Foi utilizada a técnica estatística denominada análise de sobrevivência, por meio do modelo semiparamétrico de Cox. Os dados foram obtidos no site da ANS (agência reguladora do setor) e referem-se a 929 operadoras de todas as regiões do país, em 2011-2018. As seguintes variáveis foram analisadas: Beneficiário (número médio de beneficiário por operadora), Porte (Porte 1: até 20 mil beneficiários, Porte 2: entre 20 mil e 100 mil beneficiários, Porte 3: acima de 100 mil beneficiários), Tempo no Mercado (quantidade de trimestres que a operadora permaneceu no mercado), Receita/Despesa (Muito baixa, Baixa, Alta e Muito alta), Lucro (Operadoras que lucraram e Operadoras que não lucraram), Tipo de Gestão (Gestão sem fins lucrativos e Gestão empresarial) e por último tem-se a variável (dependente) Falência, que indica se a operadora solicitou o encerramento das suas atividades. Resultados: Observou-se uma taxa de mortalidade para operadoras de pequeno porte maior comparativamente às demais, com probabilidade de não sobrevivência no mercado duas vezes menor em relação às empresas de médio porte e três vezes menor se comparada às de grande porte. Conclusões: Empresas de pequeno porte encontram-se em grande desvantagem no panorama brasileiro de operadoras de planos de saúde, qualquer que seja seu tempo de vida no mercado.

Objective: In Brazil, studies on the survival time of health insurance providers are scarce. Thus, this article aims to investigate economic factors that explain the survival of these companies. Methods: The statistical technique survival analysis was used (Cox semi-parametric model). Data were obtained from the ANS (regulatory agency) website and refer to 929 operators from all regions of the country, 2011-2018. The following variables were analyzed: Beneficiaries (average number of beneficiaries per provider), Size (Size 1: Up to 20 thousand beneficiaries, Size 2: Between 20 thousand and 100 thousand beneficiaries, Size 3: Above 100 thousand beneficiaries) Time in market (Number of quarters that the provider remained in the market), Revenue/Expenses (Very Low, Low, High and Very High), Profit (Providers that profited and providers that did not profit), Type of Management (Nonprofit Management and For profit/Business Management) and lastly the (dependent) Bankruptcy variable, which indicates if the operator requested the ending of its activities. Results: A higher mortality rate was observed for small providers compared to the others, with a probability of non-survival in the market two times smaller in relation to medium-sized companies and three times lower than the large ones. Conclusions: Small businesses are at a great disadvantage in the Brazilian panorama of health insurance providers, regardless of their life time in the market.

Review of statistical methods for survival analysis using genomic data

Survival analysis mainly deals with the time to event, including death, onset of disease, and bankruptcy. The common characteristic of survival analysis is that it contains “censored” data, in which the time to event cannot be completely observed, but instead represents the lower bound of the time to event. Only the occurrence of either time to event or censoring time is observed. Many traditional statistical methods have been effectively used for analyzing survival data with censored observations. However, with the development of high-throughput technologies for producing “omics” data, more advanced statistical methods, such as regularization, should be required to construct the predictive survival model with high-dimensional genomic data. Furthermore, machine learning approaches have been adapted for survival analysis, to fit nonlinear and complex interaction effects between predictors, and achieve more accurate prediction of individual survival probability. Presently, since most clinicians and medical researchers can easily assess statistical programs for analyzing survival data, a review article is helpful for understanding statistical methods used in survival analysis. We review traditional survival methods and regularization methods, with various penalty functions, for the analysis of high-dimensional genomics, and describe machine learning techniques that have been adapted to survival analysis.

Discussion on Methods for Tied Survival Times in Cox Model / 世界科学技术-中医药现代化

Cox regression model is one of the most widely used methods in the survival analysis.One assumption of this model is that there is no tie in the failure times,that is,individual has different failure times.In practical applications,the existence of ties in time data is very common.In this paper,four common methods of dealing with ties in Cox model,including Exact method,discrete model method,Efron method and Breslow method,were compared with simulation.The results showed that Exact method and discrete model were the best,but they took the longest time.Efron method and Breslow method were faster but there was a greater deviation in parameter estimation.Moreover,the sample amount and ties degree also affect the results.In general,when there are a few ties,the difference between four methods was small;and in the case of large datasets or a large number of ties,the bias of three approximation methods increased except Exact method.However,there was no significant change on computational time.While the computational time of the Exact method increased rapidly.Therefore,if the estimation precision is not as important as the estimation time,Efron method and Breslow method will be good choices.Efron method is more preferably as it is more precise.And Breslow method tends to underestimate the true β.If there is no limit in time,Exact method and discrete model can be chosen to achieve more accurate results.

