Research article · 2018 · Full text
International Journal of Statistics and Applied MathematicsSurvival analysis of broilers in two poultry farms in Kaloleni Sub County
Volume 3(5) · Pages 28–32
Research areasLivestock and Poultry Management
Abstract
Author-writtenThis research is about a survival analysis on broilers in two poultry farms in Kaloleni sub-county. Chapter one gives an insight into the introduction of the paper, chapter two discusses the methodology used, chapter three gives the results, chapter four discusses the findings briefly and chapter five gives the conclusions arrived at and some recommendations.
Summary
Source-checkedPlain-language reading of the full paper, prepared with AI and checked against the text. Each point links to the authors' own words.
Why it matters
- Broilers are a type of poultry specifically raised for meat production. View evidence ↗
- Survival analysis is used in this context to determine the expected time until the death of the broilers occurs. View evidence ↗
- The authors argue that previous studies focusing only on hazard rates were inadequate for showing bird trends, necessitating a full survival analysis. View evidence ↗
The question
- The study aims to perform a survival analysis of broilers across two different poultry farms located in Kaloleni sub-county. View evidence ↗
What they did
- The researchers tagged samples of 20 broilers from la Nyevu farm and 30 broilers from Detʼeni farm. View evidence ↗
- The observation period for the sampled birds lasted for 28 days. View evidence ↗
- R software was utilized to determine various survival functions for the data analysis. View evidence ↗
- A log-rank test was employed to compare the survival curves of Farm A (control) and Farm B (treatment). View evidence ↗
What they found
- In Farm A, survival probabilities decreased from 0.778 at 14 days to 0.395 by 28 days. View evidence ↗
- In Farm B, survival probabilities were 0.967 at 7 days and dropped to 0.566 by 28 days. View evidence ↗
- The difference in survival rates between Farm A and Farm B was not statistically significant (p = 0.635). View evidence ↗
- The proportional hazards assumption for the Cox model was not violated, as indicated by a p-value of 0.741. View evidence ↗
What it means
- The authors conclude that there is no significant difference in survival rates between the two selected poultry farms. View evidence ↗
- The authors recommend that agriculturalists increase farmer sensitization on proper farming procedures to reduce losses and increase revenue. View evidence ↗
- The authors suggest that the government provide more financial and personnel resources at the grassroots level to inform farmers of the best poultry methods. View evidence ↗
Visual summary
3 visualsIllustrations explain the paper; charts are replotted from the paper's own table values.
Study Design Overview
AI-generated conceptual illustration (broiler chickens in poultry farm pens). It explains the idea and does not show study data.
View source evidence ↗
Survival probabilities: 14 vs 21 vs 28
Replotted from Table 4 (page 2) of the original paper. Every bar is the paper's own table value.
View source evidence ↗
Survival Probabilities: 7 vs 14 vs 21 vs 28
Replotted from Table 5 (page 3) of the original paper. Every bar is the paper's own table value.
View source evidence ↗Figures & tables
From the original paper
Table 1
Table 2
Table 3
Table 4
Table 5
Figure 1
Figure 2
Table 6
Table 7
Table 8
Figure 3
Figure 4Introduction
Broilers are birds reared for meat. Survival analysis is a branch of statistics which deals with analyzing the expected time until one or more events (in this case, death of broilers) happen. Many different researchers have tried to study this scenario. Some of them include and many more did a similar task however their studies were based on the hazard rates only which is inadequate to show the trend of the birds whereas this research did a survival analysis of the broilers.
Methodology
Two samples of 20 and 30 broilers from la Nyevu and Detʼeni poultry farms in Kaloleni subcounty respectively, were tagged. These sampled broilers were observed for a period of 28 days then the observation stopped. Different survival functions were determined using the R software for analysis.
The Survivor function, s (t)
This is a function that gives the probability that a broiler will survive beyond any given specified time. Let T, be the time to failure. The survivor function at a time t is defined as, s (t) = pr (T>t), which is the probability that a broiler doesn't die within the interval (0, t). s (t) = pr (T>t) = 1-pr (T≤t), But pr (T≤t
The product limit (Kaplan-Meier) estimator of the survivor function
It is a non-parametric statistic used to estimate the survival function from life time data. This research assumed a discrete failure time distribution with probability f j , at the many points, u 0 ≤u 1 ≤u 2 ≤u 3 ≤u 4 ≤u 5 ≤… The K-M estimate is a table called ‛life-tableʼ. Let N = sample size. t j = the time at death for j = 1, 2, 3,….k such that t< 1 t 2< t 3 ……<t k. d j = number of deaths at time t j , d 1 +d 2 +…d k = m. c j = the total number of birds censored = N-m. n j = the number of birds at risk just before time t j . The K-M estimator is given by, S (t) = Π [1-(d j /n j )]. In tabular form it is as given below.
