Three Types of Hazard Functions Curves Described

Sidorovich G.I., Shamansky S.V., Pop V.P., Rukavicin O.A.

Burdenko Main Military Clinical Hospital, Moscow, Russia [email protected]

Summary. Not doubts that measures of short-term treatment effects (remission or response rates) are presenting great interest to provide more efficient treatments. However, for all diseases with unfavorable prognosis, to which pertains hemoblasto-sis, life expectancy is the most important feature. The irrevocable decision about the choice between two different treatment options is usually based on survival functions comparison. Unfortunately, this analysis is not able to reveal critical periods in disease course with distinct maximum mortality rates. Clearly, this information is very important for clinicians efforts to distinguish time intervals when patients should be specially carefully monitored. A retrospective study of the overall survival function among patients with multiple myeloma (MM), acute nonlymphoblastic leukemia (ANLL) and chronic myeloprolypherative disorders (CMPD), treated in our hospital, was performed. These data were complemented with results for the hazard function estimations for each form of hemoblastosis. We found different types of hazard function curves, and we expect that it would be better for treatment results evaluation to use together both survival and hazard function analysis.

1 Patients and method

163 MM patients (120 male and 43 female), 125 ANLL patients (102 male and 23 female) and 106 patients with CMPD (79 male and 27 female) were registered. Age of MM and CMPD patients has demonstrated typically elderly patients predominance. Three fourth of those patients were more than 50 years old. However, ANLL patients age was atypical as three fourth of those patients were less than 50 years old [OLS99]. MM patient age ranged from 33 to 83, with a median of 66. ANLL patient age ranged from 18 to 86, with a median of 34. CMPD patient age varied from 26 to 84 with a median of 60. One may notice that all cohorts had an abnormally high male rate. Female fraction varied from 17,5% in ANLL patients to 26,4% in MM. This is a consequence of peculiar properties of contingent supervised in military hospital. Among patients with ANLL M0 leukemia subvariant was diagnosed in 3 patients, M1 - in 12, M2 - in 28, M3 - in 15, M4 - in 20, M4eos - in 5, M5

- in 6 and M7 - in 1 patient. Both lymphoid and myeloid antigen coexpres-sion was revealed in 2 ANLL patients. In the CMPD structure, idiopathic myelofibrosis dominated (n = 71), then came polycythemia vera (n = 29) and essential trombocythemia was on the third place (n = 6). Diagnosis was defined according to standard criteria for each hemoblastosis form. All patients admitted to the hospital were included, without any exclusion. Patients were treated according to the standard options accepted in our clinic. Particularity of treatment methods have non been registered. Follow-up period for each patients was the time interval between the date of disease morphologic verification and the date of death or the date of last contact (according to the data obtained in January 2004). For analysis of the survival function, Kaplan-Meier method was used [KM58]. Overall survival was computed from diagnosis to death or last follow-up. STATISTICA 5.5 (StatSoft) software were used.

2 Results

In MM patients 75th survival percentile was 14,5 months (95% CI 8,8 - 20,2), median - 34,6 months (95% CI 27,5 - 41,7), 25th percentile - 68,0 months (95% CI 49, - 87,4). 12-month survival in MM patients was 0,78 (95% CI 0,72 - 0,85), 24-month survival - 0,63 (95% CI 0,55 - 0,71), 36-month survival - 0,49 (95% CI 0,41 - 0,58), 48-month survival - 0,37 (95% CI 0,29 - 0,46). 5-year survival was 0,29 (95% CI 0,21 - 0,38), 10-year survival - 0,10 (95% CI 0,04 - 0,17). MM survival curve shown on Fig. 1. Mean follow-up of MM patients who where alive was 38,6 months.

0 12 24 36 48 60 72 84 P6 108 120 132 144 months after diagnosis

Figure 1. Overall survival curve of multiple myeloma patients

Fig 2. Estimated survival function of ANLL patients. 25th survival percentile was 2,9 months (95% CI 1,14 - 4,58), median - 14,6 months (95% CI 7,7 - 21,5). 12-month survival in ANLL patients was 0,54 (95% CI 0,44 -0,64), 24-month survival - 0,38 (95% CI 0,27 - 0,49), 36-month survival - 0,32 (95% CI 0,21 - 0,43). 5-year survival was 0,27 (95% CI 0,13 - 0,40). Mean follow-up of ANLL patients who where alive was 17,8 months.

In CMPD patients 75th survival percentile was 65,0 months (95% CI 46,0 - 84,0), median - 142,0 months (95% CI 103,3 - 180,7), 25th percentile - 225,0 months (95% CI 200,5 - 249,5). 12-month survival in CMPD patients was 0,95 (95% CI 0,91 - 1,00), 24-month survival - 0,93 (95% CI 0,88 - 0,98), 36-month survival - 0,88 (95% CI 0,81 - 0,95), 48-month survival - 0,83 (95% CI 0,74 -0,91). 5-year survival was 0,80 (95% CI 0,71 - 0,89), 10-year survival - 0,57 (95% CI 0,45 - 0,69). Mean follow-up of CMPD patients who where alive was 62,0 months. CMPD survival curve shown on Fig. 3.

Figure 2. Overall survival curve for acute nonlymphoblastic leukemia patients
Figure 3. Overall survival curve of chronic myeloprolyphetative disorders patients

Average probability of death within the month in MM patients was 0,02; in ANLL - 0,05 and in CMPD - 0,005. It was shown that in MM the hazard function remained comparatively constant for the whole follow-up period (Fig.

0,030

G,G25

0,020

0,015

0,010

G,G25

0,015

0,026

0,024

n,02i .

0,021 / \

0,019

0,010

0,000

- 0,011

12 24 3G 48 SO 72 84 96 108 120 132 144 months after diagnosis

12 24 3G 48 SO 72 84 96 108 120 132 144 months after diagnosis

Figure 4. Hazard function of death in patients with multiple myeloma

ANLL course was described by "U"-formed hazard function curve. Mortality rate was maximal at the initial period (death probability within month was 0,05) with tenfold reduction to 36th month. Then it increased again (Fig. 5). In CMPD, hazard function showed linear death probability increase from 0,003 (during the first 12 months) to 0,02 at time of observation cessation

Thereby, three types of hazard function curves in different hemoblastosis have been estimated. MM course was characterized by comparatively constant death risk. In ANLL, mortality rate is the highest at first months after diagnostics, it decreased to minimum by 36 month and then increased. In CMPD patients death hazard constantly increases during the disease. We suggest that hazard function is important characteristic, describing the disease course. We recommend using this function with survival function in hematology and oncology practice for evaluation of treatment results.

0,000 12,00 24,00 3d,00 4S,00 60,00 72,00 84,00 96,00 months after diagnosis

0,GS3U7

0,000 12,00 24,00 3d,00 4S,00 60,00 72,00 84,00 96,00 months after diagnosis

Figure 5. Hazard function of death in patients with acute nonlymphoblastic leukemia

Figure 2. Hazard function of death in patients with chronic myeloprolyphetative disorders

References

[KM58] Kaplan, E.L., Meier, P. : Non-parametric estimation from incomplete observation. J. Am. Stat. Assoc., 53, 457-481 (1958) [OLS99] Olsen, J.H. : Epidemiology. In : Degos L., et al. (eds) The Textbook of malignant hematology. Martin Dunitz, London (1999)

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