A comparison of cox and Poisson regression in the analysis of survival data

Abstract

When analyzing event data, one can decide to analyze either individual patient survival times or aggregated patient event rates. In this study two methods are used to analyze data arising from a study where the response variable is the length of time taken to change in nutritional status using body mass index (BMI). Patients whose BMI changed from < 18.5 Kg/m2 to 2: 19.5 Kg/m2 are considered to experience an event. The study adopted an interventional comparative design with 12 months follow-up after which, patients who improved within this period were considered to experience an event while those whose event could not be clearly established were censored. The Kaplan-Meier method, log rank test, Cox proportional hazards model and Poisson model are described. Out of 330 adult PL WHA enrolled in the FBP program, 58.8% were females and 41.2% were males. Median age was 35 (IQR, 30 - 42) years with females generally younger than males (33 [IQR, 28 - 40] years vs. 37 [IQR, 33 - 44] years), (p<O.OOl). Median BMJ of eligible clients was 17.35 (IQR, 16.40 - 17.96) kg/m.There was no significant difference in BMI between females and males. A total of 123 (37.3%) clients experienced nutritional improvement after 12 months of follow-up. There was no significant difference in distribution of nutritional outcome between the two treatment modalities (P=0.245). A higher proportion of clients on nutritional counseling alone (40.7%) experienced nutritional improvement compared to those on food and nutritional counseling (34.4%). Kaplan-Meier method revealed no significant difference in survival probabilities between the two treatment modalities (P=O.l62). Median time to nutritional improvement among clients receiving food and nutritional counseling was 9 [95% CI= 8 - 10] months compared to 8 [95% CI= 7 - 9] months for clients place on nutrition counseling alone. Application of Cox and Poisson regression in bivariate and multivariate analysis generated similar results. Adjusting for treatment modality, CD4 change [1 to 100 counts (RR,= 4.22; 95%CI 0.94-18.95); 101 - 200 counts (RR = 5.81; 95%CI 1.30-25.81); >200 counts (RR = 6.24; 95%CI 1.37-28.41); Deteriorated / No change in CD4 = Reference category] and source of socio-support [Medical professional and family members (PR = 5.04; 95%CI 1.05-1.24); Other= Reference category] were identified as significant factors associated with nutritional improvement. Alluding to the outcome of the results, survival analysis is not limited by the nature of data presented, whether on rates or on survivorship. When presented with data on survivorship, Cox regression is the better option and when presented with data on rates, Poisson regression is the recommended option. Even though the input variables (dependent) are different in nature (Time-to-event for Cox and Count of events per time for Poisson), the output measurement is the same i.e. Relative risk. Both analysis yield to the same conclusion.