Estimation of the integrated hazard function
When T is continuous, we have seen previously that, s (t) = e -H(t) , where H(t) is the integrated hazard function. By using logarithms, it gives Log s (t) = -H (t) and now H (t) = -log s (t). For the discrete case, s (t) = ∏ (1-h j ). The K-M estimator, s (t) = ∏ (1-h j ) = ∏ (1-d j /r j ). H (t) = -log s (t) = -∑log (1-d j /r j ). h j = d j /r j , therefore H(t) = -∑log(1-h j ) for the discrete case. If the h j are small then h j ≈ -log (1-h j ) so that H (t) = ∑h j. H (t) ≈ ∑d j /n j, which is the Nelson-Aallen estimator of H (t). In tabular form, it is given as
Testing of Hypothesis of survival curves
The research used the log-rank test statistic to test H 0 : s 1 (t) = s 2 (t) against H 1: s 1 (t) ≠ s 2 (t), where farm A was assumed to be the control farm, and farm B was the treatment farm. Let t 1 <t 2 <…. < t k , be the times to death of broilers that are ordered. If at time t j , for j=1, 2... k. d j = total number of events, n j =broilers at risk, d ij = number of deaths for farm i, i=1,2. n ij = those at risk in farm i=1, 2. This information can be summarized in a 2x2 contingency table as follows. At time t j ]/√(∑vard 1j )] ~ N(0, 1), then Z 2 ~ χ 2 with 1 df. This is the log-rank test statistic. If the Z 2 calculated value is less than χ 2 with 1 df at 95% level of significance then the null hypothesis is rejected, otherwise it is accepted.
Results
The results were obtained using the R software for data analysis As the K-M curves indicate, broilers in farm A have similar survival rates as compared to broilers in farm B. The difference in the survival rates of the broilers in farms A and B are non-significant at 0.05 level of significance with a p-value of 0.635 which is greater than 0.05. These results indicate that the proportional hazards assumption was not violated at 5% level of significance in the entire study period with a p-value of 0.741 which is greater than 0.05. The proportionality assumption was also assessed graphically by plotting the scaled Schoenfeld residuals of the covariate firm against log-time. There was no trend or pattern with time throughout the study period.
Discussion
It is therefore apparent that there is no significant difference between the survival rates of the broilers in the two select poultry farms. Such a scenario borders on the fact that agriculturalists should do even more to sensitize the farmers on proper farming procedures so as to increase revenue and reduce losses
Conclusion
The government should put more resources in terms of personnel and money in the grassroots to enable each farmer gets information on the best poultry methods to undertake in order to realize the millennium goals.
Acknowledgement
I take this opportunity to thank the Almighty God for guiding me through the entire period of my studies at C.U.E.A. I thank the DVC-Academics, Prof. Kaku Sagary Nokoe for his unwavering support in making sure that the study at C.U.E.A is smooth. I also thank, our H.O.D, Mr. Mbaya, more regards go to our two former deans of faculty, Prof. Karoki and Dr. Bethwel, not forgetting our library staff. May the Almighty God bless all abundantly.
Figures and tables from the paper
| j | tj | dj | cj | nj | dj/nj | 1-dj/nj | S(t) |
|---|---|---|---|---|---|---|---|
| 0 | t0 | d0=0 | c0=0 | no=N | d0/no | 1 | 1 |
| 1 | t1 | d1 | c1 | n1 | d1/n1 | 1-d1/n1 | 1(1-d1/n1) |
| 2 | t2 | d2 | c2 | n2 | d2/n2 | 1-d2/n2 | 1(1-d1/n1)(1-d2/n2) |
| 3 | t3 | d3 | c3 | n3 | d3/n3 | 1-d3/n3 | . |
| . | . | . | . | . | . | . | |
| k | tk | dk | ck | nk | dk/nk | 1-dk/nk | 1(1-d1/n1). (1-dk/nk) |
| ∑ | m | N-m |
Table text extracted from the original PDF; superscript letters are shown inline. The original table image is below.
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| j | tj | dj | cj | nj | dj/nj | H(t)=∑(dj/nj) |
|---|---|---|---|---|---|---|
| 0 | t0 | 0 | c0 | no=N | 0 | 0 |
| . | . | . | . | . | . | . |
| k | tk | dk | ck | nk | dk/nk | 0+d1/n1+…dk/nk |
Table text extracted from the original PDF; superscript letters are shown inline. The original table image is below.
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| — | Number dead | Number alive | Number at risk |
|---|---|---|---|
| Farm A | d1j | nij-d1j | n1j |
| Farm B | d2j | n2j-d2j | n2j |
| dj | nj-dj | nj |
Table text extracted from the original PDF; superscript letters are shown inline. The original table image is below.
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| Firm | Number at Risk of Death | Observed Deaths | Expected Deaths | (O-E)2/E | (O-E)2/V |
|---|---|---|---|---|---|
| Farm A | 20 | 8 | 7.13 | 0.1060 | 0.225 |
| Farm B | 30 | 8 | 8.87 | 0.0852 | 0.225 |
Table text extracted from the original PDF; superscript letters are shown inline. The original table image is below.
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| — | Coef | Exp (coef) | Exp (-coef) | Se (coef) | z | Pr (>|z|) | Confidence imterval | — |
|---|---|---|---|---|---|---|---|---|
| Lower 95% | Upper 95% | |||||||
| FarmB | -0.2188 | 0.8034 | 1.245 | 0.5007 | -0.437 | 0.662 | 0.3011 | 2.144 |
Table text extracted from the original PDF; superscript letters are shown inline. The original table image is below.
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References
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- Investopedia. Retrieved May 12, from Investopedia, 2018. https://www.investopedia.com/terms/h/hazard-rate.asp
- OK Awobajo Y. The mortality rate in two breeds of broilers on brooding stage. World applied sciences, 2018.
- Real-Statistics. Retrieved May 14, 2018. From www.real-statistics.co/survival-analysis/cox-regression/baseline-hazard-function. www.realstatistics.com/survival-analysis/cox-regression/baseline-hazard-function
- Reporter B. Better Business Better Life, 2016.