Cox model analysis of long-term survival results from renal transplant recipients over 15 years / 中华器官移植杂志

Objective To analyze the clinical data of recipients over 15 years after renal transplantation,and to find the factors that affect the long-term survival of recipients after renal transplantation.Method Before June 30,2000,326 renal transplant recipients in our hospital were collected retrospectively.The risk factors which affect the survival of kidney transplant recipients and kidney were analyzed from four dimensions.A Cox model was established to analyze these multi factors.Result Cox hazard model indicated that advanced age (P=0.010,RR =1.052),AMR (P＜0.001,RR =18.311),nonadherence (P =0.001,RR =2.854),smoking (P =0.025,RR =2.097)were the risk factors for recipients' survival.Using immunosuppressive regimen FK506 + MMF+ Pred (P =0.019,RR =0.433),or CsA + MMF + Pred (P =0.019,RR =0.413) was the protective factor for recipients' survival.Nonadherence (P＜0.001,RR =5.645),and diabetes (P＜0.001,RR =3.310) were the risk factors of grafts' survival.Using immunosuppressive regimen FK506 + MMF + Pred (P＜0.001,RR =0.236),or CsA + MMF + Pred (P =0.002,RR =0.317) was the protective factor of grafts' survival.Conclusion To enhance the long-term outcome of recipients and grafts,the individualization of immunosuppressive regiments and controlling of the chronic diseases progress by changing the unhealthy life style are cutting on edge.

Os fatores clássicos e a falha dos implantes dentários: qual o significado estatístico para a prática clínica? / On classic factors and dental implant failures: what is the statistical significance for the daily practice?

Objetivo: identificar quais dos fatores clássicos (material, desenho, superfície do implante, hospedeiro, técnica cirúrgica, protocolo de carga) possuem significado estatístico no prognóstico dos implantes. Material e métodos: uma busca eletrônica foi realizada no sistema PubMed/Medline até junho de 2015 com palavras-chave representativas dos estimadores, combinadas por operadores booleanos. Foram incluídos estudos clínicos contendo amostras com pelo menos 50 pacientes e 100 implantes, mínimo de um ano de acompanhamento, apresentando os estimadores obtidos através de modelo de Cox (Hazard ratio) ou regressão logística (Odds ratio, Risk ratio). O desfecho primário foi a falha do implante. Resultados: das 871 referências iniciais, foram selecionadas 20 após leitura integral, com mais de dez mil pacientes e mais de 30 mil implantes. Nos artigos com modelo de Cox, foram identificados o tabagismo (valores entre 1,04 e 3,9), o diâmetro (valores HR entre 1,72 e 6,35) e o comprimento (valores HR entre 0,8 e 2,7) do implante, as técnicas cirúrgicas específicas para melhorar o leito receptor (HR entre 2 e 5), os protocolos de carga (HR entre 0,1 e 9,7), o operador (HR=4,2; um estudo) e a maxila (HR=10; um estudo). Nos artigos com regressão logística, foram identificados os maiores valores de risco para implantes de largo diâmetro (OR=4,25; um estudo), implantes colocados na região posterior da maxila (OR=6,83; um estudo) e ausência de gengiva queratinizada (OR=4,7; um estudo). Conclusão: os fatores têm frequência variada, dependem da homogeneidade das amostras e nem sempre demonstram significado estatístico. Possíveis explicações podem ser atribuídas para as falhas. Mesmo assim, a documentação clínica detalhada continua fundamental para anteciparmos problemas em áreas estratégicas.

