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.
Citation
Masters of Science Degree in Medical Statistics at the University of Nairobi, Institute of Tropical and Infectious Diseases (UNITID)Publisher
University Of Nairobi
Description
A Project submitted in partial fulfillment for the award of Masters
of Science Degree in Medical Statistics at the University of Nairobi,
Institute of Tropical and Infectious Diseases (UNITID)