Objective: to identify which of the classic factors (implant material, design, surface; host, surgical technique, loading protocol) can have a statistical significance on dental implant prognosis. Material and methods: an electronic search at the PubMed/Medline was made until June 2015 with representative keywords combined by Boolean operators. Clinical studies with at least 50 patients and 100 implants, 1 year of follow-up, having statistical estimators such as Cox model (Hazard ratio) or logistic regression (Odds ratio, Risk ratio) analyses were included. The primary outcome was implant failure. Results: of the 871 retrieved records, 20 references were finally selected, summing up more than 10 thousand patients and 30 thousand dental implants. For articles using the Cox´s model, tobacco (HR values between 1.04 to 3.9), diameter (HR between 1.72 to 6.35), and implant length (HR between 0.8 to 2.7); specific surgical techniques to improve the recipient bed (HR between 2 and 5), loading protocols (HR from 0.1 to 9.7), the operator (HR=4.2, one study), and the maxillary arch (HR=10, 1 study) were identified. For articles containing logistic regression, the highest chance values were identified for large diameter implants (OR=4.25, one study), implants at the posterior maxillary region (OR=6.83, one study), and the lack of keratinized gingiva (OR=4.7, one study). Conclusion: these factors have a varied frequency, depend on sample´s homogeneity, and not always provide statistical meaning. Possible explanations can be attributed to failures. Even thus, a detailed clinical documentation remains mandatory to anticipate problems in strategic areas.

The Methods of Survival Analysis for Clinicians.

The methods of survival analysis are required to analyze duration data but their use is restricted possibly due to lack of awareness and the intricacies involved. We explain common methods of survival analysis, namely, life-table, Kaplan- Meier, log-rank and Cox model, in a simple and friendly language so that the medical fraternity can use them with confidence where applicable.

Correlation between prognosis and histopathologic factors in patients with hepatocellular carcinoma after liver transplantation: A multivariate analysis / 第二军医大学学报

Objective: To evaluate the effect of histopathologic factors in patients with hepatocellular carcinoma after liver transplantation(LT) on the prognosis of liver transplantation. Methods: The clinical data of 272 HCC patients, who had received liver transplantation, were retrospectively analyzed. The survival rates were analyzed using the actuarial life-table method. Multivariate and univariate COX proportional hazards model were used to investigate the correlation between histopathologic factors and survival time. Kaplan-Meier method was used to plot the curves of accumulative survival rates and Log-rank tests were used to compare the curve of the survival rates. Results: Univariate analysis using a COX model revealed that scores of model of endstage liver disease(MELD), alphafetoprotein, size of tumor, capsule invasion, Eggel's classification, Edmonson-Steiner grade, microvascular invasion, regional lymph node metastasis and TNM staging were significantly related to the prognosis of the patient after LT(P<0.05). Multivariate COX model analysis showed that alphafetoprotein(RR:1.459, P=0.002), Eggel's classification(RR:1.617, P=0.004), microvascular invasion(RR:2.631, P<0.001) and MELD(RR: 2.194, P = 0.011) are independent factors of patient prognosis. Conclusion: Alphafetoprotein, Eggel' s classification, microvascular invasion and MELD are the independent prognostic factors of HCC patients after LT. More attention should be paid to the influence of MELD on prognosis of HCC patients after LT.

An Application of the Clustering Threshold Gradient Descent Regularization Method for Selecting Genes in Predicting the Survival Time of Lung Carcinomas

In this paper, we consider the variable selection methods in the Cox model when a large number of gene expression levels are involved with survival time. Deciding which genes are associated with survival time has been a challenging problem because of the large number of genes and relatively small sample size (n << p). Several methods for variable selection have been proposed in the Cox model. Among those, we consider least absolute shrinkage and selection operator (LASSO), threshold gradient descent regularization (TGDR), and two different clustering threshold gradient descent regularization (CTGDR)- the K-means CTGDR and the hierarchical CTGDR - and compare these four methods in an application of lung cancer data. Comparison of the four methods shows that the two CTGDR methods yield more compact gene selection than TGDR, while LASSO selects the smallest number of genes. When these methods are evaluated by the approach of Ma and Huang (2007), none of the methods shows satisfactory performance in separating the two risk groups using the log-rank statistic based on the risk scores calculated from the selected genes. However, when the risk scores are calculated from the genes that are significant in the Cox model, the performance of the log-rank statistics shows that the two risk groups are well separated. Especially, the TGDR method has the largest log-rank statistic, and the K-means CTGDR method and the LASSO method show similar performance, but the hierarchical CTGDR method has the smallest log-rank statistic.

Correlation Between in vitro Chemosensitivity of Antineoplastic Drugs and its Clinical Response and Prognosis in Human Colorectal Cancers / 药物流行病学杂志

Objective:To study the correlation between in vitro chemosensitivity of Fluorouraci(5-Fu) + Mitomycia (MMC) and its clinical response and prognosis in human colorectal cancers. Method:The chemosensitivity of 5-Fu + MMC was tested in 169 Dukes B and C colorectal cancers with the MTT method,and the progression-free internal and prognosis in 4 years following the surgery were observed. Result:Based on the in vitro chemosensitivity of 5-Fu + MMC, 100 patients were divided into an antagonistic group(28 patients) in which their relapse rates were 57. 1% and a synergistic-additive group(72 patients) in which their relapse rates were 22.2% (P

Analysis of Factors Influencing Prognosis of Patients with Bile Duct Carcinoma after Resection / 中国普外基础与临床杂志

Objective To analyze the factors influencing the prognosis of patients with bile duct carcinoma after resection. Methods The clinical data of 120 patients with bile duct carcinoma receiving resection in our hospital from 1980 to 2004 were collected retrospectively and clinicopathologic factors that might influence survival were analysed. A multiple factor analysis was performed through Cox proportional hazard model. Results The overall 1-year, 3-year and 5-year survival rates were 71.7%, 32.5% and 19.2% respectively. The single factor analysis showed that the major significant factors influencing survival of these patients were histological type of the lesions, lymph node metastasis, pancreatic infiltration, duodenal infiltration, resected surgical margin, perineural infiltration, peripheral vascular infiltration and depth of tumor infiltration (P

Multivariate analyses of prognostic factors for breast cancer patients with liver involvement / 中国癌症杂志

Purpose:To investigate the prognostic factors for breast cancer patients with liver involvement.Methods:114 breast cancer patients with liver metastases,who were hospitalized in Fudan University Cancer Hospital between January,1996 and December,2003,were included in this study.Their survival data were analyzed.Results:The response rates with first-,second-,third-,fourth-line chemotherapy were 31.9%,27.8%,16.7% and 0%,respectively.Univariate analyses indicated that patients with impaired liver function and patients with a short interval between surgery and the first recurrence or metastasis had a poor prognosis.Multivariate analyses suggested that the presence of liver function impairment was an independent prognostic factor for overall survival.Conclusions:The response rates of chemotherapy drop with number of lines of chemotherapy.Breast cancer patients with liver involvement and impaired liver function have a poor prognosis.

The COX regression analysis of prognosis factors of stomach carcinoma / 临床外科杂志

Objective To determine the effective prognostic parameter and the best prognostic index of gastiric carcinoma.Methods The prognostic relevance of clinical and pathological variables were evaluated in 83 patients with histologically proved stomach carcinoma (including the expression of nm23, c erbB2, microbloodvessel and PTNM) by the multivariate analysis of COX regression.Result PTNM staging was the only parameter to enter the COX model.Conclusion The PTNM staging is the most important, reliable and best varible factor in predicting the clinical outcome of stomach cancer.

Significance of Time-dependent Exposure Variable in Occupational Disease Study / 대한산업의학회지

Although the final cumulative exposure has been used as a exposure variable on the cohort study for the relation between exposure and disease, the bias from the use of fixed exposure can be developed because the exposure amount changes across the time. We developed the program to handle the Cox model with irregularly changing time-dependent exposure variable and covariates, and the validity about the application of time-dependent exposure variable and lagged interval was practically evaluated by analyzing the data collected for typical retrospective cohort study with that program. The results were as follows : The exposure-response relations between the deaths from lung cancer and exposures (fixed or time-dependent) were not clear when 0 year lagged interval was applied. When 15 years lagged interval was applied, the exposure-response relations between the deaths from lung cancer and the time-dependent exposures to crystalline silica were observed and relative risky increased like 1.00, 1.17, 1.30 and 2.45 across the exposure levels. The relative risk estimates for lung cancer with time-dependent exposure variable were higher than those with fixed exposure variable without regard to the application of lagged interval. The exposure-response relations between the deaths from non-malignant respiratory disease (NMRD) and exposures (fixed or time-dependent) were observed across exposure levels when 0 year lagged interval was applied. When 15 years lagged interval wag applied, the exposure-response relations between the deaths from NMRD and the time-dependent exposures to crystalline silica were observed, but were not with fixed exposure variable. The relative risk estimates for NMRD mortality with time-dependent exposure variable were higher than those with fixed exposure variable, and the application of lagged interval on the evaluation of NMRD mortality was meaningless. The results suggests that the application of time-dependent exposure variable on the study of exposure-effect relation should be considered and the application of lagged interval should be decided according to the time needed from disease detection to death.